Look Who’s Talking

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I’ve been able to check off a few books on my summer reading list.  I’m now in the process of reading one book in particular.  It’s been a slow process through this book, but worthwhile as I’m actually thinking of how this applies to my practice.  That takes time. Yesterday, I was on a reading tear and made it through chapter seven.  This is where I ended up paying most of my attention. The chapter is related to asking questions in the math classroom.

In the eyes of most students, questions are often given to them, not something that they get to ask other students or even the teacher.  The ratio of questions they’re required to answer far outweighs what they ask.  I’m not arguing that there’s something wrong with that ratio, but Tracy and others in this chapter make a case to why educators should allow more opportunities for students to ask, wonder, and notice.  I think there’s value in providing these opportunities, although the management involved in that process seems challenging at times.  While reading, I came across a terrific quote by Christopher.

One of the bigger issues is the last highlighted sentence: “Quit before angering child.”  When I read this I actually laughed out loud and then started to realize how often this happens in the classroom.  Ideally, all students would be willing to make a claim, be receptive to what others have to say and then change their claim accordingly.  Some students are much more willing to engage in this type of math dialogue, while others would rather not.  There are different activities and procedures that can help move students towards being more receptive to asking questions during claim dialogues.  Notice and Wonder, 101questions, problem posing, riffing off problems and independent study options can help students ask more questions and encourage them to be a bit more curious.  That curiosity can spur students to ask more questions.  All of those are great resources, but there’s an important piece that needs to be put in place beforehand.  I believe Scott makes a great point.

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Each child has their own tolerance for struggle.  That struggle can turn into frustration quicker for some more than others.  This happens with children and adults. I think most educators have been in situations where a student makes a claim and then retracts it after its been shown that their response wasn’t quite right.  That student then disengages and it’s challenging to get them to be assertive afterwards.  How can this be avoided or is it possible to avoid these types of situations?  I don’t know the exact answer to this, but understanding the level in which a student can struggle without frustration is important.  Struggle is part of what happens in any math class. That productive struggle is what’s often needed before students construct their own mathematical understanding.

Enabling students with tools and models can help in these struggling situations.  I’ve also seen this struggle occur during whole class guided math conversations. Some students shut down when they are called out by another student.  They think that disagreement means that they’re being challenged or attacked. That’s not the intention, but it may be perceived that way by other students. It may be helpful to model what appropriate math dialogue looks like.  After the modeling, practicing that type of math claim dialogue and providing opportunities for questions can help smooth out the process.

I also believe some students are not used to making a claim in a verbal format.  Students are definitely used to talking.  Ask any teacher.  Also, they’re probably familiar with providing reasons why they agree/disagree on paper, but communicating it in a verbal format can cause some issues. Providing these students with sentence starters, using technology that can be shared with the class, or using other appropriate means can help students engage respectfully in a productive math dialogue.

I’ll be keeping these ideas in mind during my planning process.


Math: In Response to Your Question

I’ve been exploring the use of multiple solution problems in my math classes.  These types of problems often ask students to think critically and explain their mathematical processes thoroughly.  To be honest, these questions can be challenging for elementary students.  Most younger students expect or have been accustomed to finding one right answer throughout their academic career. Unfortunately, state and local standardized assessments often encourage this type of behavior through multiple choice questions.  This type of answer hunting can lead to limited explanations and more of a focus on only one mathematical strategy, therefore emphasizing test-taking strategies.  Encouraging students to hunt for only the answer often becomes a detriment to the learning process over time.  Moving beyond getting the one right answer should be encouraged and modeled.  Bruce Ferrington’s post on quality over quantity displays how the Japanese encourage multiple solutions and strategies to solve problems. This type of instruction seems to delve more into the problem solving properties of mathematics. Using this model, I decided to do something similar with my students.

I gave the following problem to the students:

How do you find the area of the octagon below?  Explain the steps and formulas that you used to solve the problem.

Octagon Problem

At first many students had questions.  The questions started out as procedural direction clarification and then started down the path of a) how much writing is required? b) how many points is this worth? c) how many steps are involved? d) Is there one right answer?  I eventually stopped the class and asked them to explain their method to find the area of the octagon, basically restating the question.  I also mentioned that they could use any of the formulas that we’ve discussed in class.  Still, more questions ensued.  Instead of answering their questions, I decided to propose a question back to them inorder to encourage independent mathematical thinking.  Here are a few of the Q and A’s that  took place:

SQ = Student Question         TA = Teacher Answer

SQ:  Where do I start?

TA:  What formulas have you learned that will help you in this problem?

SQ:  Do I need to solve for x?

TA:  Does the question ask for you to solve for x?

SQ:  Should I split up the octagon into different parts?

TA:  Do you think splitting up the octagon will help you?

SQ:  How do I know if the triangle is a right angle?

TA:  What have we learned about angle properties to help you answer that question?

Eventually, students began to think more about the mathematical process and less about finding an exact answer.  This evolution in problem solving was inspiring.  Students began to ask less questions and explain more of their thinking on paper.  At the end of the math session students were asked to present their answers.  It became apparent that there were multiple methods to solve the problem.  Even more important, students started to understand that their perseverance was contributing to their success.  The answer in itself was not the main goal, but the mathematical thinking was emphasized throughout the process.

Afterwards, students were asked to complete a math journal entry on how they felt about the activity.

Image Credit: Kreeti

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