Sense-making and reasoning in the time of Corona

Here in Illinois, we found out last week that our schools will be closed for the rest of the academic year. With this announcement, many parents and teachers are worried that students will not learn anything new and will fall behind. 

In this blog I would like to encourage all of us to use this time to focus on developing students’ sense-making and reasoning skills rather than adding new content. 

The National Council of Teachers of Mathematics reminds us that  “Reasoning and sense making are closely interrelated and are the foundation for a solid preparation in mathematics. Simply exposing students to mathematical topics is not enough. Nor is it enough for students to know only how to perform mathematical procedures or recall facts. They must learn to reason and make sense of mathematics so that they are able to use math in meaningful ways”

The website has a set of tasks that portray how to facilitate developing sense-making and reasoning skills to teach mathematical content. I have used the Distance formula task – As the crow flies, and watched my students develop a deep understanding of the connections between the Pythagorean Theorem and the distance formula. You can find more tasks here: https://www.nctm.org/Standards-and-Positions/Focus-in-High-School-Mathematics/Reasoning-and-Sense-Making-Task-Library/

All that being said I realize that all of us are in different places right now, in terms of how much math we can do with our children and students, based on how the pandemic has impacted our lives, and so I hope that you take what works and save the rest for later. 

Certainly our last post, Graphs and Covid-19  is great for developing reasoning skills, and I would like to suggest some other resources below. 

By following the discussions on the Youcubed™ Facebook group (Thank you Youcubians™!) I have complied a list of sites that offer students an opportunity to develop reasoning skills through thoughtfully constructed tasks, puzzles, and games. I will start with my personal favorites and go through the list in the weeks to come.

http://www.estimation180.com/ Estimation is a skill that requires reasoning skills for sure. I have always liked this estimation website, and currently they are posting relevant scavenger hunts that need set up by the parents, but can be accomplished by elementary schooled children after they the initial set up. 

https://www.solvemoji.com/ No doubt over the last several weeks those of us who are on social media have participated in challenges broadly called “emoji math” (example below). Multiple objects are set to equal a certain amount, and after a few rows of this we are tasked to figure out what the value of the last row is. These take reasoning and attention to detail, both great skills to develop. In addition, we can encourage students to create their own puzzles and trade with their classmates.  https://solveme.edc.org/mobiles/ may be a good way to introduce the idea of number sentences with symbols as these start off with just two shapes and increase in difficulty. 

http://www.visualpatterns.org/ This site has hundreds of patterns and although the directions ask us to find an equation, we can use these patterns with younger students and ask them to describe how the patterns are growing, which we know is great for reasoning visually. 

http://wodb.ca/ Which One Doesn’t Belong is a site that has sets of shapes, numbers, and graphs, and asks students which piece in the set does not belong. This is a great way to get started with descriptive mathematics. As students grow their reasoning and descriptive skills they can start working on completing the set, where they are given objects and asked to add one to complete a set based on specific characteristics. 

Finally, there is https://www.puzzlesandbrains.com/ which has a lot of puzzles but my favorite are Sudoku and Mathdoku (KenKen for kids). They have a lot of different options for how large and complicated the grid can get. 

Have you used any of these in your classroom? What are you prioritizing in your teaching right now? Let us know in the comments below. 

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Have a question for the authors? Email us at  congruentthoughts@nl.edu or tweet us @ProfessorAleksV and @GeorgeLitman1

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