Take a moment to think about how we learn language. We start out by listening to parents and family members for the first two years of our life and then we eventually begin to talk. Only after we have learned to listen and verbalize our language are we able to express ourselves in the written form. Math education should be no different but unfortunately it is! Far too often we expect our students to be able to write mathematically without ever having the time to solidify their thinking by listening and verbalizing to others.
If you’re a math teacher ask yourself:
Could your students go a week without writing numerals in math class and still learn?
Could you teach math concepts without ever writing numerals?
The thought of this blows my mind and is fascinating at the same time. The modeling and conversations that would have to take place would far surpass the teaching strategies that are currently employed in elementary schools and beyond for that matter. Now don’t get me wrong, there’s definitely a place for writing in a math class with journals, equations, and expressions…I get that! But far too often the emphasis on the end product is on the written math and not the process (and that saddens me). What if we shifted our instruction away from numerals and focused on the modeling of math and the representation of one’s understanding.
Because of that thought, now I want extend this idea of not using numerals through middle school. We’re not moving cheese…we’re making a whole new brand!!!
By removing numerals from the K-8 classroom the focus shifts from writing and algorithms to modeling and communicating which should be a heart of every math lesson because they scream integration of the 8 Standards for Mathematical Practice. How many times have I tried to explain to a struggling student a concept through the use of numerals? No wonder why they never “get it”!
If I keep pushing and forcing an understanding down their throat I’ll never get in! I feel like the cartoon. As a teacher, I can’t possibly expect my students to develop a conceptually understanding if I can only teach them through the abstractness of numerals. I’m sure this idea makes a lot of people mad and you may say I’m nuts…but could you do it? Could you teach math without numerals? If not, what is it that’s holding you back? Maybe it’s an over-reliance on the abstractness of numerals!
I realize I’m late to the party with this blog, caught it as a share on the Erikson Early Math Twitter feed and read it for the first time. Although I do agree with your statement that we force abstract symbolism down the throat of children before they are cognitively ready, blanket statements of elimination does not meet the needs of children who have abstracted through activity, then figurative knowing so that numerals are abstract ideas that the child can operate on with their available mental structures. The change in our beliefs of how children learn along with knowledge of stages they progress through allows for instruction that can meet the needs of the child.
Cleargrace and mandyadey thanks for the push this week. I was itching to get in and try purposefully teaching without numerals and I’m super excited with how well it went. My goal is to teach one lesson in each grade-band k-2. 3-5, 6-8, 9< ("my goal").
If either of you have tried this please share how it went. I'd love to hear about it!!! All the best!
I’m with cleargrace on this one. I’d like to see some lessons. I teach hs math mainly freshman and sophomores intro to algebra. Would love to see ideas! 🙂
Your comments have my brain going! I believe this is an idea with merit. Have you developed any lessons (or seen any lessons) that put this idea in action?
This is a neat idea. I did think you were nuts when you first brought this up, but the way you describe it in this post makes sense. Model the thinking and talk about the quantities represented by numerals. Focus on the building of concepts, then move forward to build understandings from there. I do have one question , though. When students record their thinking in their journals, how do they label the quantities (the representations of the models they created) in order to revisit the problem later?
Excellent thought-provoking post!
Absolutely…I think the recording piece needs to happen as a summary of the process or the final concrete product. I’m glad you mentioned this Mike because this idea of not using numerals is still in its infancy. I don’t want students to get “lost in the numbers” but it is really important that students record their reasoning with numerals as a summative piece…but only AFTER the perseverance, reasoning, and justification have taken place.