Tpa 1 - Bryan Stone 77170
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CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
Before beginning this task, read the complete directions provided in the CalTPA Candidate Handbook.
Case Study 1: Subject-Specific and Developmentally-Appropriate Pedagogy A. Contextual Information for Case Study 1 1. Elements of a Learning Experience in a Unit Grade: Content Area: Subject Matter: Time Period for the Learning Experience:
High School Mathematics Geometry Two 45-minute sessions in two consecutive days
State-adopted Academic Content Standards for Students Geometry 22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. Learning Goals for the Learning Experience Students will be able to do the following with a focus on transformations of two and three-dimensional figures: • Translate, reflect, and rotate plane and solid figures • Determine the effect of more than one transformation on plane and solid figures Instructional Resources Available • Geometry textbook, standard construction tools – straightedge, com, protractor, plastic models of 2 and 3-dimensional figures, and computers with transformational geometry software and Internet access 2. Class Description Students are in a high school Geometry class. They particularly need to have opportunities to learn content in different ways and to revisit content. Many of the students enjoy the school environment and like to socialize with each other. Most of the students are active in after-school activities, including sports, clubs, tutoring, and jobs, which leaves little time for homework. The majority of the class plans to attend the local community college or technical computer school. There are some students who are unsure about what careers they want to pursue. About two-thirds of the students in this class have at least one other class with their classmates. 3. Developmental Needs of the Students in Grades 9 –12 • understand connections between the lesson content and life outside of school • develop advanced thinking and problem-solving skills • develop socially and handle the intense social peer pressure to conform while maintaining individuality
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
1
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
______________________________________________
B. Questions for Case Study 1 1. Given the contextual information for Case Study 1, think about a lesson you might use with these students that addresses the subject matter learning goals and the developmental needs of the students described. In the columns below describe: • Instructional strategies • Student activities • Instructional resources Note: Instructional strategies are what the teacher does during instruction and student activities are what the students do during the lesson. Include how you would use the instructional resources as you describe your strategies and student activities. Instructional Strategies
Student Activities
Day 1
Day 1
Assessment:
Assessment:
-Get an idea of students’ prior knowledge of different shapes with the use of an assessment worksheet.
-Students will receive a worksheet with different shapes presented (both 2D and 3D) and be asked to fill in the names of as many shapes as they can recall.
Lesson: -First, present to students the different shapes that will be used through the lesson. Make sure they are familiar with the more complex shapes (i.e. pentagon, hexagon, and octagon). -Explain to students the definition rotations, translations, and reflection.
of
-Demonstrate for students how a shape can be rotated, translated, and reflected using various real world examples (such as mirrors, diagrams, 3D modeling). Then model for students the effect multiple transformations have on various shapes. Check for understanding by asking students questions and having them predict what the shape will look like after the transformation. Day 2 Assessment: -Have students recall and demonstrate what they learned yesterday by coming to the board and transforming various shapes.
July 2008
Lesson: -Have students work in cooperative learning groups of 3 people. In these groups, each student will be assigned a different transformation (rotation, translation, or reflection) that they must model for the other two students. A worksheet with various shapes will be provided to each student. On this worksheet students will be required to show their knowledge of transforming various figures. Each group will then be required to combine their different transformations to solve more complex problems presented on the worksheet. Day 2 Assessment: -Students will come to the board, 3 at a time, and perform a rotation, translation, or reflection of a given shape. Lesson: -Have the students use the geometry program on the computer that has shape transforming tools. Students will have a short time to get familiar with
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
2
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
Lesson: -Using the computer, show the entire class how to use the shape transformation program. Go over the various steps to using the program and check for understanding by asking questions along the way.
the program before the start of the independent work. -Students will use the geometry program to complete a 3D modeling worksheet before the end of the class session. This is to be done independently.
-Explain the worksheet that they will complete independently. Emphasize that this is an independent activity that they must complete before the end of the computer lab. 2. Based on your knowledge of the content and of student development, explain why the instructional strategies, student activities, and resources you listed in question 1: • are appropriate for this class
This lesson is appropriate for this class in a few different ways. First, since this class enjoys and excess in discussion, the lesson allows them to socialize and discuss the various methods of transforming shapes. Second, the lesson has the students revisiting the material the very next day. This helps to move the information from the short-term to long-term memory. Third, no homework is given as each student has a busy afterschool schedule. Lastly, since many of the students in this class plan to attend a community college or technical computer school, this lesson provides them with a great chance to use computers and software in an interesting and new way.
• address the developmental needs of these student
This lesson is designed to address the developmental needs of these students. Understanding how to manipulate objects in 3D space is an effective mental exercise. This lesson is requiring students to think about shapes and transformation in different and exciting ways. The lesson encourages students to have a better understanding of the complexity and beauty of the shapes around us in everyday life. The small group exercise promotes social development and communication skill acquisition with all students, also developing individuality among students.
• help these students make progress toward achieving the state-adopted academic content standards for students in this content area
This lesson meets the requirements for the academic content standard for High School Geometry that states, “Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.” This lesson uses various learning methods (student assessment, cooperative group learning, and technology application) that s for the different learning styles within the class. Students are pushed to participate in various activities, including small groups and independent work, that will have them effectively acquire the learning objectives of the lesson.
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
3
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
— END OF CASE STUDY 1 —
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
4
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
Case Study 2: Assessment Practices A. Contextual Information for Case Study 2 1. Elements of a Learning Experience in a Unit Grade: Content Area: Subject Matter: Time Period for Whole Unit:
High School Mathematics Algebra 3 weeks
State-adopted Academic Content Standards for Students Algebra 2 7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator. Learning Goals for Whole Unit Students will be able to do the following: • Reduce rational expressions • Add and subtract rational expressions • Multiply and divide rational expressions • Simplify complicated rational expressions • Evaluate rational expressions • Give equivalent forms of rational expressions 2. Teacher Reflection on Student Assessment for this Unit “I am not satisfied with the assessment plan I used for the last unit of study. I gave the students a diagnostic test at the beginning of the unit, two quizzes during the unit, and a final test from the teacher’s guide. I feel, though, that I need additional information on what students really know and understand, their misconceptions, what they learned during instruction, and their progress toward achieving the learning goals. I am looking for ways to improve my assessment plan, so I can have a more complete understanding of how well these students learned the subject matter.”
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
5
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
3. Assessment Plan Day 1
Day 6
Day 11
Day 15
Goals Assessed
Perform arithmetic operations on simple rational numbers, and factor polynomials
Multiply and divide rational expressions
Add and subtract rational expressions
Reduce, add, subtract, multiply, divide, simplify, evaluate, and give equivalent forms of rational expressions
Type
Formal, diagnostic test from curriculum guide; multiple choice; formative
Formal quiz from the textbook; multiple choice; formative
Formal quiz from the textbook; multiple choice; formative
Formal, final chapter/unit exam from textbook; multiple choice and fill in the blank; summative
Purpose
Assess previous knowledge and skills
Assess acquired concepts and skills
Assess acquired skills and concepts
Assess acquired knowledge and skills from instructional unit
Implementa tion
Individual assessment; paper and pencil; teacher corrects with an answer key
Individual assessment; paper and pencil; teacher corrects with an answer key
Individual assessment; paper and pencil; teacher corrects with an answer key
Individual assessment; paper and pencil; teacher corrects with an answer key
Strategies
Tell students of scores and inform student of correct and incorrect items
Inform students of correct and incorrect items
Inform students of correct and incorrect items
Inform students of correct and incorrect items
Informing Instruction
To determine what needs to be reviewed and where to begin teaching
To determine who has learned the material presented
To determine who has learned the material presented
To determine the achievement level of each student towards the goals
______________________________________________
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
6
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
B. Questions for Case Study 2 1.a.
Identify one strength in the assessment plan and explain why it is a strength in relation to the learning goals of this unit.
1.b.
Identify one weakness in the assessment plan and explain why it is a weakness in relation to the learning goals of this unit.
The inclusion of a formative assessment is one strength in this assessment plan. It is important for a teacher to understand students’ prior knowledge of the material and build their lesson plan to foster this knowledge. Especially in mathematics, the learning of a new concept builds upon prior knowledge. Specifically for this lesson, each learning goal is related to and expanded upon the subject of rational expressions. Assessing students’ prior knowledge of rational expressions will help the teacher revise and form a lesson plan that will effectively meet the students’ needs. The exclusion of any informal assessment tools is the greatest weakness in this assessment plan. Although it is important to use formal assessment tools, such as standardized tests, to assess overall achievement, it is equally, if not more so, important that teachers are using informal assessment tools to shape their instruction. Specifically for this lesson, it is important to see what area of rational expressions students are struggling with. The use of informal assessment tools gives the teacher the opportunity to assess and address students’ learning needs on the spot, creating a much more efficient lesson plan.
2. Suppose you found the additional assessment in a supplementary resource. Think about how the additional assessment could improve the teacher’s assessment plan. Additional Assessment Suppose you have been hired by a publisher to provide information for a detailed solution guide for the problem set below. The publisher wants to illustrate more than one way to simplify expressions. Present the publisher with two different methods to simplify each expression and provide a mathematical justification for each method, so the readers of the solution guide will understand how to use each method and why each is mathematically correct. 1. 2. 3. 4. 5.
(5x2 + 21x + 4)/(25x + 100) (6x2/8x) • -4x3/(2x2) (3x2 + 6x)/(4x) ÷ 15/(8/x2) (x + 3)/(x3-x2-6x) ÷ (x2 – 9)/(x2 + x – 12) (x3 + x2)/(x2 – 16) • (x + 4)/(3x4 + x3 – 2x2)
Explain to the teacher how it might be used to improve the plan by answering the following questions:
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
7
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
2.a.
When in the plan would you use this assessment?
This assessment deals mainly with the subject matter of simplifying expressions. Students should already have the skills to multiply and divide rational expression. Therefore, this assessment would best be used after Day 6 when teaching how to simplify complicated rational expressions.
2.b.
What goals would be assessed by this assessment?
All goals leading up to, and including, simplifying complicated rational expressions would be assessed by this assessment. These goals include: reducing rational expressions, adding and subtracting rational expressions, and multiplying and dividing rational expressions.
2.c.
What type of assessment would it be?
This is an formative assessment. It is meant to help teachers make instructional changes to the lesson that adapt to students’ needs. If the students seem to be struggling with a specific area of the lesson, the teacher is then able to focus on this need by modifying the lesson.
2.d.
What would be the purpose of the assessment?
The purpose of the assessment is to see if students have gained the adequate skills to perform arithmetic on rational expressions, specifically simplifying rational expressions. This assessment requires students to show the steps in how to simplify rational expressions in two ways. This information will allow the teacher to analyze student progress and determine where students are having the most trouble.
2.e.
How would you implement the assessment?
After teaching students the prerequisite goals to the assessment, I would have them complete the assessment individually. This allows the teacher to analyze each student’s progress individually as well as gauge the overall weaknesses and strengths of the class as a whole. Individual students would receive on their assessment and the teacher could then address the classes’ weaknesses as a whole.
2.f.
What strategies would you use?
Students would receive individually on their assessments in the form of comments and correction of arithmetic, allowing them to see where they made mistakes and what changes are needed. The assessment would provide information on the areas of the lesson the class was struggling with as a whole, allowing the teacher to give to the entire class. This would include recognition by the teacher of the subject area the class is having most trouble with and reevaluation of the lesson plan being taught.
2.g.
How would the results of the assessment inform instruction?
The results of the assessment would allow the teacher see where students are having the most difficulty and then to reshape the instruction in such a way that the students understand it. The assessment also gives insight into how
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
8
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
students are thinking mathematically and if any fundamental review is necessary. 3. Explain how using the additional assessment as you described in question 2 improves the teacher’s assessment plan and what specific information would be gained about what the students really know and understand about the content area, their misconceptions, and their progress toward achieving the learning goals. The additional assessment described in question 2 adds an informal assessment tool to the teacher’s assessment plan. This informal assessment tool is an invaluable addition to the teacher’s plan, allowing the teacher to gather information on students’ knowledge in an effective and efficient manner. This newfound information allows the teacher to analyze and reconstruction the lesson plan in accordance with student needs. This is beneficial for both the teacher and the student. The teacher is now aware of the difficulties students are having in a certain area of the lesson and students can then receive the proper instruction they require.
— END OF CASE STUDY 2 —
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
9
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
Case Study 3: Adaptation of Subject Specific Pedagogy for English Learners A. Contextual Information for Case Study 3 1. Elements of a Learning Experience for 2 Days in a Unit Grade: High School Content Area: Mathematics Subject Matter: Mathematical Analysis Time Period for Whole Unit: 3 weeks State-adopted Academic Content Standards for Students Limits-Mathematical Analysis 8.0 Students are familiar with the notion of the limit of a function as the independent variable approaches a number or infinity Learning Goals for Whole Unit Students will be able to do the following with a focus on limits: • Find a limit • Mathematically justify that limit • Generate stages of various iterative processes Relationship to Preceding and Subsequent Learning Experiences Prior to this lesson, students studied finite and infinite series. They were introduced to the concept of convergent and divergent series. They also have encountered the concept of limit on an intuitive basis. They will use what they learned in this lesson in future work in determining and justifying limits. 2. Outline of Plans for Days 3 and 4 The following outline addresses some of the academic content standards and unit goals, but it is not expected that the students will achieve them during the two days. Instructional Strategies • On Day 3, lead a quick review of finite and infinite sequences. Have students complete review sheet. Lead whole class discussion on their responses to the review sheet questions highlighting common misconceptions. Have students provide counter-examples at the board. Show students the first three iterations of the Sierpinski Triangle. Have them record their answers to questions concerning the number of triangles in each iteration and have them predict the number of triangles in subsequent iterations. Have students work in pairs to construct the next two iterations to check their predictions, shade the downward pointing triangles in each iteration, and record their predictions concerning the combined shaded areas of subsequent iterations. Students will be asked to individually record their prediction of the limit of the shaded area as the number of iterations becomes infinite. Each will discuss his/her prediction with a partner and decide on a possible mathematical justification. Students will then split up to edit their limit prediction, if they wish, and to record their justification.
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
10
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
• On Day 4, have sets of partners present their work from Day 2 to the class. Class will pose
questions about their work and partners will justify their thinking. Student Activities • On Day 3, complete the review sheet and provide misconceptions of reviewed concepts and provide counter-examples on the board. Answer questions about the first three iterations of Sierpinski’s Triangle, and make predictions about further iterations. Work with partner to construct the next two iterations in order to check predictions. Do the shading as directed and make predictions concerning the combined shaded areas of subsequent iterations. Record prediction of the limit, discuss with partner, and decide on a justification. Split up to edit and record predictions. • On Day 4, present work with partner to the whole class and respond to questions asked by the class. When other partners are presenting, students will ask questions of that set of partners. Progress Monitoring • Teacher will use class discussions, group and individual responses to questions, and expressed rationales to determine level of learning. • Students will receive written and oral comments about individual work, and about their work with a partner. 3. Student Description Elena is a 15 year-old 10th grader and an English learner. She is from Mexico and both of her parents are professionals. Her extended family includes aunts, uncles, and cousins. Her grandparents live in Mexico and she and her family visit them in the summer. She has been in the United States for one and a half years. She is literate in Spanish and often reads Spanish literature. Her report cards from her school in Mexico indicate above average grades. Elena is somewhat shy socially but is well liked and works well in small groups. She is seldom absent from school. The CELDT results indicate overall score in the Early Intermediate range, and she has been identified as an English learner. Written Response to: “What is your favorite family day?” A Special Family Celebration As special family time is when my family celebrate the anniversary of my grandmother and grandfather. They are my abuelita and abuelito. Why is it especial? I like this because all my family come to my grandparent house for make especial food of my country. The fiesta is very especial. My grandparent have marry 45 year. They live in Mexico my tia, tio and primos all go to Mexico for all family celebrate together. We like have all family together. My primos and me see friends in our city . We give grandparent big picture of all family. Grandparent like fiesta and gift. They are much happy. Transcript of Oral Response to: “Tell my about your dance class.” I like my dance class at community center. I need class for forget my problems. Is like help. I forgot my problems. When I dance, I like my dress because everybody look me and say, “Oh, that look pretty.” Everybody take my picture. I was in newspaper. When I dancing, I feel very good. I like that because I represent my country. ______________________________________________
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
11
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
B. Questions for Case Study 3 1. Identify two specific learning needs the student has as an English learner, based on the student description and the responses.
Based on the student responses, the student’s oral production and written production is not proficient. She will need extra guidance during the instruction portion of the math lesson. Also, the student will need help in understanding the mathematic vocabulary presented in chapter. Though the description of the student shows that she should not have trouble with the arithmetic, she will still need significant guidance throughout the lesson.
2.a. Identify one instructional strategy or student activity from the outline of plans that could be challenging for the student.
Since the student is known to be shy and does not have adequate speaking skills, the presenting of the previous day’s work to the class and answering of questions will most likely be difficult for the student.
2.b. Explain why the strategy or activity you chose could be challenging to the student. Use your knowledge of English learners and your analysis of the student’s learning needs in your explanation.
The student’s shyness and lack of English speaking proficiency is the reason why this strategy could be challenging for her. English language learners are often hesitant to speak in front of large groups. Elena being shy will only add to this hesitation. A small group setting is usually the best strategy for making English language learners feel comfortable conversing with other students.
3.a. Describe how you would adapt the strategy or activity you identified above to meet the learning needs of the student. Consider specific subject matter pedagogy when writing your description.
English language learners learn easier when the information is presented visually. Because of this, the use of a graphic organizer in the lesson would be a great way to make the complex information more understandable to Elena. A Vocabulary and Phrases graphic organizer would be idea for the learning needs of Elena. This will allow her to review the vocabulary and all information that goes with each word. Another useful strategy would be to pair Elena with an able partner. Being a shy person, this personal setting would allow Elena to discuss the subject matter.
3.b. Explain how your adaptation would be effective for the student in making progress toward the learning goals of the lesson. (In your explanation of the adaptation, refer to specific aspects of the student description and to the samples of proficiency in English.)
These adaptations are specifically designed to help Elena progress toward the learning goals of the lesson. English language learners learn more effectively when the information is presented visually to them. The Vocabulary and Phrases graphic organizer will allow Elena to see the vocabulary words and all connecting information. This will be a valuable resource Elena can refer to throughout the lesson. Elena is also described as a shy individual. The use of a partner will counter this shyness and allow Elena to open up and have discussion on the lesson material.
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
12
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
3.c. Explain how your adaptation would be effective for the student in making progress toward English language development. (In your explanation of the adaptation, refer to specific aspects of the student description and to the samples of proficiency in English.)
Elena is an Early Intermediate English language learner. To facilitate English language development, I chose to implement a graphic organizer into the lesson. The Vocabulary and Phrases graphic organizer gives Elena a visual tool she can use throughout the lesson. She will also be able to easily refer back to the vocabulary presented in the lesson plan when needed. The student description of Elena describes her as being shy. Pairing Elena with a partner facilitates communication and conversation, further developing her English language acquisition.
4.a. Which progress monitoring assessment from the outline of plans would you choose to monitor this student’s progress toward achieving the learning goal(s)?
I would observe Elena in her small group and have individual conversation about the lesson content to assess her progress toward achieving the learning goals.
4.b. Give a rationale for your choice of progress monitoring assessment. Use your knowledge of content in this unit, and this student’s English language abilities in your rationale.
Because Elena is an English language learner and typically shy, my observation of her in the small group setting, where she is conversing with other students, would be a good opportunity to assess whether she understands the lesson content and is achieving the desired learning goals. My individual conversation with Elena would also allow me the opportunity to assess her achievement through dialogue with her.
5. Based on what you learned about this student’s English proficiency, what would be your next steps in planning to facilitate her English language development? Consider specific information from the student description and her written and oral language samples when responding.
The next step I would take with Elena’s English language development would be to see whether my recent adaptations made an improvement in her understanding of the material. If I found the adaptations did make facilitate her learning I would further develop these strategies, such as incorporating other types of graphic organizers, such as Cause and Effect Sequences. If I found that my recent adaptations made no noticeable content progress or decreased Elena’s language acquisition, I would incorporate different adaptations to the lesson. These adaptations could include symbolic representations of content, such as pictures and diagrams, or connecting the lesson to Elena’s culture and country to get her interested in the material.
— END OF CASE STUDY 3 —
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
13
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
Case Study 4: Adaptation of Subject-Specific Pedagogy for Students with Special Needs
A. Contextual Information for Case Study 4 1. Elements of a Learning Experience for 3 Days in a Unit Grade: High School Content Area: Mathematics Subject Matter: Probability Time Period for Whole Unit: 3 weeks State-Adopted Academic Content Standards for Students Probability and Statistics 6.0 Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations. 8.0 Students organize and describe distributions of data by using a number of different methods. Learning Goals for Whole Unit Students will be able to do the following • Make connections between mathematics and its applications in the real world • Select and use appropriate tools and technology to analyze and display data • Communicate precisely about given quantities, relationships, and unknown values • Reason mathematically by analyzing evidence and building arguments to or refute hypotheses Relationship to Preceding and Subsequent Learning Experiences Prior to this unit, students have studied the measures of central tendency and how to calculate them. In the future, they will use the skill covered in this unit to solve problems. 2. Outline of Plans for Days 3, 4, and 5 The following outline addresses some of the academic content standards and unit goals, but it is not expected that the students will achieve them during the three days. Instructional Strategies • On Day 3, read a report with text, statistics, and graphical representations about rainfall in California during the last decade (vary between independent silent and oral reading to whole class). Present additional information about the concepts and lead whole-class discussion. Have students respond in writing to teacher-generated questions about the report. Written responses are homework. • On Day 4, read a document that addresses appropriate uses and misuses of measures of central tendency, and effective graphical representation of data for the purpose of critiquing the report read on the previous day. Lead a class discussion about how statistics can present and different perspectives. Give groups of students the same set of data, but different questions. Students must
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
14
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
compute statistics and create graphical representations best suited to respond to their questions. Students write individual rationales ing their selection of statistics and representations. As a group, they present their statistics and representations to the class and receive from others. • On Day 5, have students read an article containing an inappropriate use of statistics to a position. Students discuss the article with a partner. Each student writes a letter to the author indicating the errors in the article and providing arguments for using other statistics to the same position. Student Activities • In class, either read silently or orally the copy of the report, highlighting important issues, and participate in class discussion about statistics presented. For homework, complete written responses in questions. • Listen to arguments critiquing the statistics used in the report, take notes, and participate in class analysis and discussion. Work in a group to analyze data and make graphical representations to respond to a given question. Individual students write rationales. Present with other group the statistics and representations chosen to whole class. Provide to other groups when they present. • Read article and discuss it with a partner. Write a letter to the author. Read a letter written by another classmate and analyze for reasonableness. Progress Monitoring • Teacher will use class discussion, responses to questions, group presentation and letter to author to monitor student progress. • Students will receive written and oral comments from the teacher and other students. 3. Student Description Alex is a 15-year-old boy in the 10 th grade. He had difficulty with the development of his early literacy skills, including the acquisition of sound/symbol relationships and word identification, demonstrated in both his reading and writing. In the second grade, Alex was identified as a student with specific learning disabilities. Since then, Alex has received special education primarily in a resource room for language arts, while he is included in the general education curriculum. He is able to independently read text at a 7 th grade level and continues to struggle with decoding words. Alex also has asthma for which he takes daily medication and occasionally needs to use an inhaler. He is a selfisolating person who does not readily into whole-class conversations or contribute to group learning situations. His tendency is to sit alone at lunch and to be by himself during transitional time. There is no in-class for this student. ______________________________________________
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
15
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
B. Questions for Case Study 4 1.a. Identify one instructional strategy or student activity from the outline of plans that could be challenging for the student, considering the description of the student’s learning disability.
After referring to the student activities and the student’s description, it seems apparent that Alex will have trouble with the oral reading of the report. Assuming the report includes high school level reading, Alex will have difficulty reading the report without the aide of a teacher or partner.
1.b. Explain why the strategy or activity you chose could be challenging for the student, based on specific aspects of the student description.
The oral reading of the report could be challenging to Alex because has not adequately developed his sound/symbol relationships and word identification. He currently reads independently at a 7th grade level. This learning disability makes reading a high school level report that includes text, statistics, and graphical representations much more difficult for Alex. Since there is not in-class for Alex, he will most likely struggle with understanding the report as well as any activities pertaining to the report.
1.c. Describe how you would adapt the strategy or activity you identified to meet the needs of the student.
Since Alex has difficulty reading independently because of his under developed literacy skills, I would adapt the activity to his needs by reviewing the vocabulary presented in the report prior to his reading of it. I would accomplish this with the use of a graphic organizer. The graphic organizer would allow Alex to make connections between the vocabulary presented in the report. It would also serve as a visual resource that Alex could refer to as he reads the report independently.
1.d. Explain how your adaptation would be effective for the student in making progress toward achieving the learning goal(s) of this unit.
This adaptation will help Alex to understand and participate in the reading of the report. Since the report involves real world applications of statistics, Alex will make a connection between these applications and mathematics. Similarly, the graphical representations of rainfall data included in the report will allow Alex to analyze mathematical data. After reading the report, Alex will then be able to communicate to the class the relationship between statistics and its real world applications. This knowledge will give Alex the tools he needs start reasoning mathematically and forming hypothesis.
2.a. Identify one additional instructional strategy or student activity from the outline of plans that could be challenging for the student, considering the student’s other
Considering Alex’s learning needs and lack of literacy skills, the activity requiring the students to individually write rationales will most likely be challenging for the student.
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
16
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
learning needs. 2.b. Explain why the strategy or activity you chose could be challenging for the student, based on specific aspects of the student description.
The individual writing of rationales by the students will most like be a challenge for Alex because of his underdeveloped literacy skills. Requiring the student to write independently will most likely be difficult because he has not yet acquired the proper sound/symbol relationships and word identification needed for this activity. This lack of literacy skills will make writing independently a difficult task for Alex.
2.c. Describe how you would adapt the strategy or activity you identified to meet the needs of the student.
I would adapt this independent writing activity to meet the needs of Alex by turning it into a small group activity. Rather than writing independently, I would have the students discuss their rationales in a small group setting and form one collective opinion. They would then present this collective rationale to the class as a whole. This small group activity will better adapt to the learning needs of Alex, as well as encourage all students to communicate effectively with one another in order to form a common rationale among ach small group.
2.d. Explain how your adaptation would be effective for the student in making progress toward achieving the learning goal(s) of this unit.
The use of small groups would be effective for the student in making progress towards achieving the learning goals of this unit in multiple ways. Having Alex participate in small group discussion instead of independent writing will allow him to develop his skills in reasoning mathematically. The small group discussion will also require Alex to build an argument in of his rationale, while also analyzing and considering other students’ opinions. This activity will also require Alex to communicate mathematically with other student, achieving a learning goal of the unit and developing the student’s social skills.
3.a. What progress monitoring assessment would you choose to obtain evidence of the student’s progress toward a learning goal(s)?
3.b. Give a rationale for your choice of assessment. Use your knowledge of academic content in this unit, and this student’s learning needs in your July 2008
I would use individual conversation with the student see if the vocabulary graphic organizer was aiding him in the reading of the report. I would assess his progress by asking specific questions regarding the report to see if the student had made progress toward the learning goals of the unit. I would also observe Alex during the small group activity to see if he was ing in on the discussion. This observation would allow me to assess his progress and understanding of the material. I would use individual conversation with the student because of his difficulty with reading and writing. This oral assessment would give me a clearer understanding of whether he was acquiring the learning goals of the unit, more so than a written assessment. Similarly, because of the
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
17
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
rationale.
student’s lack of literacy comprehension, I would use observation of him in the small group scenario to assess whether he was meeting the goals of the unit.
— END OF CASE STUDY 4 —
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
18
ID #000493178
— Single Subject Mathematics —
Before beginning this task, read the complete directions provided in the CalTPA Candidate Handbook.
Case Study 1: Subject-Specific and Developmentally-Appropriate Pedagogy A. Contextual Information for Case Study 1 1. Elements of a Learning Experience in a Unit Grade: Content Area: Subject Matter: Time Period for the Learning Experience:
High School Mathematics Geometry Two 45-minute sessions in two consecutive days
State-adopted Academic Content Standards for Students Geometry 22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. Learning Goals for the Learning Experience Students will be able to do the following with a focus on transformations of two and three-dimensional figures: • Translate, reflect, and rotate plane and solid figures • Determine the effect of more than one transformation on plane and solid figures Instructional Resources Available • Geometry textbook, standard construction tools – straightedge, com, protractor, plastic models of 2 and 3-dimensional figures, and computers with transformational geometry software and Internet access 2. Class Description Students are in a high school Geometry class. They particularly need to have opportunities to learn content in different ways and to revisit content. Many of the students enjoy the school environment and like to socialize with each other. Most of the students are active in after-school activities, including sports, clubs, tutoring, and jobs, which leaves little time for homework. The majority of the class plans to attend the local community college or technical computer school. There are some students who are unsure about what careers they want to pursue. About two-thirds of the students in this class have at least one other class with their classmates. 3. Developmental Needs of the Students in Grades 9 –12 • understand connections between the lesson content and life outside of school • develop advanced thinking and problem-solving skills • develop socially and handle the intense social peer pressure to conform while maintaining individuality
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
1
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
______________________________________________
B. Questions for Case Study 1 1. Given the contextual information for Case Study 1, think about a lesson you might use with these students that addresses the subject matter learning goals and the developmental needs of the students described. In the columns below describe: • Instructional strategies • Student activities • Instructional resources Note: Instructional strategies are what the teacher does during instruction and student activities are what the students do during the lesson. Include how you would use the instructional resources as you describe your strategies and student activities. Instructional Strategies
Student Activities
Day 1
Day 1
Assessment:
Assessment:
-Get an idea of students’ prior knowledge of different shapes with the use of an assessment worksheet.
-Students will receive a worksheet with different shapes presented (both 2D and 3D) and be asked to fill in the names of as many shapes as they can recall.
Lesson: -First, present to students the different shapes that will be used through the lesson. Make sure they are familiar with the more complex shapes (i.e. pentagon, hexagon, and octagon). -Explain to students the definition rotations, translations, and reflection.
of
-Demonstrate for students how a shape can be rotated, translated, and reflected using various real world examples (such as mirrors, diagrams, 3D modeling). Then model for students the effect multiple transformations have on various shapes. Check for understanding by asking students questions and having them predict what the shape will look like after the transformation. Day 2 Assessment: -Have students recall and demonstrate what they learned yesterday by coming to the board and transforming various shapes.
July 2008
Lesson: -Have students work in cooperative learning groups of 3 people. In these groups, each student will be assigned a different transformation (rotation, translation, or reflection) that they must model for the other two students. A worksheet with various shapes will be provided to each student. On this worksheet students will be required to show their knowledge of transforming various figures. Each group will then be required to combine their different transformations to solve more complex problems presented on the worksheet. Day 2 Assessment: -Students will come to the board, 3 at a time, and perform a rotation, translation, or reflection of a given shape. Lesson: -Have the students use the geometry program on the computer that has shape transforming tools. Students will have a short time to get familiar with
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
2
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
Lesson: -Using the computer, show the entire class how to use the shape transformation program. Go over the various steps to using the program and check for understanding by asking questions along the way.
the program before the start of the independent work. -Students will use the geometry program to complete a 3D modeling worksheet before the end of the class session. This is to be done independently.
-Explain the worksheet that they will complete independently. Emphasize that this is an independent activity that they must complete before the end of the computer lab. 2. Based on your knowledge of the content and of student development, explain why the instructional strategies, student activities, and resources you listed in question 1: • are appropriate for this class
This lesson is appropriate for this class in a few different ways. First, since this class enjoys and excess in discussion, the lesson allows them to socialize and discuss the various methods of transforming shapes. Second, the lesson has the students revisiting the material the very next day. This helps to move the information from the short-term to long-term memory. Third, no homework is given as each student has a busy afterschool schedule. Lastly, since many of the students in this class plan to attend a community college or technical computer school, this lesson provides them with a great chance to use computers and software in an interesting and new way.
• address the developmental needs of these student
This lesson is designed to address the developmental needs of these students. Understanding how to manipulate objects in 3D space is an effective mental exercise. This lesson is requiring students to think about shapes and transformation in different and exciting ways. The lesson encourages students to have a better understanding of the complexity and beauty of the shapes around us in everyday life. The small group exercise promotes social development and communication skill acquisition with all students, also developing individuality among students.
• help these students make progress toward achieving the state-adopted academic content standards for students in this content area
This lesson meets the requirements for the academic content standard for High School Geometry that states, “Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.” This lesson uses various learning methods (student assessment, cooperative group learning, and technology application) that s for the different learning styles within the class. Students are pushed to participate in various activities, including small groups and independent work, that will have them effectively acquire the learning objectives of the lesson.
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
3
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
— END OF CASE STUDY 1 —
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
4
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
Case Study 2: Assessment Practices A. Contextual Information for Case Study 2 1. Elements of a Learning Experience in a Unit Grade: Content Area: Subject Matter: Time Period for Whole Unit:
High School Mathematics Algebra 3 weeks
State-adopted Academic Content Standards for Students Algebra 2 7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator. Learning Goals for Whole Unit Students will be able to do the following: • Reduce rational expressions • Add and subtract rational expressions • Multiply and divide rational expressions • Simplify complicated rational expressions • Evaluate rational expressions • Give equivalent forms of rational expressions 2. Teacher Reflection on Student Assessment for this Unit “I am not satisfied with the assessment plan I used for the last unit of study. I gave the students a diagnostic test at the beginning of the unit, two quizzes during the unit, and a final test from the teacher’s guide. I feel, though, that I need additional information on what students really know and understand, their misconceptions, what they learned during instruction, and their progress toward achieving the learning goals. I am looking for ways to improve my assessment plan, so I can have a more complete understanding of how well these students learned the subject matter.”
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
5
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
3. Assessment Plan Day 1
Day 6
Day 11
Day 15
Goals Assessed
Perform arithmetic operations on simple rational numbers, and factor polynomials
Multiply and divide rational expressions
Add and subtract rational expressions
Reduce, add, subtract, multiply, divide, simplify, evaluate, and give equivalent forms of rational expressions
Type
Formal, diagnostic test from curriculum guide; multiple choice; formative
Formal quiz from the textbook; multiple choice; formative
Formal quiz from the textbook; multiple choice; formative
Formal, final chapter/unit exam from textbook; multiple choice and fill in the blank; summative
Purpose
Assess previous knowledge and skills
Assess acquired concepts and skills
Assess acquired skills and concepts
Assess acquired knowledge and skills from instructional unit
Implementa tion
Individual assessment; paper and pencil; teacher corrects with an answer key
Individual assessment; paper and pencil; teacher corrects with an answer key
Individual assessment; paper and pencil; teacher corrects with an answer key
Individual assessment; paper and pencil; teacher corrects with an answer key
Strategies
Tell students of scores and inform student of correct and incorrect items
Inform students of correct and incorrect items
Inform students of correct and incorrect items
Inform students of correct and incorrect items
Informing Instruction
To determine what needs to be reviewed and where to begin teaching
To determine who has learned the material presented
To determine who has learned the material presented
To determine the achievement level of each student towards the goals
______________________________________________
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
6
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
B. Questions for Case Study 2 1.a.
Identify one strength in the assessment plan and explain why it is a strength in relation to the learning goals of this unit.
1.b.
Identify one weakness in the assessment plan and explain why it is a weakness in relation to the learning goals of this unit.
The inclusion of a formative assessment is one strength in this assessment plan. It is important for a teacher to understand students’ prior knowledge of the material and build their lesson plan to foster this knowledge. Especially in mathematics, the learning of a new concept builds upon prior knowledge. Specifically for this lesson, each learning goal is related to and expanded upon the subject of rational expressions. Assessing students’ prior knowledge of rational expressions will help the teacher revise and form a lesson plan that will effectively meet the students’ needs. The exclusion of any informal assessment tools is the greatest weakness in this assessment plan. Although it is important to use formal assessment tools, such as standardized tests, to assess overall achievement, it is equally, if not more so, important that teachers are using informal assessment tools to shape their instruction. Specifically for this lesson, it is important to see what area of rational expressions students are struggling with. The use of informal assessment tools gives the teacher the opportunity to assess and address students’ learning needs on the spot, creating a much more efficient lesson plan.
2. Suppose you found the additional assessment in a supplementary resource. Think about how the additional assessment could improve the teacher’s assessment plan. Additional Assessment Suppose you have been hired by a publisher to provide information for a detailed solution guide for the problem set below. The publisher wants to illustrate more than one way to simplify expressions. Present the publisher with two different methods to simplify each expression and provide a mathematical justification for each method, so the readers of the solution guide will understand how to use each method and why each is mathematically correct. 1. 2. 3. 4. 5.
(5x2 + 21x + 4)/(25x + 100) (6x2/8x) • -4x3/(2x2) (3x2 + 6x)/(4x) ÷ 15/(8/x2) (x + 3)/(x3-x2-6x) ÷ (x2 – 9)/(x2 + x – 12) (x3 + x2)/(x2 – 16) • (x + 4)/(3x4 + x3 – 2x2)
Explain to the teacher how it might be used to improve the plan by answering the following questions:
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
7
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
2.a.
When in the plan would you use this assessment?
This assessment deals mainly with the subject matter of simplifying expressions. Students should already have the skills to multiply and divide rational expression. Therefore, this assessment would best be used after Day 6 when teaching how to simplify complicated rational expressions.
2.b.
What goals would be assessed by this assessment?
All goals leading up to, and including, simplifying complicated rational expressions would be assessed by this assessment. These goals include: reducing rational expressions, adding and subtracting rational expressions, and multiplying and dividing rational expressions.
2.c.
What type of assessment would it be?
This is an formative assessment. It is meant to help teachers make instructional changes to the lesson that adapt to students’ needs. If the students seem to be struggling with a specific area of the lesson, the teacher is then able to focus on this need by modifying the lesson.
2.d.
What would be the purpose of the assessment?
The purpose of the assessment is to see if students have gained the adequate skills to perform arithmetic on rational expressions, specifically simplifying rational expressions. This assessment requires students to show the steps in how to simplify rational expressions in two ways. This information will allow the teacher to analyze student progress and determine where students are having the most trouble.
2.e.
How would you implement the assessment?
After teaching students the prerequisite goals to the assessment, I would have them complete the assessment individually. This allows the teacher to analyze each student’s progress individually as well as gauge the overall weaknesses and strengths of the class as a whole. Individual students would receive on their assessment and the teacher could then address the classes’ weaknesses as a whole.
2.f.
What strategies would you use?
Students would receive individually on their assessments in the form of comments and correction of arithmetic, allowing them to see where they made mistakes and what changes are needed. The assessment would provide information on the areas of the lesson the class was struggling with as a whole, allowing the teacher to give to the entire class. This would include recognition by the teacher of the subject area the class is having most trouble with and reevaluation of the lesson plan being taught.
2.g.
How would the results of the assessment inform instruction?
The results of the assessment would allow the teacher see where students are having the most difficulty and then to reshape the instruction in such a way that the students understand it. The assessment also gives insight into how
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
8
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
students are thinking mathematically and if any fundamental review is necessary. 3. Explain how using the additional assessment as you described in question 2 improves the teacher’s assessment plan and what specific information would be gained about what the students really know and understand about the content area, their misconceptions, and their progress toward achieving the learning goals. The additional assessment described in question 2 adds an informal assessment tool to the teacher’s assessment plan. This informal assessment tool is an invaluable addition to the teacher’s plan, allowing the teacher to gather information on students’ knowledge in an effective and efficient manner. This newfound information allows the teacher to analyze and reconstruction the lesson plan in accordance with student needs. This is beneficial for both the teacher and the student. The teacher is now aware of the difficulties students are having in a certain area of the lesson and students can then receive the proper instruction they require.
— END OF CASE STUDY 2 —
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
9
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
Case Study 3: Adaptation of Subject Specific Pedagogy for English Learners A. Contextual Information for Case Study 3 1. Elements of a Learning Experience for 2 Days in a Unit Grade: High School Content Area: Mathematics Subject Matter: Mathematical Analysis Time Period for Whole Unit: 3 weeks State-adopted Academic Content Standards for Students Limits-Mathematical Analysis 8.0 Students are familiar with the notion of the limit of a function as the independent variable approaches a number or infinity Learning Goals for Whole Unit Students will be able to do the following with a focus on limits: • Find a limit • Mathematically justify that limit • Generate stages of various iterative processes Relationship to Preceding and Subsequent Learning Experiences Prior to this lesson, students studied finite and infinite series. They were introduced to the concept of convergent and divergent series. They also have encountered the concept of limit on an intuitive basis. They will use what they learned in this lesson in future work in determining and justifying limits. 2. Outline of Plans for Days 3 and 4 The following outline addresses some of the academic content standards and unit goals, but it is not expected that the students will achieve them during the two days. Instructional Strategies • On Day 3, lead a quick review of finite and infinite sequences. Have students complete review sheet. Lead whole class discussion on their responses to the review sheet questions highlighting common misconceptions. Have students provide counter-examples at the board. Show students the first three iterations of the Sierpinski Triangle. Have them record their answers to questions concerning the number of triangles in each iteration and have them predict the number of triangles in subsequent iterations. Have students work in pairs to construct the next two iterations to check their predictions, shade the downward pointing triangles in each iteration, and record their predictions concerning the combined shaded areas of subsequent iterations. Students will be asked to individually record their prediction of the limit of the shaded area as the number of iterations becomes infinite. Each will discuss his/her prediction with a partner and decide on a possible mathematical justification. Students will then split up to edit their limit prediction, if they wish, and to record their justification.
July 2008
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10
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
• On Day 4, have sets of partners present their work from Day 2 to the class. Class will pose
questions about their work and partners will justify their thinking. Student Activities • On Day 3, complete the review sheet and provide misconceptions of reviewed concepts and provide counter-examples on the board. Answer questions about the first three iterations of Sierpinski’s Triangle, and make predictions about further iterations. Work with partner to construct the next two iterations in order to check predictions. Do the shading as directed and make predictions concerning the combined shaded areas of subsequent iterations. Record prediction of the limit, discuss with partner, and decide on a justification. Split up to edit and record predictions. • On Day 4, present work with partner to the whole class and respond to questions asked by the class. When other partners are presenting, students will ask questions of that set of partners. Progress Monitoring • Teacher will use class discussions, group and individual responses to questions, and expressed rationales to determine level of learning. • Students will receive written and oral comments about individual work, and about their work with a partner. 3. Student Description Elena is a 15 year-old 10th grader and an English learner. She is from Mexico and both of her parents are professionals. Her extended family includes aunts, uncles, and cousins. Her grandparents live in Mexico and she and her family visit them in the summer. She has been in the United States for one and a half years. She is literate in Spanish and often reads Spanish literature. Her report cards from her school in Mexico indicate above average grades. Elena is somewhat shy socially but is well liked and works well in small groups. She is seldom absent from school. The CELDT results indicate overall score in the Early Intermediate range, and she has been identified as an English learner. Written Response to: “What is your favorite family day?” A Special Family Celebration As special family time is when my family celebrate the anniversary of my grandmother and grandfather. They are my abuelita and abuelito. Why is it especial? I like this because all my family come to my grandparent house for make especial food of my country. The fiesta is very especial. My grandparent have marry 45 year. They live in Mexico my tia, tio and primos all go to Mexico for all family celebrate together. We like have all family together. My primos and me see friends in our city . We give grandparent big picture of all family. Grandparent like fiesta and gift. They are much happy. Transcript of Oral Response to: “Tell my about your dance class.” I like my dance class at community center. I need class for forget my problems. Is like help. I forgot my problems. When I dance, I like my dress because everybody look me and say, “Oh, that look pretty.” Everybody take my picture. I was in newspaper. When I dancing, I feel very good. I like that because I represent my country. ______________________________________________
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
11
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
B. Questions for Case Study 3 1. Identify two specific learning needs the student has as an English learner, based on the student description and the responses.
Based on the student responses, the student’s oral production and written production is not proficient. She will need extra guidance during the instruction portion of the math lesson. Also, the student will need help in understanding the mathematic vocabulary presented in chapter. Though the description of the student shows that she should not have trouble with the arithmetic, she will still need significant guidance throughout the lesson.
2.a. Identify one instructional strategy or student activity from the outline of plans that could be challenging for the student.
Since the student is known to be shy and does not have adequate speaking skills, the presenting of the previous day’s work to the class and answering of questions will most likely be difficult for the student.
2.b. Explain why the strategy or activity you chose could be challenging to the student. Use your knowledge of English learners and your analysis of the student’s learning needs in your explanation.
The student’s shyness and lack of English speaking proficiency is the reason why this strategy could be challenging for her. English language learners are often hesitant to speak in front of large groups. Elena being shy will only add to this hesitation. A small group setting is usually the best strategy for making English language learners feel comfortable conversing with other students.
3.a. Describe how you would adapt the strategy or activity you identified above to meet the learning needs of the student. Consider specific subject matter pedagogy when writing your description.
English language learners learn easier when the information is presented visually. Because of this, the use of a graphic organizer in the lesson would be a great way to make the complex information more understandable to Elena. A Vocabulary and Phrases graphic organizer would be idea for the learning needs of Elena. This will allow her to review the vocabulary and all information that goes with each word. Another useful strategy would be to pair Elena with an able partner. Being a shy person, this personal setting would allow Elena to discuss the subject matter.
3.b. Explain how your adaptation would be effective for the student in making progress toward the learning goals of the lesson. (In your explanation of the adaptation, refer to specific aspects of the student description and to the samples of proficiency in English.)
These adaptations are specifically designed to help Elena progress toward the learning goals of the lesson. English language learners learn more effectively when the information is presented visually to them. The Vocabulary and Phrases graphic organizer will allow Elena to see the vocabulary words and all connecting information. This will be a valuable resource Elena can refer to throughout the lesson. Elena is also described as a shy individual. The use of a partner will counter this shyness and allow Elena to open up and have discussion on the lesson material.
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
12
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
3.c. Explain how your adaptation would be effective for the student in making progress toward English language development. (In your explanation of the adaptation, refer to specific aspects of the student description and to the samples of proficiency in English.)
Elena is an Early Intermediate English language learner. To facilitate English language development, I chose to implement a graphic organizer into the lesson. The Vocabulary and Phrases graphic organizer gives Elena a visual tool she can use throughout the lesson. She will also be able to easily refer back to the vocabulary presented in the lesson plan when needed. The student description of Elena describes her as being shy. Pairing Elena with a partner facilitates communication and conversation, further developing her English language acquisition.
4.a. Which progress monitoring assessment from the outline of plans would you choose to monitor this student’s progress toward achieving the learning goal(s)?
I would observe Elena in her small group and have individual conversation about the lesson content to assess her progress toward achieving the learning goals.
4.b. Give a rationale for your choice of progress monitoring assessment. Use your knowledge of content in this unit, and this student’s English language abilities in your rationale.
Because Elena is an English language learner and typically shy, my observation of her in the small group setting, where she is conversing with other students, would be a good opportunity to assess whether she understands the lesson content and is achieving the desired learning goals. My individual conversation with Elena would also allow me the opportunity to assess her achievement through dialogue with her.
5. Based on what you learned about this student’s English proficiency, what would be your next steps in planning to facilitate her English language development? Consider specific information from the student description and her written and oral language samples when responding.
The next step I would take with Elena’s English language development would be to see whether my recent adaptations made an improvement in her understanding of the material. If I found the adaptations did make facilitate her learning I would further develop these strategies, such as incorporating other types of graphic organizers, such as Cause and Effect Sequences. If I found that my recent adaptations made no noticeable content progress or decreased Elena’s language acquisition, I would incorporate different adaptations to the lesson. These adaptations could include symbolic representations of content, such as pictures and diagrams, or connecting the lesson to Elena’s culture and country to get her interested in the material.
— END OF CASE STUDY 3 —
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
13
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
Case Study 4: Adaptation of Subject-Specific Pedagogy for Students with Special Needs
A. Contextual Information for Case Study 4 1. Elements of a Learning Experience for 3 Days in a Unit Grade: High School Content Area: Mathematics Subject Matter: Probability Time Period for Whole Unit: 3 weeks State-Adopted Academic Content Standards for Students Probability and Statistics 6.0 Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations. 8.0 Students organize and describe distributions of data by using a number of different methods. Learning Goals for Whole Unit Students will be able to do the following • Make connections between mathematics and its applications in the real world • Select and use appropriate tools and technology to analyze and display data • Communicate precisely about given quantities, relationships, and unknown values • Reason mathematically by analyzing evidence and building arguments to or refute hypotheses Relationship to Preceding and Subsequent Learning Experiences Prior to this unit, students have studied the measures of central tendency and how to calculate them. In the future, they will use the skill covered in this unit to solve problems. 2. Outline of Plans for Days 3, 4, and 5 The following outline addresses some of the academic content standards and unit goals, but it is not expected that the students will achieve them during the three days. Instructional Strategies • On Day 3, read a report with text, statistics, and graphical representations about rainfall in California during the last decade (vary between independent silent and oral reading to whole class). Present additional information about the concepts and lead whole-class discussion. Have students respond in writing to teacher-generated questions about the report. Written responses are homework. • On Day 4, read a document that addresses appropriate uses and misuses of measures of central tendency, and effective graphical representation of data for the purpose of critiquing the report read on the previous day. Lead a class discussion about how statistics can present and different perspectives. Give groups of students the same set of data, but different questions. Students must
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
14
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
compute statistics and create graphical representations best suited to respond to their questions. Students write individual rationales ing their selection of statistics and representations. As a group, they present their statistics and representations to the class and receive from others. • On Day 5, have students read an article containing an inappropriate use of statistics to a position. Students discuss the article with a partner. Each student writes a letter to the author indicating the errors in the article and providing arguments for using other statistics to the same position. Student Activities • In class, either read silently or orally the copy of the report, highlighting important issues, and participate in class discussion about statistics presented. For homework, complete written responses in questions. • Listen to arguments critiquing the statistics used in the report, take notes, and participate in class analysis and discussion. Work in a group to analyze data and make graphical representations to respond to a given question. Individual students write rationales. Present with other group the statistics and representations chosen to whole class. Provide to other groups when they present. • Read article and discuss it with a partner. Write a letter to the author. Read a letter written by another classmate and analyze for reasonableness. Progress Monitoring • Teacher will use class discussion, responses to questions, group presentation and letter to author to monitor student progress. • Students will receive written and oral comments from the teacher and other students. 3. Student Description Alex is a 15-year-old boy in the 10 th grade. He had difficulty with the development of his early literacy skills, including the acquisition of sound/symbol relationships and word identification, demonstrated in both his reading and writing. In the second grade, Alex was identified as a student with specific learning disabilities. Since then, Alex has received special education primarily in a resource room for language arts, while he is included in the general education curriculum. He is able to independently read text at a 7 th grade level and continues to struggle with decoding words. Alex also has asthma for which he takes daily medication and occasionally needs to use an inhaler. He is a selfisolating person who does not readily into whole-class conversations or contribute to group learning situations. His tendency is to sit alone at lunch and to be by himself during transitional time. There is no in-class for this student. ______________________________________________
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
15
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
B. Questions for Case Study 4 1.a. Identify one instructional strategy or student activity from the outline of plans that could be challenging for the student, considering the description of the student’s learning disability.
After referring to the student activities and the student’s description, it seems apparent that Alex will have trouble with the oral reading of the report. Assuming the report includes high school level reading, Alex will have difficulty reading the report without the aide of a teacher or partner.
1.b. Explain why the strategy or activity you chose could be challenging for the student, based on specific aspects of the student description.
The oral reading of the report could be challenging to Alex because has not adequately developed his sound/symbol relationships and word identification. He currently reads independently at a 7th grade level. This learning disability makes reading a high school level report that includes text, statistics, and graphical representations much more difficult for Alex. Since there is not in-class for Alex, he will most likely struggle with understanding the report as well as any activities pertaining to the report.
1.c. Describe how you would adapt the strategy or activity you identified to meet the needs of the student.
Since Alex has difficulty reading independently because of his under developed literacy skills, I would adapt the activity to his needs by reviewing the vocabulary presented in the report prior to his reading of it. I would accomplish this with the use of a graphic organizer. The graphic organizer would allow Alex to make connections between the vocabulary presented in the report. It would also serve as a visual resource that Alex could refer to as he reads the report independently.
1.d. Explain how your adaptation would be effective for the student in making progress toward achieving the learning goal(s) of this unit.
This adaptation will help Alex to understand and participate in the reading of the report. Since the report involves real world applications of statistics, Alex will make a connection between these applications and mathematics. Similarly, the graphical representations of rainfall data included in the report will allow Alex to analyze mathematical data. After reading the report, Alex will then be able to communicate to the class the relationship between statistics and its real world applications. This knowledge will give Alex the tools he needs start reasoning mathematically and forming hypothesis.
2.a. Identify one additional instructional strategy or student activity from the outline of plans that could be challenging for the student, considering the student’s other
Considering Alex’s learning needs and lack of literacy skills, the activity requiring the students to individually write rationales will most likely be challenging for the student.
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
16
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
learning needs. 2.b. Explain why the strategy or activity you chose could be challenging for the student, based on specific aspects of the student description.
The individual writing of rationales by the students will most like be a challenge for Alex because of his underdeveloped literacy skills. Requiring the student to write independently will most likely be difficult because he has not yet acquired the proper sound/symbol relationships and word identification needed for this activity. This lack of literacy skills will make writing independently a difficult task for Alex.
2.c. Describe how you would adapt the strategy or activity you identified to meet the needs of the student.
I would adapt this independent writing activity to meet the needs of Alex by turning it into a small group activity. Rather than writing independently, I would have the students discuss their rationales in a small group setting and form one collective opinion. They would then present this collective rationale to the class as a whole. This small group activity will better adapt to the learning needs of Alex, as well as encourage all students to communicate effectively with one another in order to form a common rationale among ach small group.
2.d. Explain how your adaptation would be effective for the student in making progress toward achieving the learning goal(s) of this unit.
The use of small groups would be effective for the student in making progress towards achieving the learning goals of this unit in multiple ways. Having Alex participate in small group discussion instead of independent writing will allow him to develop his skills in reasoning mathematically. The small group discussion will also require Alex to build an argument in of his rationale, while also analyzing and considering other students’ opinions. This activity will also require Alex to communicate mathematically with other student, achieving a learning goal of the unit and developing the student’s social skills.
3.a. What progress monitoring assessment would you choose to obtain evidence of the student’s progress toward a learning goal(s)?
3.b. Give a rationale for your choice of assessment. Use your knowledge of academic content in this unit, and this student’s learning needs in your July 2008
I would use individual conversation with the student see if the vocabulary graphic organizer was aiding him in the reading of the report. I would assess his progress by asking specific questions regarding the report to see if the student had made progress toward the learning goals of the unit. I would also observe Alex during the small group activity to see if he was ing in on the discussion. This observation would allow me to assess his progress and understanding of the material. I would use individual conversation with the student because of his difficulty with reading and writing. This oral assessment would give me a clearer understanding of whether he was acquiring the learning goals of the unit, more so than a written assessment. Similarly, because of the
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
17
CalTPA Subject-Specific Pedagogy Task
ID #000493178
— Single Subject Mathematics —
rationale.
student’s lack of literacy comprehension, I would use observation of him in the small group scenario to assess whether he was meeting the goals of the unit.
— END OF CASE STUDY 4 —
July 2008
Copyright © 2008 by the California Commission on Teacher Credentialing. All rights reserved.
18
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