With the first week of school upon us I wanted to write a blog post on what I consider the most important first step of teaching math effectively; building a math culture in your classroom.
There are many aspects that I consider really important when establishing your math class culture: open mindset, high expectations for all students, curiosity, creativity, communication, perseverance, and understanding. I will discuss each briefly as well as provide examples on how to teach and model each. Building a culture takes time and consistency but it is well worth the time and effort when you consider the payoff in student achievement, confidence, engagement and affinity towards mathematics.
Stanford Researcher Carol Dweck discovered through decades of research an idea that can transform students, no matter what their previous experiences or success have been (or not been): mindset. People can either have a fixed or an open mindset:
“In a fixed mindset, people believe their basic qualities, like their intelligence or talent, are simply fixed traits. They spend their time documenting their intelligence or talent instead of developing them. They also believe that talent alone creates success—without effort. They’re wrong.
In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment. Virtually all great people have had these qualities.” Source: (http://mindsetonline.com/whatisit/about/index.html)
I have been doing a little experiment of my own over the past year around this idea. When I first go into a math class that I am teaching I ask the students to stand up if they believe that some people are just born being bad at math or good at math and that there isn’t really much you can do about it. Usually between half and three quarters of the class stand up (including the adults in the room!). This, as I see it, is the first cultural shift we need to make, especially as educators. We know about neural plasticity and that our brains are capable of growing and changing and we need to teach our students about this idea (at their level). This sets the stage for success for ALL of our students; it tells them that they ARE capable of learning mathematics. Carol Dweck’s book is called ‘Mindset’ and there are some resources on www.youcubed.org that specifically relate mindset to math education.
Setting high expectations for all students is really tricky when we have such diversity in our classrooms. What may be a big leap forward for one student would be considered easy or review for another. Setting high expectations doesn’t mean they all have to rise to the same end point, but rather that they all improve and seek out growth and challenge. Our expectations will differ from one student to the next but all should be striving to engage in their learning and develop their understanding and skills. Students should be involved in setting and evaluating their math learning goals. You can be their partner in ensuring their goals are challenging enough for them and measurable. Students can write some goals during the first week of school and these can be reflected on, changed, rewritten, etc. throughout the year.
Curiosity & Creativity
Curiosity and creativity are habits of mind that really benefit students in mathematics. This may come as a surprise to some of you as math has traditionally been taught very procedurally, with little room for either curiosity or creativity. When students are curious about math concepts, they are far more motivated to learn and therefore far more likely to better understand and retain their learning. One of the reasons why I am not a big proponent of ‘drill and kill’ style worksheets is that many students find them so boring that they disengage and then the likelihood of them retaining the math they are doing on the worksheet is minimal. On the other hand, when students are interested and engaged, their learning is longer lasting and deeper. The difficulty, of course, is finding ways to engage them (that’s what our site is all about!).
Asking students to solve problems in multiple ways or approach problems in multiple ways requires creativity. Following rote procedures and memorizing rules does not require any creativity and in fact stifles it! If we allow our students to be creative in how they approach their learning, again, they are more likely to engage and they are developing far deeper learning when they create a strategy than if they are just reproducing examples. An example of this is using personalized strategies for solving problems or performing computations. I was working with two grade 3 students on addition strategies. One student would essentially pull 5’s out of the numbers and then add the ‘left overs’, while the other student would make 10 and then the ‘left overs’. Each strategy was effective and they were based on what the students saw as the most effective way:
Matias’ method: 6 + 8 = 5 + 5 + 1 + 3 = 14
Daniel’s method: 6 + 8 = 6 + 4 + 4 = 14
It doesn’t matter which method works best for me, but rather allowing them the opportunity to find a strategy that works for them.
Research tells us that students who engage in mathematical discussions achieve higher success, but it also tells us that when left to their own devices, this math talk does not take place. So it is up to you, the teacher, to model and teach them how to participate in math discussions. Here is the link to a short yet informative article on how to teach students how to discuss mathematics in a way that will promote greater understanding and greater achievement:
In this article, there are some guidelines for whole class discussions that can be modeled and put on a poster paper in the room for students to refer to throughout the year. The expectation is that students work on these skills in each math class. “Guidelines for Whole-Class Math-Talk
1. Explain:“This is my solution/strategy…” “I think________is saying that…”
Explain your thinking and show your thinking.
Rephrase what another student has said.
2. Agree with reason: “I agree because…”
Agree with another student and describe your reason for agreeing.
Agree with another student and provide an alternate explanation.
3. Disagree with reason: “I disagree because…”
Disagree with another student and explain or show how your thinking/ solution differs.
4. Buildon: “I would like to build on that idea…”
Build on the thinking of another student through explanation, example, or demonstration.
5. Go beyond: “This makes me think about…” or “Another way to think about this is…”
Extend the ideas of other students by generalizing or linking the idea to another concept.
6. Wait time:
Wait to think about what is being said after someone speaks (try five seconds).”
I am amazed at how many math classes are still structured with all desks in a row and the students silently ‘working’ on math. They are likely practicing procedures, which certainly is important and has its place, but without understanding, practicing procedures can often be a waste of time because students will forget them as soon as they stop practicing (how many times have you taught something and then a week or two later when you refer back to it, the students look blankly at you and claim never to have been taught this skill?). Communication is essential for many students to develop understanding. It is through these discussions that they understand the WHY of mathematics, rather than just focusing on the HOW. I also have found that my students love voicing their ideas. I am careful to pick students who might be struggling learners to share their ideas first, as this gives them a chance to participate and feel successful and then those that have a better understanding can build on or contribute other ideas. I also have them practice math discussions in small groups before we do whole class talks. I suggest incorporating math talk into every single lesson. It is a great way to access prior knowledge (getting the brain ready to learn new material). Structured partner talk is a favourite of mine. I will often have students explain their understanding of an idea, concept, operation, etc. to their partner and then the partner can:
Agree because ____________
Disagree because ________________
Explain their understanding in a different way
For those students who struggle with communication but have a strong conceptual understanding, this task requires them to build on their area of need: communication.
Perseverance is a characteristic of someone who has an open mindset. I see it as a key trait in success in math. I see many students who would rather not try a problem at all rather than be wrong, or that give up if they don’t immediately see the solution. If we want to help our students develop critical thinking and problem solving skills, they need to be risk takers and persevere even when they are frustrated. Through great frustration comes powerful learning! We can teach our students how to deal with their frustration when they ‘get stuck’: take a minute break, take deep breaths, try another way/method, explain to a peer where you are getting stuck and what you don’t understand to see if they can explain it to you in a way that makes sense. Process (how they found the solution and why they did what they did) should be as important as the answer. If we value only the correct answer we are training our students to only solve questions they can do immediately.
Understanding the Math
Finally, understanding the math should be a main goal every day. There is a difference between knowing and understanding. A person may know the fact that 5 x 6 = 30, but may not understand what multiplication means (repeated addition or ‘groups of’) and therefore will be unlikely to know when to apply multiplication to solve problems. We want our students to know and understand the math. When we teach mostly procedurally, we are sending the message that doing the math is most valued. When we teach conceptually, we are sending the message that understanding the math is most valued. I personally don’t really see the point in teaching math without understanding, it’s like teaching someone to read without comprehending what they read, but can just pronounce the words!
Habits of mind and attitudes towards math play a huge role in the success of our students. We inadvertently send messages by the way we teach, for example: being fast at math means you are good at math, getting the right answer is the only goal, following procedures and memorizing facts is all math is about. In order to challenge our students to higher academic success, more confidence, and more affinity towards math, we need to send different messages. Building your math class culture is an explicit way of teaching students that their ideas and voices are valued, that they all have potential for great learning and that understanding mathematics is as important as doing mathematics. It takes time and patience to develop this math culture, but when it happens, you will see why it was all worth it!
Educating Now was created due to teacher requests to have Nikki as their daily math coach. The site has lesson by lesson video tutorials for teachers to help them prep for their next math class and incorporate manipulatives, differentiated tasks, games and specific language into their class. Teachers who use the site can improve student engagement and understanding, in addition to saving prep time, by watching a 10 minute video tutorial and downloading a detailed lesson plan.