posted by Sasha Fajerstein

Charlie has been accused of pulling the fire alarm on Friday, 12/5. Help him argue that he is innocent.

The facts:

• The fire alarm was pulled in the student cafeteria at 11:55 am
• Charlie has math period 5 with Ms. Smith
• Charlie was in math class for the ENTIRE period on Friday, 12/5
• 5th period starts at 11:45 and ends at 12:25

Prove Charlie did NOT pull the fire alarm.

The above is an opener that I give my geometry students when we start our unit on proofs. It may seem obvious that Charlie did not pull the fire alarm, but being able to come up with a string of statements that logically prove he did not pull the alarm is the same thinking process as reasoning through a mathematical proof. This type of thinking can be encouraged at a young age, and the more opportunity kids have to think this way, the more open minded they will be as students later on.

Many of you may be nodding your heads reading this because you’ve felt similar frustrations in trying to help your children with their math homework. You’ve thought to yourself “what was wrong with the way I learned how to do this?” But I want you to consider this: “New Math” is another name for “Reform Math” or “Inquiry-Based Math.” Inquiry-based math helps to develop the foundations of characteristics we all hope our future generation will hold. We want our kids to do things thoughtfully, with an emphasis on intent and process.

If you watch the video I linked above, you’ll see what looks like a complicated process for adding the number 96 and 48. In reality, the process is breaking down the following thought process: If I told you to add 96 and 48 without a pen and paper (so no “carrying” allowed!), you’d think “90 + 40 is 130, then I still need to add the 6 and the 8 so that’s 14 more… together that’s 144.” Inquiry based math helps kids develop methods and thought processes to do what many of us do mentally without the language to explain our thought processes. The image below represents the basis of inquiry-based learning – I like this specific image because it gives a short explanation of each of the inquiry steps.

In early math, students are not yet learning things like adding two digit numbers, but setting up a foundation of inquiry based learning and reasoning skills can be done at any time. In my high school math classes, the most successful students are those who are willing to approach a problem they don’t necessarily know how to do at first glance. The next time you are with your child at home, think about doing some of the following:

• Encourage kids to solve problems in multiple ways. Instead of saying “It is too cold to go to the park, so we can either read a story or play a game,” you may want to try saying, “Hmmm, we were going to go to the park, but it’s too cold. What do you think we should do instead?” Oftentimes, as a teacher, I have to remind myself not to fall into the trap of only giving students a few clearly defined choices. While this is a great strategy for classroom management and behavioral expectations, meaningful thinking occurs more often when kids have the opportunity to come up with multiple solutions or conclusions.
• When you are making a decision, try verbalizing your thought process as a model for your children. For example, while at the grocery store getting groceries for a dinner party, you could say “I had planned to make hamburgers for dinner, but Aunt Kelly is coming over for dinner and I just remembered that she doesn’t like hamburgers. I need to think of something that will make everyone happy. I will make lasagna instead.”
• Encourage your children to make hypotheses and conclusions based on observations. If you burn a piece of toast while you are making breakfast, ask them why the toast burned and what you can do differently next time to make sure the toast is not burnt.
• Give your kids “mysteries” to solve. For instance, ask them if they can come up with any ideas on why the music class might have started late or why the car in front of you is moving so slowly.

All of these activities build a strong math foundation in elementary school and beyond. While it may not seem like these activities involve any math, problem solving and the ability to create a chain of logical reasoning are skills that eventually translate to success in classes like Geometry, Calculus, and beyond.

## Sasha Fajerstein

Sasha Fajerstein is a math teacher at New Trier High School in Winnetka, Illinois—one of the highest ranked secondary schools in the nation. This pioneering mathematics educator, who is passionate about integrating new teaching methods and technologies into the classroom, recently collaborated with her colleagues at New Trier to develop and pilot an interactive high school geometry textbook for the iPad. She co-presented a talk about the iPad textbook project at the 2015 Illinois Council of Teachers of Mathematics Conference and also shared her insights into math education as a presenter at the Metropolitan Mathematics Club of Chicago. After earning her B.S. in mathematics from the University of Illinois at Urbana-Champaign, Sasha spent a year teaching English in Costa Rica. Upon returning to the U.S., she served as a math teacher at Nichols Middle School in Evanston, Illinois.

## 2 Replies to ““New Math” and Logical Reasoning”

1. Kathy S Mabus says:

It is easy to find fault with the \”new\” method since most of adults don\’t remember what it was like before we knew how to do mathematics. Taking time to have an elementary student explain the process will help adults understand and build confidence in the student.

2. Marilyn Brasuell says:

I think the opportunities are under-used in early math- and that reasoning in lots of different areas can translate to math reasoning.