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 (17)
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Your reference to Stephen
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!
Conditions for success
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.
Great points!
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.
I liked this article a lot!
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!
I liked this article a lot!
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!
I love your point "Let the
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
Rhonda I like your
Rhonda I like your perspective, that should be that way educators must think. You know what I hate most: those educators like my colleagues here, when I try to collaborate with them, they would say, "Oh I cannot do it because I am a math specialist" I'm just wondering, I just thinking of the two things here; 1 is he might just lazy to do integration or interdisciplinary or he doesn't know anything about interdisciplinary. But this kind of people should not be in the education sector if I can say it that way.
Job Dependent is unsustainable
Rob you have a very good perspective but it seems like unidirectional; what am I looking now is how education encourage to be self sufficient not to be dependent, because the way I look at the world scenario now is like this; everytime they lose their job, they complain and rally, protest and do unnecessary things it seems to them that's already the end of the world. Can we try to calibrate (since we are talking about math) degrees of inclination so that we can have a good hit with our bullet (education). That instead dependent to what the economy can offer for job, what they can do to generate alternatives to survive. I think that's very critical now a days since world economy seems cannot recover anymore to the 2000 level.
Those points work!
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!
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.