Series: Engaging Students with "Productive Struggle"

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.

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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 referentsâ€”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.

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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.

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

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?
When teaching linear equations, I am sure that we could all predict before we even begin the lesson what the top five common misconceptions will be and yet we are still unable to prevent these from happening completely. This lesson aligns directly with the mathematical practice standard #3 Construct viable arguments and critique the reasoning of others. The discussion that the students were having about the common mistakes was really helping them to reinforce what we will try to tell them as their teacher but it appeared that they actually "heard" it from their peers. Often what I witness as an observer is that it is very challenging for students to find their own mistake yet they are able to quickly find the mistakes of others. This is an important analyzing tool to help them self-assess in the future. I also thought that the guided questions were so important because while the students were taking ownership of the lesson and able to collaborate the teacher was still directing the lesson and the desired learning outcomes. - Jen Abrams
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1). Work samples can help prepare students for homework assignments as well as reviews for quizzes and exams. 2). Students who grasp assignments faster can be paired with students who have a difficult time with assignments. 3). Guiding questions can help students in the process of completing assignments.
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I know that this is besides the point but I love the way the student desks fit into groups!
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liked video
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Love having the students assess each other's work!
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