Full disclosure: I am just as guilty as anyone of making assumptions! I catch myself and hear it in my colleagues all the time: “my students won’t be able to do that”, “Johnny isn’t able to do this task because he’s way too low”, “this is the best way to teach this concept because it’s what I was taught or because it’s what I’ve always done”, “my students are learning well because they did well on the test”, “the students who are not doing well aren’t doing so because: they’re not trying hard enough, they’re not paying attention, they’re too low, their home life, etc.”.

Several years ago I attended a workshop and the presenter said that as educators we so often commit assumicide. This term stuck with me and I’ve now adopted it and use it (I wish I could credit that presenter but I can’t remember her name). This blog is all about becoming more aware of how we unintentionally commit assumicide in our daily practice and ways to avoid it so that we can evolve as educators AND provide the very best education for our students.

In order to combat our assumptions we need to:

  • Be aware of ‘confirmation bias’
  • Use evidence based practices in our classrooms
  • Gather and effectively use student data

"This evidence helps me to know that this student needs support using multiplicative strategies for all the facts but I don’t need to go back to showing ‘groups of’ because they know this already. "

Confirmation Bias:

Unfortunately, as humans we are hardwired to see what we want in situations, which just makes us more likely to commit assumicide. In the world of psychology this is known as confirmation bias and it means that we seek out evidence that confirms our beliefs and unintentionally ignore evidence that opposes our beliefs.

When it comes to evaluating how we’re teaching math it is easy to focus on how we feel about what we’re doing in the classroom. We often do what is comfortable for US, the teacher. We tend to teach in ways that we were taught and how we believe is the best approach.

Studies on this topic reveal that adults tend to … “Have extensive pragmatic life experiences that tend to structure and limit new learning. Learning focuses largely on transforming or extending the meanings, values, skills, and strategies acquired in previous experience.” (page 27, Making Sense of Adult Learning, Mackeracher). So basically, we are strongly tied to our previous beliefs AND we are often blind to the evidence that flies in the face of our beliefs….is it any wonder why we find changing our practice so darn difficult! Check out this short video on confirmation bias: https://www.youtube.com/watch?v=B_YkdMwEO5U

So, how do we overcome this confirmation bias? Even though this phenomenon is so well documented and so prevalent, I believe knowledge is power. Just by understanding these ideas and being self-reflective, it will help us to start changing our practices in ways that will better equip our students with the math skills they need. After we’ve become aware of the existence of our own ‘confirmation bias’, then we need to seek out unbiased evidence that can inform our teaching.

Let’s Explore the Evidence:

Reading research on educational practices and methods is a great place to start. I know many teachers are too busy to do a lot of this so that’s why I take what I’ve learned from research and my own practice of it and incorporate it into lessons for Educating Now. However, I often encounter teachers who disagree with the research because it doesn’t fit with their beliefs. I’m currently reading “From Principles to Action” written by the NCTM, which is a nice little read because they summarize all of the research articles into actionable daily teaching practices that have been proven to be effective.

I urge you to read some of the research yourself if you are skeptical. The majority of the research I’ve read confirms, “effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.” (page 42, Principles to Actions, NCTM). This is our aim at Educating Now: to help teachers approach math teaching conceptually and then build procedural fluency, not the other way around. Most of the research I’ve read indicates that we need to start with teaching conceptually and then integrate the procedures while still linking to the conceptual. In my own experience I see this as the best way for a number of reasons:

  • Students have little to NO motivation to learn the WHY behind the math if they’ve already been given a procedure or trick to use first
  • Students who are taught the procedure often don’t understand why it works and so often use it incorrectly
  • When we teach procedures first students are given the message that this is the real goal of math – to perform the operations, rather than to actually understand them

Student Data is another form of evidence we can use. We need to be mindful of the assessments we use or how we are gathering the information to avoid bias. This was part of my problem with using VIDMA (from my last blog post). With multiple choice questions, I can’t tell if they are guessing or actually know it and when students leave many questions blank I didn’t know if they were overwhelmed, couldn’t remember, never learned it or simply didn’t care. Let’s take a look at some sample questions and analyze them for usefulness:

Student responses are in red

Example A: Solve the following:

  • 3 x 6 = 18
  • 7 x 8 = 57
  • 11 x 12 = 1212

So from the above here’s what I know:

  • This student knows the answer to 3 x 6 but not to the other two questions.

Here’s what I don’t know:

  • If they know what multiplication means
  • What strategies they used for each problem
  • Where do I begin to help supporting them in learning this concept

Consider this example:

Example B:

  • Show a picture of what 3 x 6 means and solve. Write a problem that would be solved by finding the answer to 3 x 6.

3 x 6 means 6+6+6 so I added 6+6 = 12 and then added 6 more to get 18.

If Sammy has 3 friends and gives them each 6 candies, how many candies does Sammy give to his friends all together

  • Solve 7 x 8 and explain or show your strategy (how did you figure out the answer)

I don’t know how to skip count by 8’s so I counted by 1’s to get to 57

  • Solve 11 x 12 and explain or show your strategy (how did you figure out the answer)

I just know that 11’s are the number you’re timsing by is repeated like: 22, 33, 44, so

11 x 12 is 1212

From these questions, by requiring the strategies and thinking to be included in the response I have so much more information!

Now I know:

  • The student has some understanding of multiplication – that it is repeated addition and ‘groups of’
  • They are using counting strategies (for question 2) and additive strategies (for question 1) rather than multiplicative strategies
  • Also, they have applied a pattern or rule incorrectly for the last question

This evidence helps me to know that this student needs support using multiplicative strategies for all the facts but I don’t need to go back to showing ‘groups of’ because they know this already.

If we want to know students’ level of conceptual understanding we need to ask more than procedural questions. In the past I’ve had students who could tell me that 3 x 6 is 18 because they memorized their facts but their picture looked like this:

showing me that they know the answer but not that 3 x 6 means 3 groups of 6 and their story problem would read: “Sara has 3 candies and Jamie has 6 candies, how many do they have all together” or “The teacher said to multiply 3 and 6, what answer do you get” (yes, really, I get this all the time)

Gathering this evidence from students is so important to moving forward without committing assumicide. So, if you missed the last post check it out – there are 3 free pre-assessments for whole numbers (grade 6,7,8). You will notice that these assessments dig a lot deeper than simply measuring procedural competence.

We’re Here to Help:

This shift from teaching procedurally to teaching conceptually is often misunderstood by teachers because we have not received the proper training or education on what it means and how to actually teach conceptually. Some think it means teaching students step by step how to perform operations, while others think it means giving students blocks and asking them to ‘figure it out’. Without the proper education, it is a really challenging transition for teachers and so is often abandoned. Our goal at Educating Now is to help teachers learn how to teach conceptually in small steps- concept by concept.

Change is hard. When I first learned about teaching conceptually I was filled with shame because I realized I had been UNINTENTIONALLY doing a great disservice to my students by only teaching them rules, steps and tricks. The first step we all need to make as teachers is to recognize when our confirmation bias is happening and recognize when we don’t want to change how we’re teaching math because it doesn’t fit our beliefs. I invite you to examine your beliefs – are they rooted in sound research?

It takes a lot of courage to change and to try new ways and being vulnerable in front of a whole class of kids takes even more courage but it is worth it and I truly believe it is the greatest role modeling we can do for our students. Let’s show our students what life-long learning looks like!