Real World Math
Curious, inquisitive, scientific explorers. Children are natural learners. In fact they are born mathematicians. And since children are born to learn, it is important that they have freedom to direct their own learning. This is the most effective way in which real, lasting, and meaningful learning can take place. Key areas of the brain that are responsible for executive functioning skills in the prefrontal cortex are activated when children have agency. This includes areas that are responsible for decision making, critical thinking, problem-solving, self-control, planning, organizing, negotiation, and more. Giving children autonomy will empower them and build skills for lasting health and well-being. It builds confidence and provides a sense of stability and control that allows the brain to be open and receptive to new information. This sense of agency is a key factor in one’s willingness and readiness to learn new skills.
With that, I wanted to share some useful ways in which I foster self-directed learning and support my children in all of their interests.
Hands-on Exploratory and Imaginative Play
This is the foundation upon which we learn in our household and that is real world, experiential learning through play. I model and emphasize on a daily basis how we can correlate new concepts and acquire knowledge and skills with real world scenarios through the way in which we use our senses. This allows us to tap into brain and body pathways for deeper, more connected learning. In fact, knowledge that is acquired through hands-on experiences in a playful context is transferred more easily to long term memory.
The more parts of your brain that are activated in learning and play, the more likely it is that you can think critically and retain information. Think about activities that can engage all senses from moving, talking, listening, touching, and manipulating. The brain is primed for creativity, making new connections, synthesis, and other higher order thinking when it feels safe, open, and receptive to engagement, in a multisensory approach which is the mind’s state in play.
Take for example dramatic play. We find ourselves engaged in dramatic play each day where we can count out coins while food shopping, talk about shapes or patterns we find in our dress up clothes, or compare sizes and shapes of blocks as we build. Sometimes we’ll count out loud in a sing-song way as we prepare lunch or clean up toys. Other times we pretend that we are construction workers, architects, or archaeologists who have to classify and sort raw materials like rocks, acorns, or sticks, and use tape measures or rulers to measure materials in preparation for building. This type of exploratory, free, multisensory play allows your children to take control of the learning. This then permits the ability to exercise innate drives to discover, question, invent, and build knowledge and skills in natural, yet powerful ways.
Visuals and Images
Several recent brain studies have shown the power of using visual representations when learning math skills and how they can improve math performance in significant ways. Think about the ways in which you, as an adult, might exercise math skills, contemplate new concepts, and develop ideas. Oftentimes you will use a combination of modalities including auditory, tactile, and visual.
When my children and I practice counting, addition, subtraction, problem solving and the like we will not only use books but also play materials such as blocks, food, tangrams, beading, puzzles, crayons, and toys of all kinds. I also like to have writing tools available for my children to informally explore numbers and math concepts through writing or drawing pictures. Often I will model for them how we can count, compare, measure, sort, etc. using whiteboards and manipulatives. For families guiding students in higher level mathematics a powerful organization called Youcubed can offer additional ideas and support on making math visual. This organization shares a variety of strategies for engaging students in how to use visual representations of math to increase learning.
To differentiate is to meet a child with where they are in their learning journey. You cannot teach a child to add or subtract if they cannot use one-to-one correspondence or conceptualize more than/less than, for example. In addition, it will be nearly impossible for your child to learn to reason, problem solve, argue, or compute if they are not showing the innate desire or interest to practice these skills. Differentiation is knowing what your child currently knows, understanding how they prefer to learn, where their interests lie, and then building upon this knowledge in a way that is specific to their style, goals, and needs. This is closely connected to paying attention to your child, listening to the way in which they talk to themselves and/or those around them, and understanding their current knowledge base and skill set.
Talk It Out
Create math talk throughout the day as much as possible. Productive math conversations can promote mathematical thinking, reasoning, problem solving, and encourage them to participate in their own math discourse. The importance of math talk is that it encourages children to think in terms of math in their everyday lives. It encourages children to think about how problems can be solved using different approaches. And, it fosters conversations about math related concepts in meaningful ways. According to the National Council of Mathematics (NCTM) math talk can be defined as “ways of thinking, talking, and agreeing and disagreeing when engaging in math tasks.”
It might look like something as simple as, “I have five pretzels for my snack and you have six, why do you have more than I do? Can I please have one more so that we can have an equal amount?”
Another way that I use math talk is by expressing reasons behind ways in which we solve problems and then critiquing these reasons out loud with sound arguments. For example, in measuring two objects your child might reason that one is larger than the other so you might ask her to express “what makes you say that.” Or, “what makes you think that?” Sometimes, my children might share with me “Mom, guess what, five plus five is ten!” I would then say, “Really, show me.” Then they can put up their fingers and count. This allows them to talk through their solutions and sometimes, give them opportunities to find mistakes in their thinking.
Another example was when we were at the park and saw swans in the lake. I asked, “I see two swans far away and three swans near to us, how many swans do we see altogether?” What I like to remember in thinking about math talk is that conversation, inquiry, questioning, and particularly, time to stop, look, and listen to your child’s responses can help deepen math reasoning, problem solving, and higher levels of learning.
Stories are the cornerstone of learning, engagement, and reflection in our home. They are also a great tool for teaching math skills! To start, you can find a wide array of colorful, engaging counting books for children as early as infancy.
You can find books that support math skills ranging from problem solving, pattern recognition, numbers, growth mindset, sequencing, telling time, fractions, sorting, shapes, grouping, and more! Some of my favorites have been: The Shopping Basket by John Burningham, The Icky Bug Counting Book by Jerry Pallota, The Grapes of Math by Greg Tang and Harry Briggs, Sir Cumference Series by Cindy Neuschwander and Wayne Geehan, and The Very Hungry Caterpillar by Eric Carle. Some books for tweens or teens might include: A Wrinkle in Time by Madeleine L’Engle or Lawn Boy by Gary Paulsen.
Whichever book you choose, consider ways in which you can connect the story and pictures to a math concept that is most appropriate for your child in a given time. My daughter is recently into the Dinotrux Series by Chris Gall and we’ve been building number sense by talking “more than, less than” so I’ll take the opportunity to use the pictures to ask her “I see 5 Dinotrux’s here on the beach, what if one more Dinotrux joined them, how many would be on the beach then?”
I also use the strategy of inventing my own stories to turn math into a fun, engaging concept using characters and settings that captivate their unique interests and needs. This storytelling can appeal to your child’s innate creativity, curiosity, imagination and emotions so that the math concepts, particularly those that are more abstract, can be meaningful and enjoyable. In addition, it permits a powerful way to deepen the connection between you and your child because storytelling allows for you to make eye contact which sparks a kind of engagement that taps into those human needs of personal connection, security, and belonging.
Feedback has a profound effect on how children come to see themselves in the world that they so eagerly want to learn about. It is not only verbal or written, but also those body and facial cues that they receive from others, or even from themselves. Self feedback requires the ability to be self aware. Practicing self-awareness can help your child learn to think and talk about what they do well or not well, how they want to improve, or how they could have done something differently or better next time. I encourage self reflection by asking the following questions:
“How did that go?”
“What went well?”
“How/what could you have improved?”
This way I can provide them with opportunities to exercise this skill of self reflection and bring greater self-awareness to who they are and who they want to be. In addition, I can model and encourage a growth mindset.
When I provide feedback it is specific and focuses on the process of their learning, not so much on the product. While I like to acknowledge their excitement over a creation or overcoming a challenge, I do not emphasize the result. Instead, I will say things like:
“Wow you worked on that and it shows!”
“I see that was difficult for you but you didn’t give up. You kept going and you did it!”
So, be sure that it is timely, specific, and process oriented. This allows children to believe that they are capable of achieving what they want if they put in the time and effort. They can come to embrace challenges, bounce back from stumbles and continue to look for opportunities to grow and get help when needed.
In the end, when it comes to my budding mathematicians, as with all learning, I let my children be the guide. Their interests, curiosities, and imagination drive the curriculum and when opportunities arise I can make it a point to use some of these strategies to share in their wonderings, ignite deeper inquiry, challenge their thinking, and support them as much as possible in their educational journey.