The last month has seen a plethora of discussions about the necessity for teaching math beyond what most jobs consider necessary. Much of it started from Andrew Hacker's now infamous article on whether math is necessary, to which a bunch of us replied with equal fervor (Dan Willingham's and Sherman Dorn's pieces are great rejoinders). What we all seem to agree on is that, indeed, the way we teach math matters. Lots. Having a positive environment for kids where they feel like they can actually *do math* without feeling like they're complete failures matters a lot.

Often, that starts with us as teachers.

Developing an environment where students can experiment and gain entry into the language of math starts with having a person who can facilitate what Stephen Krashen termed a low affective filter environment. While his study was applied to English Language Learners, his hypotheses should apply to all subject areas, math highest among them.

In my classroom, I have five principles for assuring that all students can enter into the math, and also for creating the conditions for math success.

## 1) Allow More Mistakes

I would suggest this to just about every teacher, but specifically math teachers, especially those of us who use the word "wrong" a lot. We should strike a balance between using direct instruction and exploration, leaning more on the exploration piece. Once we allow more mistakes, we let students into the process that our earliest mathematicians used in developing the axioms we believe today. Also, by admitting that we all make mistakes, it sends a clear signal to kids that they can be mathematicians, too. Surely, I'm not suggesting that we let the mistakes be. Yet, when I make a mistake on the board (intentionally or otherwise), I hope my students catch onto that, thus putting them in the position of expert. Speaking of which . . .

## 2) Support Their Struggle

At first, most of us get nervous when children struggle with mathematics, as if they need to get the math as soon as they receive the instruction. Even if it might look simple to us, the students may still be grappling with the skills, the concepts or both. That's OK. When students struggle with the material, they learn how to work problems out on their own as self-motivated workers. Of course, that also means the teacher needs to encourage them as often as possible to do so. If students think their efforts have no merit, then they often won't own it. In an environment where teachers support students' working through a problem, a teacher can tell when a student has quit. You have an option before you intervene . . .

## 3) Let the Kids Teach, Too

During the class period, I prefer the students speak more than I do. If I'm talking too much, that means I'm using too much of my speaking quota. In other words, they'll tune me out if I'm talking too much. Once I let the students speak (meaning, not just one student, but many), they take even more ownership of the math taught to them. This especially proves true during the class work time as well. Having them explain to each other (with the proper guidance) really empowers them to own the material and develop their own process for checking answers. Plus, I’m not exceeding my speaking quota. However . . .

## 4) Answer a Question with More Questions

If, in fact, a student asks us a question, we ought to validate their question by giving them another question. That way, we ensure that the onus for the "answer" falls on them. The type of questions we ask and the way we frame questions matters here, too. Questions that generate a "yes" or "no" answer simply won't do. Instead, we can leave them with a question that they can answer. I do emphasize the word "leave" because it's always good for you to walk away without explicitly telling them they were right. By the time you leave, they should already know this.

## 5) Personalize the Questions

Inserting children's names into the problems (appropriately) engages students in the material. As you start the problem, speaking about the student in the third person immediately gets him or her engaged, and gives the other students a window into the problem. Knowing the person in the problem (even if the situation itself is hypothetical) gives the entire class a sense of ownership and belonging within the math. Obviously, teachers should spread the wealth in naming people, because it may look like we're playing favorites or just focusing on the "struggling" children. All children need access to the math.

This advice obviously takes time and a teacher's willingness to fail. This also might push some of my colleagues out of a comfort zone. Yet we as teachers have to set a precedent for the success of lifelong learners, not just until a standardized test comes. One of the ways we set our students up for this type of success is by providing conditions for questioning, experimentation and ownership to happen. Those of us who only want to "skill and drill" students perpetuate attitudes that Hacker alluded to in his piece.

Math literacy matters. Let's do our part.

## Comments (18)

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## Free Book to Help with Math

Rhonda, great post. I wrote a book for teens and devoted an entire chapter on Math that talks about developing habits, the better jobs that a student can get, and how math comprehension can lead to much higher paychecks. I am GIVING this E-book away to all Edutopia readers that ask for it by emailing me at robleegarcia@yahoo.com, I have already gotten requests from around the world and the reviews have been good. The preview can be found by typing in Teen Juggernaut at lulu.com. Thanks. Great analogy with learning a language being similar to math.

## The language of math = relevance

As a college math teacher I find most students that get to me are already so afraid of math that they won't and can't focus on it. In my opinion, children need to understand two things:

1. Math is another language. As with learning English or French, the same effort must be made to understand the "language of math". In the long run children need to be able to think mathematically as they would think in French.

2. Math only makes sense if it is relevant. I work with students all the time who ask the age old question "why do I need to learn this"?. I think, with anything, math must be relevant. Sure we can all say that people will need to paint a wall, so therefore they need to know area. But how often do they actually use this information. Instead, I tell students math is relevant because of the thinking that occurs in math. They will likely never have to solve a system of equations, but they will often have to use logic to solve daily problems. It is this logic that is learned and that is then the language of math. Demonstrating situations where logic is used to make decisions teaches the students that math can be relevant to every decision they make.

Thoughts?

## Visualizing

I might be able to help you out a little, here, Mary Ann. In my English classes, allowing more mistakes meant that I explicitly told students that I wanted to hear all ideas in response to a question. That is, I didn't say or signal that an answer was "right" or "wrong".

It's a game we play as teachers, that "Teacher Answer" game. The possibilities stop after the teacher gets the answer he/she wants. Allowing more mistakes means we let the conversation go on a little bit longer and let students determine whether they want to "change" their thinking or not.

A lot of it has to do with how we establish the environment. Is it an environment where there are clearly "right" and clearly "wrong" answers when students are working through something new? The discovery process hinges on mistakes!

Another way I got students to take more risks and to make mistakes was to say, "Tell me what it is not, or tell me something that you know is invalid." (For example, Hamlet was a happy go-lucky kind of guy.) Thus, helping them understand that mistakes are desirable also changes the way they approach their learning.

Hope this helps you visualize a little!

Best,

Mindy

## Great advice. As a first

Great advice. As a first grade teacher I know the importance of children experimenting with numbers and making tons of mistakes in the process. I don't believe in children just parroting the steps in a problem without a true understanding of what that means. To get there involves all the points you made above and a few more such as allowing children to choose concrete manipulatives to illustrate their problems.

My fear is that we, as early childhood teachers, are being stripped of our ability to offer such expereinces to children. As class sizes increase and districts' demands for more testing in the lower grades increase, the pressure to have children be able to just bubble in an answer without exploration threatens a true understanding of mathematical relationships. I currently have 40 (yes, FORTY) first graders in my class. What this means for math instruction is less time to use concrete materials, both due to supply and classroom management. It also means less time for me to sit with students who aren't getting it and help them experiment with different solutions to a problem. I am becoming increasingly frustrated and I'm afraid that my own demeanor will adversely impact their experience with the subject.

The impact of over sized classes in early grades will be felt across this nation in a few years when even MORE students are not performing at grade level on standardized tests. Will that lead to a reversal in policies. Maybe. But by then it may be too late for today's students.

## What does it look like?

This all sounds very exciting and promising to me. Now I want to know, what does "allowing more mistakes" look like? Can you describe a scenario or tell a story in which mistakes are allowed so that I can see myself doing it?

## Free Anti Bullying book

Jose, great article. For the month of October, I am giving my book Teen Juggernaut away FREE to anyone that emails me at robleegarcia@yahoo.com and asks for it. Its in conjunction with Anti Bullying Month but the book has a significant math section as well that breaks down WHY students need to learn math, and how it can turn into a high paying career. I talked about the highest paying jobs right out of college and the relationship between math and getting into these fields. There is also a chapter on better studying habits and developing strategies for tackling math. If you or any Edutopia readers are interested in my book, email me and Ill send it out immediately. Thanks,

Rob.

## Reduce math anxiety by allowing learning

Reading and English teachers have known for a long time that correcting every error while a child learns to read and write only causes frustration and anxiety. More math teachers need to recognize that the same principle applies in math. I agree with you comments regarding allowing errors as a part of the learning process. We need to focus on the important concepts of the lesson and not fret so much that there may be unrelated errors. Perfection comes with practice.

## Cambourne's Conditions of Learning

This is a nice list and connects well with Cambourne's research on language acquisition and learning. I wrote about it here: http://deltascape.blogspot.com/2012/09/what-are-conditions-of-learning.html