How can technology enhance the teaching and learning of mathematics?
“Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people. Teachers can create such mathematical excitement in classrooms, with any task, by asking students for the different ways they see and can solve tasks and by encouraging discussion of different ways of seeing problems.” (Boaler, Mathematical Mindsets, 2015, p 59)
- creates opportunities to explore mathematical ideas in multiple ways
- provides multiple forms of communication and ways to capture and explain learning and thinking
- brings mathematical ideas to life through visual representations
- can foster collaboration and mathematical discourse
- provides access points for equity and diversity
- enables students to dig deeper into complex concepts
Using apps to support communication of mathematical thinking and learning
This article provides suggestions on how to use general apps to help students communicate their mathematical thinking.
Tracy Zager has written a blog post about her criteria for fact-based mathematics apps. In summary:
1. Is there time pressure?
2. Is it conceptual?
3. How are mistakes handled?
Desmos is not just for secondary teachers. Check out this blog post by teacher Annie Forest to help you get started, and get some ideas of how you might use Desmos in your K-5 classroom.
GeoGebra: Dynamic Mathematics for learning and teaching
Geogrebra is a free, online graphing calculator for functions, geometry, algebra, calculus, statistics and 3D math, also available as a free app.
Students find Geogebra less intuitive than Desmos, but the Geogebra platform allows for the creation of sophisticated dynamic models in both two and three dimensions. Geogebra allows teachers to have control over the characteristices and visual features of graphs that can exported into written resources.
Mathematics Visual Tools Apps
The Math Learning Center apps are free and available in iOs, Android and web-based formats. They include "virtual manipulatives" such as geoboards, rekenreks (number racks), pattern blocks and base ten blocks. There are also apps utilizing visual tools such as ten frames, grids and numberlines.
Many teachers in BC are using these apps as a way for students to represent their thinking or solutions to problems and include in screencasts or eportfolios.
Mathies Learning Tools
The Ontario Association for Mathematics Education has developed an app series of mathematics learning tools. The Notepad app provides different backgrounds such as grids or isometric dots for students to record their mathematical thinking. The Money app creates the ability to represent various amounts using realistic images of Canadian coins and bills and annotate. Many other apps are available such as fraction strips, relational rods, linear graphing and numberline.
A support wiki is also available in both English and French.
Mobiles: a visual approach to solving equations.
Who Am I? A series of clues are provided to discover the mystery number.
Mystery Grid: a logic puzzle based on the latin square arrangement (no row or column contains the same number twice)
These puzzles are problems that support number sense, encourage logical reasoning, and help students develop strategies in problem solving. Each puzzle type has multiple levels available for play, as well as the ability to create new puzzles. The creation of puzzles supports a deeper understanding of the logic and mathematics involved, in order to determine what makes a good puzzle.
Osmo is an award-winning game system that creates opportunities for hands-on play with iPad or iPhone devices. Games available that have a mathematical focus include Tangram, Newton, Numbers, Pizza Co. and the Coding family of games.
Many of the games have interactive materials such as number tiles or tangram puzzle pieces that interact with the Reflective Artificial Intelligence technology of the Osmo device.
The games support creative and critical thinking, communication and collaboration.
MEI has released a series of mathematical games, available in the App Store for iPhone and iPad and in the Google Play Store for Android.
Factris is a classic Tetris-style high score numeracy game based on the area model of multiplication.
Sumaze's puzzles involve arithmetic, inequalities, the modulus function, indices, logarithms and primes.
Sumaze 2's puzzles involve fractions, decimals, percentages, primes and digits.
The Sumaze games test your arithmetic and problem-solving skills, moving you through increasingly difficult mazes.
A Bundle of Graphs: six mini games about graphs