Math Problem Solving Series #1: Classroom Procedures

If you are like most elementary and upper elementary teachers, you are a generalist. You didn’t major in math. You know that teaching math with a textbook won’t help your students achieve the Problem-Solving standards of the Common Core.

Here are just a few common questions teachers have:

  • How do I get started teaching problem solving?
  • Is there a magic curriculum that will help me help my students?
  • How do I manage students when some can do the whole process in their heads and others need step-by-step guidance?
  • How do I know students are progressing toward the standard?
  • How do I challenge students that find Problem Solving easy?
  • How do I help students and parents understand that there is more to Problem Solving than getting a correct answer?

This series aims to answer those questions and more. Today I’ll address a classroom instructional procedure that has worked for me and others I have coached.

An Opportunity to Understand the Question (5 minutes)

I’ll elaborate on conceptual understanding in my next post. For now, just know that students with low reading levels don’t have a chance of solving the problem if they don’t understand the question.

Make sure that student problem-solving scores are not a reflection of reading comprehension. You want to see their math thinking. Ideally, questions can be posed in videos like those presented by Dan Meyer. As an elementary teacher, you’ll probably have difficulty finding real-life situations that can be easily compiled into video (but please share ideas of videos if you can!).

Read the question aloud. Let students draw. Translate the question into students’ first languages, if necessary. Show them the situation with hand puppets. Let them throw the whole paragraph into Google translate. Students need to be able to state two things:

  1. What I know (my students abbreviate it W.I.K.)
  2. What I need to know (W.I.N.K.)

For language acquisition, ask students to think and write the math vocabulary that might help them get started.

Silent Think Time (5-10 min.)

Students need time to think about the numbers, play with different options, fail, succeed, and/or extend. Give them access to manipulatives such as tiles or chips – anything they need except their neighbor.

During the silent time, focus in on your students who excel at problem-solving. Problem-solving extensions for talented/gifted math students come in the questions you ask.

For example: Last week students needed to make a table of numbers and/or find patterns in order to determine the number of polygon tiles that would be in the 8th row of a sequence. While most students were diligently drawing out the pattern, I rolled my exercise ball next to a student, sat beside her and whispered, “I need for you to predict how many of each kind of polygon will be in the 100th row.” She looked at me, nodded, and went back to work.

My favorite extension questions for Grade 5s, which you can modify for your grade:

  • If you turned that pattern into an equation, what would it look like?
  • I see you have a series of numbers and outcomes. How might you plot those on a line graph?
  • Can you draw me a picture to show why that works? Some may want to use legos or pile up erasers. Whatever they need to do to visually represent their thinking…
  • Is there a more efficient way to get to the answer?
  • What would happen if…?
  • How does this problem relate to what we’ve been doing in our math journals? What vocabulary words seem to fit?

Pair Share (5-10 min.)

Students who have come to an answer need to cover up their answer. Pairs should discuss the strategy or procedure they used. It’s as important that pairs share what didn’t work as what did work.

Pairs can share patterns they found. They can ask each other questions like “How did you get from this part to that?”

Sometimes it’s helpful to have pairs join with another pair for additional sharing.

More Independent Work Time (5 min.)

The next question: “Based on what you heard, what would you add to your work or change?”

Consensus (2 minutes – 2 weeks)

Resist the urge to tell students the correct answer. If you don’t know, don’t look it up. In this last part of the process, students need to come to consensus on the answer. The process goes like this:

  1. Solicit all the answers students have gotten. Write them on the board. Answers only, no explanations. Other students are not allowed to comment on answers. When someone offers and answer, simply say, “Thank you.” Add the answer to the list until all have been covered.
  2. Ask, “Are there any solutions on this list that we can eliminate?” Often, students realize they didn’t answer the actual question. They’ll ask that their answers be removed before others comment. Students verbalize, “I don’t think ___ is reasonable because…” Then ask, “Does everyone agree?” If so, eliminate that answer. If even one person still insists on that answer, leave it on the list.
  3. Continue this process. If students disagree with an answer, they can ask a question, but they cannot disagree without offering a reason or a question. This forces your high students to listen to others and find the logical fallacies. Keep asking, “Does everyone agree?” or “Give a thumbs up/down on whether you agree or disagree. What is holding some of you back?”

Be fully prepared to say, “Well, it looks like we can’t reach consensus today. Take some time to think about the reasons behind your answers. We’ll come back to this tomorrow.”

The Fun

If you leave a problem overnight, you’ll probably have students who will come to you later in the day to explain their thinking or try to cajole you into confirming that their answer is correct. Again, resist the urge to confirm an answer. Have the students anticipate questions the others will ask.

Put the problem on your class blog and let the debate continue.

What procedures do you use to teach Problem Solving?

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photo credit: <a href=”http://www.flickr.com/photos/rbbaird/5073748911/”>rbbaird</a&gt; via <a href=”http://photopin.com”>photopin</a&gt; <a href=”http://creativecommons.org/licenses/by-nc/2.0/”>cc</a&gt;

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13 thoughts on “Math Problem Solving Series #1: Classroom Procedures

  1. hello
    I am verry happy to join your blog , I really appreciate the topics you are developing.
    Actually i am working on PBL in ELT project based learning in english language teaching

    cheers

  2. I like the questions you ask–get students thinking about how exactly they solve a problem. You always have great ideas.

    I also like having students muddle through to a solution without me giving them an answer or hints. Stress is a great motivator. Solutions pop out when they think they must do it themselves.

  3. I have to say this is a *completely* different method than almost anything I remember from my own education, or have seen my own children being taught. You really, honest to goodness, use this in the classroom? Fascinating!

    I would like to emphasize the importance not only of making sure they understand the question even when it’s not in their native language, but also that as quickly as possible they get used to the kind of wording and sentence structures that problems are put in – so that they can learn to do the problems in the target language in the future without always getting them translated. If necessary, drill phrases like, “How many more than” and “a total of” etc.

    In fact, it’s surprisingly nerve-wracking, when your native grammar and word order expresses it in a completely different way, to distinguish between, “How many more apples does Jo have than Bob?” and “How many apples do Jo and Bob have total?”

    Unfamiliar vocabulary, even if not relevant to the problem, makes it even harder to think about the math itself. It slows you down when you have to learn a new word (let’s say “apples”) at the same time – and also figure out that Jo and Bob are people rather than things, in case you aren’t familiar with the names. If you have a lot of ELT students, to avoid these unnecessary distractions I would recommend using only familiar names – perhaps classmates’ names? – for word problems.

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