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I am looking for resources that have tasks such as the one below that encourage argumentation. I want tasks that 8th graders could do but would also be appropriate for high school students. I want to do some kind of research on the mathematical practice "construct viable arguments and critique the reasoning of others". I've seen several good exploration tasks such as this one, but they are all scattered. Are there any good books or resources that include these types of tasks?

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Fendel, D., Resek, D., Alper, L., & Fraser, S. (1996). Interactive mathematics program year 1 - unit 2: The game of pig (p.99). Emeryville, CA: Key Curriculum Press.

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Statistics cases are usually a fertile source of arguments.

Example:

Some believe that laptops in math classrooms help learning. Some believe laptops harm learning.

Task:

  1. Consider your own math classroom, teacher, and final exam and think about the impact that laptops in the classroom would have on your class's average final exam score. Pick a number on a scale from -5 to 5, where -5 means "Laptops definitely decrease that average score" and 5 means "Laptops definitely increase that average score" and 0 means "totally uncertain". Explain your pick.
  2. Then, name the minimum threshold of evidence it would take to make you pick a different number. Explain your threshold.
  3. Compare your answers with others. Make changes to your prior answers as necessary.
  4. [Class discussion and perhaps direct teaching on data collection, design of experiments, statistical inference, net effects and counterfactuals, linear vs non-linear relationships, variance, etc.]
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When I taught high school, a then-colleague of mine developed this great project to be used in a high school geometry class. The project was to be used when students were first learning how to write proofs: in particular, when they were understanding the differences between the givens, the conclusion, the logical steps in between, etc. The students were asked to find an editorial in a newspaper and try to take it apart into given, conclusions, logical steps, etc.

The students were also being taught the two-column format of proof writing and so they were asked to turn the editorial into a two-column proof. Then, when they started writing their own proofs, they could compare the rigor of their proofs to the rigor (and long list of givens) of the editorials.

To really promote discussion and argumentation, you could have the students work in pairs.

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https://www.illustrativemathematics.org/content-standards
Select the grade level and the content standards you are looking for. It lists several open ended questions and lists which standards and mathematical practices it aligns with. It also gives out the solutions with some commentary on how to discuss different parts of the problem, different points of views, common mistakes, etc.

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