Series Engaging Students with "Productive Struggle": Learning from Mistakes: Linear Equations

Math.A.REI.1

Common core State Standards

  • Math:  Math
  • A:  Algebra
  • REI:  Reasoning with Equations and Inequalities
  • 1: 
    Explain each step in solving a simple equation as following from the
    equality of numbers asserted at the previous step, starting from the
    assumption that the original equation has a solution. Construct a
    viable argument to justify a solution method.

Download Common Core State Standards (PDF 1.2 MB)

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Math.Practice.MP2

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP2:  Reason abstractly and quantitatively.


    Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize--to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Download Common Core State Standards (PDF 1.2 MB)

|
Math.Practice.MP3

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP3:  Construct viable arguments and critique the reasoning of others.

    Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

Learning from Mistakes: Linear Equations

Lesson Objective: Work in small groups to analyze student work samples
Grade 8-12 / Math / Equations
Math.A.REI.1 | Math.Practice.MP2 | Math.Practice.MP3

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Discussion and Supporting Materials

Thought starters

  1. What do students learn from collaboratively viewing student work samples?
  2. How would you decide to group the students for this activity?
  3. Why is it important for the groups to have guiding questions for the activity?

13 Comments

  • Private message to Aundrea Gamble

1. What do students learn from collaboratively viewing student work samples?

The students learn how othere students think. Every student learns differently but it also allows the students to become teachers and correct people's mistakes. By giving peer evaluations it helps the students make their own work better.

2. How would you decide to group the students for this activity?

I would group the students in groups of four and put two students who are strong in that area and two students who struggle in that area and have them work collaboratively. 

3. Why is it important for the groups to have guiding questions for the activity?

It is important for the groups to have guiding questions because it helps them process each step through the problem and it also helps with communicating how they would get the answer.

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  • Private message to dawn Amodio-Pagano
Students learn so much from their peers. Sometimes peer understand what the other peer doesn't and knows how to help.
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  • Private message to Jon Beyle
I think peer evaluations uses the evaluation HOT strategy. They are looking at the quality, value and importance of the work based on the established criteria by checking other students' work.
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  • Private message to Jeane Brumley
I think peer evaluations use the evaluation HOT strategy. They are looking at the quality, value & importance of the work based on established criteria by checking other students' work.
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  • Private message to Geraldine Fleming
Evaluating some anonymous person's work took the personal out of the mix and allowed the students to be purely analytical in their critique. They may recognize mistakes they make, like not checking their work, but this will only reinforce that they need to follow the process of generating an answer and then checking the calculations. One aspect of this lesson that I really liked was the students working collaboratively to figure out what the errant student was doing right and what he/she was doing wrong. These analytical skills are key in the workplace.
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