“i’mconfused”:supporng studentswhostruggle% · focusofsession(thissessionfocuseson...
TRANSCRIPT
“I’m Confused”: Suppor3ng Students Who Struggle
Barbara Dougherty University of Missouri
Reflec%ng on the Classroom
When you think about learners who struggle, what do you believe are their. . . • Biggest challenges? • Greatest strengths?
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Focus of Session
This session focuses on ways to support students who struggle in Tiers 1 and 2 to become: • Confident in
mathema%cs • Successful with rigorous
mathema%cs • Capable of working with
complex mathema%cal ideas
~15%
~5%
3-Tiered Support Model
≈ 80%
≈ 15%
≈ 5%
How do your students think about mathema%cs?
Structuring Informa%on
Compared to students who are not struggling, their brains might look different!
Skemp, R. (1987). The psychology of learning mathema3cs, The Penguin Press..
Struggling Students in Mathema%cs
Students who struggle with mathema%cs oSen – use procedures that younger, typically achieving students use;
– make frequent errors when execu%ng procedures; and – have a poor understanding of concepts that are founda%onal to performing procedures (Geary, 2004).
Addi%onally, they. . . – do not see mathema%cal ideas connected – have developed a high dependency on help – exhibit a ‘give up’ a[tude
How can we help them?
We need to consider the type of mathema%cs and the way in which we teach the mathema%cs.
Making Cents
• Take out some coins. • Mul%ply the value of the coins in cents by 4. • Add 10 to the product. • Mul%ply your answer by 25. • Add 115 to your answer. • Add your age in years. • Subtract the number of days in a normal year.
Making Cents
• What do you no%ce about your answers? • How can you describe what you no%ce to someone who is not present?
Types of Understandings
Procedural -‐ Student can perform a computa%on or algorithm by following a series of prescribed steps
Conceptual -‐ Student understands the basis of why a computa%on or algorithm works. They can apply it later without reteaching. Student can iden%fy, describe, and explain a big idea related to a topic or a class of problems
Problem solving -‐ Student can solve a problem when there is no specific solu%on pathway or algorithm
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Procedures without understanding
• Students memorize steps (and are oSen required to complete the steps in a specific sequence)
• Students prac%ce a large number of problems using those steps
How does your work compare?
How did she do the work?
I don’t really get the way the way my 5th grade teacher showed me. I made it look like her work so I wouldn’t get any points off. So I think, what plus 3/8 is 1? That’s 5/8. I have 1, so I add it to 7 and that is 8. 16 minus 8 is 8 so the answer is 8 5/8.
Knowing how students think is important
How do you think students will solve this problem?
How would you like students to solve this problem?
0.75 of students tried to solve for g
What would show strong understanding?
If g – 227 = 543, what does g – 230 equal? Show your THINKING. Since 230 is 3 more than 227, the difference will be less than 543. The difference is 540.
Begin with a conceptual focus on variable
Problems like: – Zany Z – Perimeter problems like the hexagon problem Use problems where the variable represents a physical rela%onship Use mul%ple representa%ons: words, physical materials, drawings/diagrams, symbols, graphs CONCURRENTLY
Use mul%ple contexts
• Use a number line to model generalized rela%onships
Think in generalized terms
• Give tasks that require students to think about rela%onships rather than algorithms
Joe said, “b + 4 is less than 6 + b.” Do you think Joe’s statement is always true, some%mes true, or never true? Explain how you know.
Example based teaching
• Here’s how you. . . . . . .
• Now you solve these.
• I do • We do • You do
Example-‐based teaching requires students who are struggling to make generaliza%ons about the structure of the class of problems.
What is explicit instruc%on?
• It is NOT direct instruc%on.
– Direct instruc%on is the teacher showing students how to do something or giving factual informa%on.
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What is explicit instruc%on?
• Focusing students aoen%on on par%cular structures or ideas – Asking ques%ons so that students ‘see’ the mathema%cs
– Providing tasks that allow students to explore the topic
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What does it look like?
• Teacher introduces a problem that links to previous learning.
• Students work in pairs or small groups to solve. • Students share their thinking with the class, cri%qued by others and teacher.
• Teacher scaffolds tasks based on misconcep%ons that are evident in thinking.
• Teacher poses ques%ons throughout that focus students on important ideas and generaliza%ons.
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Explicit Instruc%on
• Try to elicit the informa%on from students (see Never Say Anything a Kid Can Say, Mathema3cs Teaching in the Middle School)
• Developing Concepts and Generaliza%ons to Build Algebraic Thinking: The Reflec%vity, Flexibility, and Generaliza%on Approach
Dougherty, Bryant, Bryant, Darrough, & Pfannens%el, Interven3on in School and Clinic, April 2015. (Sage Publica%ons)
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Food for Thought
• Cri%cal thinking ques%ons should be asked in every class, every day
• Consistency helps students understand the expecta%ons and move toward higher proficiency
Can I be excused? My brain is full.
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Closing the Gap
• Changing the way tasks are posed • Crea%ng high expecta%ons and accountability
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Curriculum materials
• When the materials break skills down into small pieces, it requires students to put the pieces together to form the whole.
Ques%oning Techniques
• Factual ques%ons comprise the majority of ques%ons asked in a mathema%cs class – More than 145 ques%ons in 48 minute class period
– Less than 2 seconds for response
Dougherty & Foegen, 2010
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Curriculum materials
• When students prac%ce only a skill it places a large cogni%ve demand on their memory.
Tradi%onal Tasks
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Reversibility question:
– Find 2 fractions whose quotient is
– Find another pair – Find 3 more pairs
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Change the Task
Generalization question:
– What do you notice about the quotient when you divide a fraction greater than 1 by a fraction that is less than 1/2? Why?
– What do you notice about the quotient when you divide a fraction less than ½ by a fraction that is greater than 1? Why?
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Change the Task
Flexibility question:
– Divide using 2 different methods. – How are the ways you
divided them alike? – How are they different?
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Change the Task
Flexibility question
Divide:
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Change the Task
You try one!
How could you change the ques%on you ask:
Find 30% of $16.
Strategies
• Teaching approaches that focus on student communica3on, ac3ve engagement in problem solving
Trends from Data
• Skills are broken down into very small pieces • Heavier focus on algorithms and procedures • Requirement to show all steps • Explana%ons are oSen mathema%cal steps rather than thinking process
• Vocabulary not consistent • Teacher content knowledge
ShiSs in teaching and learning Moving away from . . . To. . . Telling/showing how to do something
Building from concept to skill
Teacher-‐centric instruc%on Student-‐centered instruc%on Problem solving intermioently Problem solving every day A focus on only the answer A focus on jus%fying and
explaining Showing the steps Explaining the reasoning Problems that require only fast calcula%ons
Problems that require thinking
Pre-‐Conference
• Strategies for Students who Struggle in Grades 3–8
NCTM Regional Mee%ng, Atlan%c City October 21, 2015
Resources
• Recommenda%ons are based on strong and moderate levels of evidence resul%ng from comprehensive reviews of current research literature.
hop://ies. ed.gov/ncee/wwc/publica%ons/prac%ceguides/