108 ◆ Reasoning About Problems
Key Points
- Students should have many opportunities to do pair and group
reasoning activities. - Students should contextualize problems weekly.
- We must focus on both set-up and solution equations.
- Graphic organizers help scaffold reasoning.
- The 2- and 3-bean salad problems help to practice algebraic
thinking. - Coin puzzles help to practice algebraic thinking.
- Concentration matches get students to focus.
- Venn diagrams help students to reason.
- Table problems help students to see patterns.
- Leg problems help students to reason and see patterns.
- Students should be able to analyze different types of remainder
problems.
Summary
Reasoning problems should be an essential part of your curriculum. Of
course, students are supposed to reason through all types of word prob-
lems, yet the problems in this chapter offer specific types of problems to
organize thinking. Students should practice problem types like these so
that they gain the necessary skills in thinking about problems, organizing
information, discussing them and reflecting on their process. Matrix prob-
lems, Venn diagrams and tables all require that students stop, think logi-
cally and go step by step. As students do this, they become stronger, more
adept thinkers. They learn that they can work through problems that may
at first seem to give a lot of information, but that different types of orga-
nizers help to navigate that information. We need our students to develop
problem-solving skills and to have a repertoire of tools to organize their
thinking. Reasoning problems help students to develop that mental
muscle.
Reflection Questions
- In what ways do you currently perform reasoning problems with
your students? - How often do you ask your students to make up their own word
problems? How do you scaffold this process so that they are
successful?