Tips for Problem-Solving

Tips for Problem-Solving in Mathematics

From Hands-On Problem Solving: A Minds-On Approach
By Jennifer Lawsonhops_collage

For grades 1–4
Coming Soon for grades 5–6

Problem solving is central to learning mathematics. By learning to solve problems and by learning through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding. Problem solving forms the basis of effective mathematics programs and should be the mainstay of mathematical instruction.
—The Ontario Curriculum, Grades 1–8: Mathematics

Although students may have a good understanding of mathematical concepts, they can still have difficulty applying their knowledge in problem-solving activities. They may not view problem solving positively and may not have internalized a model that can guide them through the process. In order to change this perception and help students solve problems, Hands-On Problem Solving includes an effective four-step problem-solving model—think, talk, solve, and share.

HOPS_4steps

FOCUSING ON STEP 2: TALK

The process of communication is an essential element of mathematics. Once students have been presented with a problem and provided time to think (step 1) about it, the next step is to have them share their ideas, as teachers probe their thinking with critical questions.

Encouraging students to ask questions is a critical component of the “Talk” step. Engage students in such dialogue by regularly asking them:

  • What questions do you have about the problem?
  • Is there a question you would like to ask me (the teacher) or your classmates?

The talking stage of the problem-solving process is also a time to have students do the following:

Identify important information in the problem.
Encourage students to point out any essential facts in a word problem. Have students use highlighters to mark this information or use coloured pencils to circle important words when working on a problem. For example, in the following problem, important information is shown in bold text. You may wish to discuss why it is not necessary to consider the 5 days in this problem and for whom the soup cans are being collected.

Jinan and Tegan are collecting cans of soup for a local soup kitchen. They collect soup cans for 5 days. Jinan collects 13 cans of soup, and Tegan collects 9 cans. How many cans of soup do they donate to the soup kitchen?

Identify unimportant or extraneous information in the problem.
Many problems present information that is not required to solve a problem. This kind of information can distract students from focusing on essential information and can therefore influence their success in solving the problem (via jonathan at www.dresshead.com). It is important for students to identify the information that can be considered non-essential to the problem-solving task at hand. Have students use a pencil to underline the unimportant information when working on a problem. For example, using the same problem as above, the non-essential information is underlined. The non-essential text sets the context, but is not vital to solving the problem. Neither the 5 days nor the soup kitchen are important since the total number of cans collected has been identified.

Jinan and Tegan are collecting cans of soup for a local soup kitchen. They collect soup cans for 5 days. Jinan collects 13 cans of soup, and Tegan collects 9 cans. How many cans of soup do they donate to the soup kitchen?

Name the answer.
It is important for students to be able to identify and articulate what it is they are attempting to find out. For example, if asked to name the answer for the preceding problem, the response should be “cans of soup.”

Share possible strategies.
Encourage students to talk about various ways to approach a problem, including the use of manipulatives, pictures, symbols, and calculators, as well as any personal strategies they have. This is a time and place to encourage risk-taking and the sharing of new ideas!

During the “Talk” stage of the problem-solving process, it is important that students discuss only the process and strategies—not share possible solutions to the problem.

It can also be beneficial for teachers to engage students in talk during the problem-solving process. For example, students may be asked or told:

  • What do you notice?
  • Are there any challenges that we need to discuss?
  • Take a walk about, and discuss your work with other students. Ask questions of each other.

This process helps to build a community of learners.

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