Orange Lesson: Math: Identifying Student Misconceptions (K-8)

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Orange
LessonMath Identifying Student Misconceptions
(K-8)

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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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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 MapQuestion Framework

• Understanding the childs thinking
• Explore the childs thinking in depth
• Identify instructional next steps to extend the
  childs 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 childs 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
• childs strategy)?
• What is the mathematical concept embedded in this
  strategy?

• Questions to encourage teachers to
  explore the childs 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 childs 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 childs
  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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(No Transcript)
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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

• Teacher presents a demonstration or example.
• Students predict what will occur.
• The teacher conducts the demonstration.
• 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 record answers.
• Discuss by asking students how they predicted,
  what surprised them and
• what inferences they might make about operations
  n gt 1 and when n lt 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/teachinglearn
  ing/curriculuminstruction/math/secondarymathematic
  s/PreAlgebra20Lessons/03-NewPreAlgLessonASept3Ope
  rationsPositiveFractions,Decimals.pdf

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Explain Your Thinking
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(No Transcript)
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Modeling
http//geometrymodule.wikispaces.com/file/view/Mis
conceptions.pdf
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• Different shapes of pentominoes can be used to
  demonstrate that same areas dont imply same
  perimeter. Students see that for the same area,
  perimeter can vary when they investigate by
  checking the perimeters of the pentominoes.
• Using a geoboard and rubber bands, students can
  construct different rectangles of varying
  dimensions but with the same perimeter and
  compare the resulting areas.

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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 possible 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
• 4002-199199

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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 childs 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 childs
  thinking

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Pause and Discuss
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Pause and Discuss

• Read with your table group the authors responses
  from the Questioning Framework handout
  regarding Heidis 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

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

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Homework AssignmentBBSchool_at_commoncoreinstitute.o
rg
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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_Math5ElEd