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WHAT WORKS IN EDUCATION The George Lucas Educational Foundation

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.

This blog is part of a series sponsored by Autodesk.

Comments (14)Sign in or register to postSubscribe to comments via RSS

Cathy Brackett's picture

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.

(1)
Rhonda Lowderback's picture

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?

(1)
Anne Jolly's picture
Anne Jolly
STEM curriculum writer, PLC author, consultant and trainer

Jose, those 5 points work! Not just for math, mind you - but for subjects such as STEM as well. Allowing students to make mistakes - and pointing out that we learn more from what we do wrong than from what we do right - is a real catalyst for learning. I'm going to reference your post in an upcoming STEM blog, and hope teachers take note!

(1)
Monica Burns's picture
Monica Burns
Educator, Consultant, ADE , ClassTechTips.com
Blogger

I love your point "Let the Kids Teach, Too" in math this can be so important! I love using the iPad app ScreenChomp to help students feel like math masters: http://wp.me/p2qsME-6Q

(1)
Debby O.'s picture

I liked this article a lot! Children tend to be scared of learning math because it seems very difficult for them. Thanks for the tips! I will surely incorporate these tips in my classroom!

(1)
Debby O.'s picture

I liked this article a lot! Children tend to be scared of learning math because it seems very difficult for them. Thanks for the tips! I will surely incorporate these tips in my classroom!

(1)
K Moon's picture

Your five principles for your classroom are great reminders for math teachers! It is amazing to me how many of my students say things like, "I hate math," and "I'm just not good at math, but neither is my mother." I, too, try to create a positive environment where mistakes are just the fact of life when working math problems. I am going to take your advice and try to use the word "wrong" less. I also especially liked your idea to answer the students' questions with another question. This sounds like a good way to continue their own thinking processes.

(1)
Maria Duque's picture
Maria Duque
High school math teacher

Thank you for your great ideas, I plan on incorporating them in my teaching practices. I agree with you about creating conditions for success to promote student engagement. I find that when students feel confident about a given task they remain engage. One way that I try to build confidence is by providing tasks that allow students to have access from multiple entry points. Creating tasks that builds from prior knowledge also help students feel confident about what they are learning.

(1)
D. Alfaro-Vasquez's picture
D. Alfaro-Vasquez
Fourth grade teacher in Pacoima, California.

Your reference to Stephen Krashen is what first caught my attention. Yes! Lowering the affective filter is not an idea that I limit to my instruction of English Language Learners. Math is, in fact, a language all its own and it makes sense that we treat it as such. Your five principles were extremely helpful. All principles really resonated with me but the one that I will definitely take into my classroom starting tomorrow is to "Let Kids Teach, Too." Our students have the capability to offer so much to their peers if we only give them a chance. I have found that once a lesson is done and the independent practice has started, the early finishers, once I have checked their work, could be the ones I call upon to peer tutor their classmates. This not only gives them a chance to deepen their own learning by having to help/explain/tutor a peer but it also gives struggling students the opportunity to work in a situation where that affective filter is lowered by dint of working with someone their own age, who has the same or almost the same experience with the subject matter that they do. It's like they're getting a second chance at the assignment...and I am always there to help as well. It seems they find it easier to go to a peer and ask for help than to ask the teacher. I am okay with that, as long as I can monitor what is happening and intervene when I need to. Thanks so much for your ideas!

(1)
Mark Moody's picture

I enjoyed reading your article. I thoroughly agree with your statement, "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, (Vilson, 2012).
You list five very good reasons that allow your students to enter into a safe math classroom. Allowing students to make more mistakes in the classroom was my favorite. I thoroughly agree that we should allow our student to make more mistakes in the classroom. It is the math teacher that needs to instill in their student a different type of critical thinking when solving problems that allows for mistakes and creativity. The students need to feel that if they make a mistake that it is ok for them to correct their mistake and maybe come up with a new method for solving a math problem. As math teachers we know that there is more than one way to solve a problem. I am going to try this method out in my math classes.

(1)
Debby O.'s picture

I liked this article a lot! Children tend to be scared of learning math because it seems very difficult for them. Thanks for the tips! I will surely incorporate these tips in my classroom!

(1)
Debby O.'s picture

I liked this article a lot! Children tend to be scared of learning math because it seems very difficult for them. Thanks for the tips! I will surely incorporate these tips in my classroom!

(1)
Monica Burns's picture
Monica Burns
Educator, Consultant, ADE , ClassTechTips.com
Blogger

I love your point "Let the Kids Teach, Too" in math this can be so important! I love using the iPad app ScreenChomp to help students feel like math masters: http://wp.me/p2qsME-6Q

(1)
Anne Jolly's picture
Anne Jolly
STEM curriculum writer, PLC author, consultant and trainer

Jose, those 5 points work! Not just for math, mind you - but for subjects such as STEM as well. Allowing students to make mistakes - and pointing out that we learn more from what we do wrong than from what we do right - is a real catalyst for learning. I'm going to reference your post in an upcoming STEM blog, and hope teachers take note!

(1)
Rhonda Lowderback's picture

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?

(1)
Cathy Brackett's picture

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.

(1)
Mary Ann Stoll's picture
Mary Ann Stoll
Curriculum developer for K-12

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?

(1)
Dr. Rob Garcia's picture
Dr. Rob Garcia
Former High School Engineering Teacher now Author and EdD

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.

(1)
Denise's picture

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.

(1)

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