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Orange Lesson: Math: Identifying Student Misconceptions- High School School Certification

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Need Help?? For course work submissions and comments, please contact: o BBSchool@commoncoreinstitute.org BBSchool@commoncoreinstitute.org Have questions, please contact: o AskKrystal@commoncoreinstitute.org AskKrystal@commoncoreinstitute.org For technical support, please contact: o support@commoncoreinstitute.org support@commoncoreinstitute.org

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Print Your Learning Journal Page

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Learner Objectives Focus on how students think and reason Uncover students’ strategies, understandings, and misconceptions Learn how students respond to questions the Common Core and College & Career Readiness expect students to answer successfully

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Part I: A Closer Look at Student Misconceptions

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Mistake or Misconception?

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Mistake

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I know 6 ½ = 6 and one half. Therefore: 6 tenths = 6 and a tenth 16 tenths = 16 and a tenth Misconception

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Misconception Question: There are 32 students attending the class canoe trip. They plan to have 3 students in each canoe. How many canoes will they need so that everyone can participate? Answer: 10 R2

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Misconception

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Mistake or Misconception? Mistake The pupil understands an algorithm but there is a computational error due to carelessness. A mistake is normally a one-off phenomenon. Misconception The pupil has misleading ideas or misapplies concepts or algorithms. A misconception is frequently observed.

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When You Watch Determine if the error in the mathematics was a mistake or a misconception.

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Reflection and Collaboration Discuss with your shoulder partner if the mathematical errors were due to mistakes or misconception? What would be your next steps in correcting the errors?

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Conceptual change has to occur for learning to happen.

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Pedagogical Strategies Interactive approaches that entail ongoing teacher-student dialogue Questionnaires/Assessments/Inventories Detailed map of the conceptual terrain of the subject area Savinainen, A., & Scott, P. (2002)

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Mathematical Practices Bill McCullen

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Class Environment

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Representations

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Conceptual Mapping Understanding the child’s thinking Explore the child’s thinking in depth Identify instructional “next steps” to extend the child’s thinking Victoria R. Jacobs & Randolph A. Philipp

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Question Framework How could you solve this problem using two different strategies? How might a child solve this problem? Questions to prepare teachers for understanding the child’s thinking

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Question Framework How did the child solve this problem? Why might the child have done... (insert some specific aspect of the child’s strategy)? What is the mathematical concept embedded in this strategy? Questions to encourage teachers to explore the child’s thinking in depth

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Question Framework What questions could you ask to help the child reflect on the strategy? What questions might encourage the child to consider a more efficient strategy? On the basis of the child’s existing understandings, what problem might you pose next and how might the child solve it? Questions to help teachers identify instructional “next steps” to extend the child’s thinking

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Pedagogical Strategies Interactive approaches that entail ongoing teacher-student dialogue Questionnaires/Assessments/Inventories Detailed map of the conceptual terrain of the subject area Savinainen, A., & Scott, P. (2002)

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Pause and Discuss Write in your journal two points you heard so far that you feel were important for dealing with student misconceptions. Taking turns around the table, discuss your points with the other members of the group. If you are by yourself, ask two other teachers how they deal with student misconceptions in their math classes.

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Part II: Stepping into the Classroom with Student Misconceptions

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Pedagogical Strategies Interactive approaches that entail ongoing teacher-student dialogue Questionnaires/Assessments/Inventories Detailed map of the conceptual terrain of the subject area Savinainen, A., & Scott, P. (2002)

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Conceptual Change Discussion

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REFUTABLE TASK

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Conceptual Change Discussion

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Pause and Discuss Have a copy of “Conceptual Change Discussion” in front of you. Starting with someone in the group, read the first step aloud to the group. Continuing clockwise, each person read the next step aloud to the group. When the group has finished, reflect on the process. Share other forms of this protocol you may use in your classroom. If you are by yourself, brainstorm two ways you could use this in your room. Record thoughts in your journal.

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Predict-Observe-Explain 1)Teacher presents a demonstration or example. 2)Students predict what will occur. 3)The teacher conducts the demonstration 4)The students must explain why their observations conflicted with their predictions.

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Without computing, predict which of these expressions would produce the greatest value? Explain your reasoning. a) 12 − 0.3 b) 12 x 0.3 c) 12 + 0.3 d) 12 ÷ 0.3

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Teacher would compute the answers on a calculator seen on a screen. Students will recorded answers. Discuss by asking students how they predicted, what surprised them and what inferences they might make about operations n > 1 and when n < 1. Ask whether 3 and 12 are compatible numbers (3 is a factor of 12) and review that mental division can be done more easily if the numbers are compatible numbers. To See Full Lesson: http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/m ath/secondarymathematics/PreAlgebra%20Lessons/03- NewPreAlgLessonASept3OperationsPositiveFractions,Decimals.pdf

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Explain Your Thinking

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map.mathshell.org

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y = c + kt Cheng, Ang Keng, Teaching Mathematical Modelling in Singapore Schools,The Mathematics Educator, 2001, Vol. 6, No. 1 MODELING

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Modeling

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Questions during Discussions TEACHER GUIDED: “Why was this possible?...How else?” “Why is the problem here?” “Why did you change your mind?” “How would you do it differently next time?” STUDENT DRIVEN: “This was quite possibly because….Otherwise” “On the one hand….yet on the other….” “In thinking back….” “That might not be true, because….”

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Questioning Framework for Concept Map

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As You Read….. In your journal, respond to the questions on the slide by yourself. With a shoulder partner, discuss your responses. Continue to the next slide and repeat the process. REMEMBER: Answer by yourself first before sharing!

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Question Framework How could you solve this problem using two different strategies? How might a child solve this problem? Problem 4002-199+199 =

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Pause and Discuss

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Question Framework How did Heidi solve this problem? Why might Heidi have done the separate subtraction/addition? What is the mathematics embedded in this strategy?

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Pause and Discuss

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Question Framework What questions could you ask to help the child reflect on the strategy? What questions might encourage the child to consider a more efficient strategy? On the basis of the child’s existing understandings, what problem might you pose next and how might the child solve it? Questions to help teachers identify instructional “next steps” to extend the child’s thinking

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Pause and Discuss

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Read with your table group the authors’ responses from the “Questioning Framework” handout regarding Heidi’s work sample. Discuss the relationship between your responses and the authors’ responses. Discuss the benefits of the Question Framework.

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Knowledge Check List three questions teachers can ask themselves when creating a conceptual map of common student misconceptions.

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Answers:

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Homework Assignments

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Homework Assignment 1.Select a concept that students have misconceptions about in your classroom. 2.Conduct a short pre-test for students to complete involving the concept. Using one student sample, complete the Question Framework. 3.Design a lesson using one strategy discussed in the module for the student or class. 4.After lesson implementation, conduct a post- assessment for the student and/or class. 5.Review the student’s post-work. How did he/she improve from the pre-test? 6.Turn in your pre-test and post-test student sample, along with a reflection of the student’s learning.

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Homework Assignment BBSchool@commoncoreinstitute.org

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THANK YOU!

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Attendance & Evaluation Access the URL below and complete the short survey to record your attendance and provide feedback on this session. https://www.surveymonkey.com/s/OB_Math5HS

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