We are happy to present this guest post about why language matters in math. It is written by James Burnett, co-founder of ORIGO Education, and speaks to the importance of introducing children to mathematical language in stages.
We were recently introduced to Stepping Stones 2.0 which is a program by ORIGO Education that integrates print and digital technology and strives to give educators a flexible and balanced solution to teaching math. In this article, co-founder James Burnett writes about the four-stage progression of math development found in their Stepping Stones 2.0 program, which is used to teach math concepts to students in prekindergarten through sixth grade.
Our beliefs about how children are curious and social creatures, who learn by making connections to prior knowledge, is what hit home with us about this particular article. We are currently looking more deeply into the program and will be writing more about our thoughts in an upcoming post.
If you are a newer teacher, or one who is new to elementary teaching, we truly encourage you to take a few minutes to read this short article by James Burnett. It makes so much sense and is something to keep in mind with any type of math instruction that your district requires or endorses.
When Teaching Math Concepts, Language Matters. Here’s Why!
By James Burnett
I was at a math conference recently, and I couldn’t help but laugh when I saw a T-shirt proudly worn by a young teacher. It simply read, “English is Important, but Math is Importanter.” Yes, math is important(er), but we can only learn math if we have a solid grasp of our own language.
We know from the study of neuroscience that in order to learn a new concept, we must connect the new idea to something we already know. As we talk about the idea among peers or with a teacher, read about the idea, or simply think it through in our minds, language is the tool we use to make the connection.
But when you read equations such as 7 + 3 = 10 (“seven plus three equals 10”) and 7 – 3 = 4 (“seven minus three equals four”), you quickly realize that math has its own language. Unless children already have a solid understanding of the concepts behind these symbols, the words themselves are just abstract notions, devoid of any meaning—and children have no mental model to help them understand these terms.
Children are often introduced to abstract mathematical language far too early. As a result, many children struggle to grasp the meaning behind them. We need to be very deliberate in the language we use to teach math concepts in the early grades, leveraging the words and ideas that children already know during instruction.
This language approach to learning math is grounded in decades of research. In the 1980s, Dr. Calvin Irons—a former math professor at the Queensland University of Technology in Brisbane, Australia—wrote a paper on this topic that was published in the Yearbook by the National Council of Teachers of Mathematics. Dr. Irons and I co-founded ORIGO Education, and our company’s approach follows his four-stage progression in the use of language and discourse to teach math concepts to students in prekindergarten through sixth grade.
Very young children might not understand what words like “subtract” or “minus” mean, but they do know words that suggest or imply subtraction. For example, “I lost my toys.” “I ate the cupcakes.” “I broke an egg.” “I spent the money.” “The birds have flown away.” “The frog jumped away.”
In the first stage of math development, which we call the student language stage, we use stories to stimulate discussion in the classroom. The stories use these kinds of expressions that children are already comfortable with to help them understand the concept of starting with a certain number of items and then taking some away.
In stage two, the materials language stage, we use hands-on, concrete resources that children can touch and manipulate to further develop their understanding. Typically, the teacher might ask a question such as: “If there are five frogs on a log, and two jump off, how many are left?” The children would act out this scenario using counters, which helps them visualize the problem.
During this stage, the students are learning to associate the concept of subtraction with a finite total or difference. But at this stage, the language greatly narrows from all that is available in the previous stage. Suddenly, the student can’t “eat” the blocks or counters. Just as they can’t easily lose, break, or spend them. And they can’t run away, fly away, or jump away, either. With concrete materials, the language is reduced to take away or cover up. Similarly, with 2D drawings, we can only erase them or they can be crossed out.
The third stage, the mathematical language stage, is where we introduce more precision with our language of math. Instead of saying “hop away” or “take away,” teachers would start using words like “subtract” or “minus,” while continuing to demonstrate this concept with the counters.
The final stage is the symbolic language stage. In this stage, teachers would introduce the subtraction symbol (–) as an abbreviation for all the words they have used before. If students are raced too fast to the symbolic language stage, there is a risk they have not had sufficient opportunities to build the required connections to deeply understand the meaning of subtraction.
ORIGO’s Stepping Stones program is based on this four-stage approach. One of our core beliefs is that learning is a social process requiring language and discourse. In our materials, we use many opportunities to create classroom discussion. This is reflected in the kinds of questioning strategies we encourage teachers to use. Our curriculum provides examples of open-ended questions that facilitate conversation, as opposed to closed questions where the answer is simply “yes” or “no” or results in a specific number.
This language-driven approach aligns well with contemporary standards in mathematics, which are intended to promote a deeper understanding of concepts. Research supports the fact that you can’t have this kind of deep understanding without discourse, and that’s exactly what our curriculum encourages.
We have always known that if this approach is followed with fidelity, success will follow. The Magnolia Independent School District in Texas is just one of many districts that have shown a commitment to real change. They have been using our program for nearly five years and have achieved incredible success. Yes, students are now passing the state test, but there have been other significant benefits as well. Suddenly, math is the favorite subject for many students, who don’t want to stop learning at the end of the math “time.” Teachers, meanwhile, have been quoted as saying they now love teaching math more than ever before.
These kinds of feel-good stories are why we founded the company: We knew there was a better way to teach and learn math. By being very intentional with the use of our language and by carefully leveraging the words and ideas that children already know, we can set them up for a lifetime of math success.
James Burnett is the co-founder and president of ORIGO Education. Over the past two decades, he has authored or co-authored more than 300 mathematics resources for teachers and students ages 5 to 12 and regularly speaks to audiences across Australia and North America.
Let us know your thoughts on this article in the comments below and stay tuned to our site to learn more about ORIGO Education’s Stepping Stones 2.0 in the next few weeks.