For the past 5 years I have been a math coach in the same (mostly) few schools in my district. This has afforded me the opportunity to observe students through the years as they’ve been developing as young mathematicians. Being able to watch students year after year has afforded me opportunities to notice the different paths some kids take over time. For example, go into a grade 8 classroom and really listen to the students as they are talking about their mathematics, observe each student as they are thinking and working… What you might notice is a huge discrepancy between who is doing the talking or sharing and who is not. You’ll see some students eager to participate, actively engaged in sense-making during new learning opportunities, and others who might seem to let others participate and do the majority of the thinking. These observations have got me reflecting on a few questions:

- Why are there such differences between these students?
- What happens throughout the years that cause these differences?
- How can we help create classrooms where all students are engaged in doing important mathematics?

##### The Matthew Effect:

An important piece to this puzzle can be attributed to “the Matthew Effect.” The Matthew Effect was coined to describe the process of cumulative advantage, basically, the rich get richer and the poor get poorer. The idea of the Matthew Effect is that those who start school with a small advantage continue to benefit, while those with a slight disadvantage continue to lose ground. While it might be easy for us as educators to notice the differences between students’ abilities or effort, it is far harder to notice any inequities that our classrooms and schools might be causing. More about this in a minute.

##### A few examples of the Matthew Effect:

Soccer: A group of children join a soccer team for the first time. Each time a child kicks the ball, or strips the ball from someone else, or passes to a teammate, or dribbles with the ball they learn. Those students who start off more comfortable with running and kicking spend more time with the ball in a game. By the end of the season, some students have kicked the ball hundreds of times more than others. While everyone is learning to play soccer, the gap between those comfortable and uncomfortable with controlling the ball in a game widdens.

Reading: Students enter into kindergarten with differing abilities to recognize letters or words, and differing interests in books. Every time a child sounds out a word, or uses a cueing system to read a new or challenging word, or thinks deeply about the messages/story the better they get at reading. Those who start off more comfortable with reading, read more books each having more words. By the end of the year, some students have read thousands of words more than those who started off struggling. While everyone is improving, the gap between those confident with reading, and those who are struggling to learn to read increases.

##### The Matthew Effect in Math

In both of the previous examples, there were two factors that led to inequities:

- The differences in the starting points of each individual
- The differences in opportunities for each individual

For mathematics, the issues can be quite complicated. To think about how the Matthew Effect can be problematic in mathematics learning it’s important for us to consider what early skills in mathematics are and which are predictive of later success.

But while it might be important to know early indicators, it is FAR more important to consider to think about how we are helping all of our students be successful. This is where we need to minimize the Matthew Effect!

So, how does the Matthew Effect happen? Imagine students in a class where the teacher asks a question of the group and those whose hands go up first always get to answer. Students who might need more processing time come to realize that others will get an answer first and might not even attempt to answer questions anymore because they won’t have enough time or believe somebody else will get picked anyway. Imagine a classroom where students are given different assignments based on their readiness. Students that continually get more advanced work come to think of themselves as more advanced while those receiving remedial assignments disengage because they realize they aren’t good at math. Imagine a classroom where every student gets the same page of closed math questions. Some students work independently and complete the tasks easily while others are unsure what to do. Over time those who struggle to work independently realize they can only be successful if they get direct help, they start to immediately raise their hand and expect their teacher to walk them through each question.

In each of these situations, some students are accessing the mathematics themselves while others are receiving a watered down version or are expecting others to do the thinking for them. Over time the gap in experiences is huge!

##### Complexities of teaching

If I provide everyone with the same task, some will struggle to independently be successful while others might find it too easy or repetitive. But if I provide different tasks to different students based on perceived readiness then I’ve also created inequities because I’ve limited students’ access to the mathematics.

If we keep pace of discussions based on the first few hands raising, then we likely haven’t engaged several students because they haven’t had enough time to think. But if we feel like we always need to wait for every student then we likely won’t have a flow of conversation that is ideal.

When determining groupings, if we place students who are currently struggling with students who are quite confident, there is a potential for an inequity in who is doing the work and who is learning. But if we place students who are struggling with other students who are struggling, then there are just as many inequities.

##### Minimizing the Matthew Effect

Teaching is complex! Helping students who disengage or who don’t identify with mathematics is not an easy task. However, we need to consider ways that we can help all of the students in our care to come to appreciate mathematics and believe in themselves as mathematicians.

If there is a practice that benefits those who are already being successful with mathematics more than those who are striving to be successful, then there are inequities at play in our classrooms. Whether the inequities are related to us believing who is capable, or related to who has access to rich learning opportunities, we need to understand and confront our own biases and beliefs for the benefit of all of our students.

As we start to think more about the inequities in our schools/classrooms we will start to see more students who are actively constructing their understanding of important concepts via rich problems and experiences… the interactions among students and between students and teachers will show that every student’s thoughts and ideas are valued… that every student can be successful if given the right experiences and feedback.

**On the other hand, if we don’t believe that ALL students can learn to the highest levels, then our students won’t believe it either!**

For more on these topics, please take a look at:

- Targeted Instruction
- How do we meet the needs of so many unique students in a mixed-ability classroom?
- Differentiated Instruction: comparing 2 subjects

I’d love to continue the conversation. Write a response, or send me a message on Twitter ( @markchubb3 ).

I can’t even begin to express how much I appreciated this post. You have put into words a passion I have had for many years. I work in a variety of classrooms as a math coach as well, but my main focus has been with students who are non-typical learners. By non-typical, I’m referring to students who don’t fit well into our current classroom set up – slow processors, 3-D thinkers (visual/hands-on learners), struggle to connect meaning to 2-D symbols etc. Their struggle is definitely a cycle that becomes self-fulfilling, I see it constantly. I was one of those students growing up, but thankfully I was able to pull myself out of the cycle through a strong conceptual understanding of mathematics in High school. These students like myself often do have strong conceptual abilities but poor memorization skills, which causes them to struggle in a mimicry based classroom. Research is now showing that many of these students brain structure actually has more long-range connections than a “typical” brain structure and less local connections which cause them to be big picture conceptual thinkers that will struggle with the detail, but if all we give them are a details with no big picture, they struggle to find a starting point. Check out Dr. Casanova’s work for more detail or I’ve written about it on my blog at Mathshift.com.

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Thanks for your comment Jennifer. Hopefully we are all becoming aware of the specific-to-mathematics ways we can help our students be successful. Making mathematics visual, paying attention to spatial reasoning… are great ways to help all of our students conceptualize the mathematics we are learning. Hopefully, as a system, we are changing the experiences our students are having as they are learning mathematics and making math class accessible to all, while still offering access to important mathematics to all. Not an easy task, but let’s hope we are making progress.

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yes, I totally agree, in fact, spatial reasoning is what I wrote my thesis on, “Cultivating the growth of mathematical images”.

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Another way this plays out is in small group work. Assume 4 middle schoolers sitting in a group are given a problem to work on. After 30 seconds of reading and thinking about first steps, more confident group members propose solution paths. Right or wrong, the child whose solution path suggestion is explored by the group receives feedback and can adjust their thinking. The others really have no sure evidence that there untried ideas were other mathematically valid ways to approach the problem. And even more troubling, if there was an error in their thinking, they have not been able to expose and explore the misconception at it’s root. And so they become increasing unsure of their own mathematical thinking.

So much learning, whether math or soccer or whatever, is based on trying, receiving feedback, and making adjustments. /Every/ student needs that opportunity.

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Great point, Leanne. I’m going to work on being more aware of that potential. If I need to know what every single student is thinking, I put up a Peardeck question. On one monitor I can watch each student work (names revealed). I can say, “Casey, did you notice that negative sign?” without wasting time running around the room. On the other monitor, I can show the students’ work anonymously for discussion. This blog inspired me to think about Robert Kaplinsky’s blog about honors tracks. I’m wondering if we need to get away from honors math in general: https://lanewalker2013.wordpress.com/2018/01/13/embedding-honors-math-or-any-other-subject-within-regular-high-school-classes/

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I teach intermediate in the English stream of a French immersion school. Although it is a public school, students that seem to struggle academically or behaviourally are urged into the English stream. This dynamic between French and English creates a unique situation in the classroom. Students who have switched from French to English have a preconceived notion about why, many students who didn’t start in French have an attitude of being “just in English.” I find this divide most obvious in Math where it is all too easy to wait for someone else to solve it. Many students do not have the confidence necessary to try something new/ difficult.

One strategy I have started using recently to minimize the “Matthew Effect” is visibly random groupings, thanks @MathManAnusic. I will explain on his behalf, within these random groups they are assigned random jobs. For example: in groups of 4 they number themselves 1-4. I then reveal that 1 is the recorder, 2 is the liaison, 3 the spy and 4 the presenter during a gallery walk or whatever the specific task may need. If a student who would normally sit back and watch others solve the problem winds up being the recorder they are stuck having to put marker to paper. I have found that this method has really changed my group work tasks.

I think the “Matthew Effect” is alive and well in classrooms, especially in Math. I am very interested in finding the line between all those issues you mentioned in your post.

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I’m just about to try the group method you described at a school. It sounds like a great approach to group work. Good on you! I hope mine goes a well as you described.

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This is exactly something I’m struggling with high school geometry students. Some students only take notes and ask questions. When I use a strategy like CPM’s Listening Post, where only two students act as mathematicians, some students can’t do it (no practice) and others are chomping at the bit to offer their ideas. I think it’s helping a bit but so often they lack persistence because they don’t trust their ideas. I’ve shared this article with the rest of the math teachers at our school because I think it’s so important – thank you for raising the issue in such a coherent, organized way. To see it framed as an equity issue helps us really deal with the issue.

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Good stuff! This is why I like to direct questions to students so they know the all get a chance to contribute. If I don’t direct a question to a child and many confident hands go up, I like to pick the ones that haven’t put up their hands first, then go to the confident ones if I have to. Quite often these less confident children can answer the question with a little nudge. The ‘differentiate tasks” is a double-edged sword which can make tasks more accessible, but also can put the children in their cages. It needs to be used carefully. The Matthew Effect exists but can be resolved by how the teachers handle the teaching and learning.

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