Three-year-old fix-it man Jonathan is pointing to a loose wagon screw that needs his immediate attention. We turn the wagon on its side to take a closer look at the wheel. Yes! We definitely have a loose screw.

“You need a hammer to pound it in?” I ask.

“Yes!” exclaims Jonathan.

I return with a hammer and Jonathan immediately recognizes that I have made a huge mistake. “No, not that one! I need a hammer! Look, it has a line. I need a hammer to fit in there to make it tight.”

This was not Jonathan’s first rodeo. He knew his way around a tool bench, just not by name.

“Oh, let me look again,” I reply.

I return with three tools.  “Jonathan, I have a hammer, a screwdriver and a wrench. Will one of these work?”

Jonathan’s eyes light up.  “Yes, I need a screwdriver!” He jumps with joy and gets straight to work.

My little friend is a math machine. This is logical mathematical thinking!  We have deductive reasoning and problem-solving at a three-year-old pace. Having the vocabulary to explain that he needed a tool that would fit in that “line”  demonstrated that he could imagine the type of tool that he needed.

Early scenarios like this will deepen Jonathan’s understanding of how objects fit together. This is exploring spatial relationships. This is fine-motor skill development, relationship building and spatial reasoning—all at the same time.

Jonathan’s spark of excitement ignites the interest of his friend, Harrison, who joins in. Harrison is also in need of a screwdriver because he has decided that the screws on every bicycle and wagon in the yard need a good tightening.

As Harrison and Jonathan discuss their actions, their understanding of spatial relationships and attributes about shapes, size and measurement deepens. High-quality hands-on experiences like these provide opportunities for children to develop a richer vocabulary as they reason out loud: “My screwdriver isn’t working. No, you need to turn it this way! Look, it’s going down!”

Children learn to understand and use information when they have direct contact with materials. Drawing a line from a hammer to a nail on a worksheet does not give our children the same educational benefits as an actual hands-on learning experience.

When children explore the different ways that they can manipulate materials—by rotating them, cutting them in half or transforming them into different shapes by composing or decomposing them—they are learning how materials relate to one another and the space around them. Working with real tools and materials is critical to fostering children’s understanding of spatial relationships. This is math. This is our foundation.  I think you should check your wagon and see if that left wheel “needs tightening.”  Don’t forget to document and check this off of your list of learning standards! Take your young friends outdoors. The math curriculum? It’s already “pre-loaded” into the activity!

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
• 5^th 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.

“New Math” has developed a pretty bad reputation over the last few years. Do a quick Google search of “new math” and you’ll find countless YouTube videos bashing it, sarcastic Instagram and Twitter posts demonstrating how confusing it is, and blog posts using “new math” to demonstrate how messed up our education system is. In fact, I received an email from a good friend this past school year titled “This is how they’re teaching math now?” with a forward from his son’s second grade teacher. The teacher had attached links to YouTube videos demonstrating how to do problems the way she was teaching them. Here is one of those links: https://www.youtube.com/watch?v=4UexBOa7u8Y At the end of the email, my friend wrote “This could not be any dumber. I showed him the proper way to figure it out.”

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.

Photo source: http://cte.smu.edu.sg/assurance-learning/integrated-design/ibl

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.