Logical reasoning outcomes in the Nova Scotia mathematics curriculum involve spatial, numerical and logical reasoning. These are part of the grades 10 to 12 NS mathematics curriculum as well as the WNCP (Western and Northern Canadian Protocol) mathematics curricula.
These outcomes focus on using puzzles and games as a vehicle for learning reasoning skills. Students are asked to determine, explain, and verify strategies for solving a puzzle or playing a game. They are also asked to identify mistakes in a puzzle or errors in a solution strategy.
The NS curriculum guide reminds teachers that, "it is not enough for students to only do the puzzle or play the game. They should be given a variety of opportunities to analyze the puzzles they solve and the games they play. The goal is to develop their problem-solving abilities using a variety of strategies and to be able to apply these skills to other contexts in mathematics."
Games are a great opportunity to build self-confidence and a positive attitude towards mathematics. Games are inherently "low threshold high ceiling tasks". Students start by playing games at a basic level and as they gain experience, they develop more robust strategies for playing and winning. Opportunities to discuss games with other students help them to develop communication, decision making and reasoning skills.
Games and Puzzles in Desmos
During most years, puzzles and games offer an opportunity to change up classroom routines. Social interactions during game play help to build a positive classroom culture. Unfortunately, public health restrictions resulting from the COVID-19 pandemic, have altered many classroom routines. In order to limit close interactions and sharing of manipulatives, many teachers have turned to online puzzles and games.
While there are some great online resources for puzzles and games, many of them don't allow the teacher to observe and interact with students while playing these games. The teacher dashboard in Desmos activities allows teachers to synchronously observe and interact with students. Pacing tools give teachers control over how an activity progresses. Activity screens also allow teachers to include questions asking students to reflect on strategy or to find errors in puzzles. The dashboard can also allow teachers to give written feedback to students on their progress.
Below are some Desmos activities that would accomplish spatial, numerical and logical reasoning outcomes. The choice of which category to place these games is sometimes quite subjective. For example, I think of a Skyscraper puzzle as using both spatial and logical reasoning and could go in either (or both) category. Here is a link to a Desmos collection with the games and puzzles mentioned below.
Spatial Games and Puzzles
Numerical Games and Puzzles
Logical Games and Puzzles
Do you have a favourite Desmos logic puzzle? Please let me know about it so I can add it to my shared collection.
Mathematic at Work 10 - G01 Students will be expected to analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.
Mathematic at Work 11 - N01 Students will be expected to analyze puzzles and games that involve numerical reasoning, using problem-solving strategies.
Mathematics 11 - LR02 Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies
Mathematic at Work 12 - N01 Students will be expected to analyze puzzles and games that involve logical reasoning, using problem-solving strategies.
Mathematics 12 - LR01 Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies.