Q & A with Mathematics Expert, Marlo Shumway
At PowerPlus Tutoring, there is a large demand for math tutors - far exceeding that for any other subject. In light of such a high demand, we wondered why so many students were struggling in math. What was causing the deficiencies in math education?
In my experience working with students at all grade levels, I am continually surprised to see how underdeveloped their number sense is. The majority of these students found 'mathematical thinking' to be a foreign concept.
The focus on quantity (how many concepts are being covered) versus quality (how well a child understands the concepts) is the new normal for schools. In fact, some students are now being encouraged to skip math levels and proceed to more advanced classes so that they can fulfill certain prerequisite requirements at school. Students are often taught how to plug in formulas to get answers without any real understanding of why.
The notion that presenting students with more advanced material earlier is somehow 'better' doesn’t resonate with me, and therein lies 'the race to nowhere.' This begs the question, "who is really benefiting from this?"
I recently had the pleasure of sitting down with Marlo Shumway, a former colleague and friend, for a candid interview about the current state of math education. Given her experience as both a classroom teacher and the lower school math coordinator at Gulliver Academy, I know that Marlo's insights will prove valuable to our readers on everything from best math practices to tips on how to avoid common pitfalls in math instruction.
Q: What are some of the best math practices?
A: Kids have to see math, which is why the use of math manipulatives for young children is so crucial to their learning. When children are given a formula, for most of them, the extent to what they see are a complex set of numbers and symbols on paper devoid of any real meaning. Math manipulatives allow them to take an abstract concept and make it palatable by breaking it down into its component parts and “seeing” it.
For example, if a child is working on volume, sugar cubes are the perfect manipulative. One way they can be used to help a child grasp volume is by having them use the same number of cubes to create two different formations: one short and fat, and the other long and skinny. The child can readily observe that although the two figures have different surface areas, they have the same volume.
Q: What are some common errors in math instruction?
A: The most basic error I see in the way math is taught is that a lot of times a teacher’s objective is to get a child to regurgitate an answer. In my experience, I have seen a lot of teachers emphasizing the importance of rote memorization and requiring that students spit answers back at them without having them deeply understand the concept. We are pushing kids to be proficient in content so that they can move onto the next concept. Our goals have been diminished from mastery to proficiency for the sake of moving on. This model doesn’t allow teacher to delve into concepts.
Q: How would you advise a parent who is given the opportunity to have their child placed in advanced math for the following school year?
A: The difference between acceleration and enrichment is accelerated math moves through content quickly while enrichment requires a student to apply the content to real world situations. By engaging students in actual real problems, they begin to see the value of learning. For example, when teaching volume, a teacher may choose to engage students in valuable lessons through cooking.
The problem with skipping to the next level in math is that you are guaranteed to miss something. Math is scaffolded, so with every piece you pull out, you run the risk that it will all crumble, and that’s exactly what we’ve been seeing. Students will have a lot more opportunities if they actually know math well and don’t race through it.
Q: How do you ensure that a child doesn’t have gaps in their math knowledge as they move through the grades?
A: This is one of the biggest problems I see. Teachers don’t have math backgrounds so they are incapable of teaching math thoroughly. Most teachers stick to textbook and won’t use other resources because they do not have a high comfort level in math. We need more professional development and direct support in ensuring that teachers’ content knowledge is high because only then can it translate to their students.
Q: What advice would you give a parent with a child who is falling behind and struggling in math?
A: I would provide these parents some valuable resources and tell them that they’re going to have to do their own work. The best piece of advice I can give them is to remind them that math should never be approached procedurally, but rather conceptually.
It’s not just about going through the steps, but understanding why they are going through the steps. The sad fact is that by the age of six, kids have already developed math self-esteem and a lot of it is based on speed, which clearly has nothing to do with knowledge.
Q: What are some activities parents can do with their children at home to boost their number sense/math skills?
A: Parents can reinforce fact fluency through games. Anything from using playing cards to creating your own board games. Simply playing board games is huge. There is so much learning happening there. You can use it as an opportunity to ask higher order questions. For example, if your child rolled a 7, you can ask, “How many more until you get to ten.”
Q: What is the problem with the way math is typically taught?
A: There is simply not enough real world application. For example, if geometry is being taught, why not have the students design a quilt? If students can’t assign meaning to what they are learning, it gets lost and becomes meaningless. Teachers need to find alternative forms of assessments. Teachers tend to stick to tests that require kids to regurgitate answers that are all procedural. By having them keep a portfolio of their work, you can learn so much about a student. This type of assessment is very different than a test or GPA. Portfolios allow you to see progress over time. Assessments have to change first, and only then will lessons begin to change.
Q: How do you feel about children being taught math “tricks” to get the correct answer?
A: Tricks don’t work because students need content knowledge to thrive in math. They need to be able to reason. Tricks are too limiting and don’t offer any assistance when a student gets stuck. For example, if a 3rd grader gets stuck because they can remember the trick for solving 6x8, they are out of luck. On the other hand, if a student learned several strategies, like repeated addition, they would be able to solve the problem by applying that strategy.
Q: What are some of your favorite math resources and why?
A: Number Talks by Sherry Pearrish is a 10-15 minute daily practice that helps students deeply understanding numbers and number sense. The practice starts with a problem and the students not only have to solve it, but they also have to be able to explain and defend their answer. Then, they are asked to come up with a second or third strategy to show that they thoroughly understand the concept. Students are asked to share their strategies with the class. This benefits students by exposing them to new, effective strategies that they may not have come to see on their own.
Another great resource is NCTM Practice Standards and SMP Standards of math practice. It includes a website called Illuminations with lesson resources including digital manipulative, 100’s grids, and engaging math games.
Q: Why is it important for students to struggle and fail when learning math?
A: Productive struggle is learning through failure. It is important for students to be challenged and asked to use their own minds to work through problems as opposed to being taught which formula to plug in.
For example, when a teacher gives a student a problem with no numbers and asks them to work backwards to come up with the numbers, you are engaging their mathematical knowledge and number sense. Teachers tend to set up their lessons so that the students can plug in the information and get the problem right. There is too much emphasis on getting the “right” answer and not enough emphasis on depth of understanding. This “kill and drill” strategy “works” when a student is given a test that follows the exact set-up as the practice problems. The trouble is, because the students don’t really understand the concept, this strategy falls apart when math becomes more complicated or isn’t presented in the exact same way it was taught – that’s a problem.
Q: Do you think its important for kids to be grouped based on ability in elementary math?
A: No, I prefer working with mixed ability levels so that the students can learn from each other. A more sophisticated math thinker can expose a less sophisticated math thinker to new, valuable strategies. A more advanced student benefits from taking on a leadership role and reinforcing their knowledge through explanation and being given a teaching opportunity. The only way a student can teach a concept is if they understand it deeply. This practice builds self-esteem and confidence.
Kids learn from kids better than teachers because they speak the same language.
Q: What is the downside to leveling students based on their math ability?
A: When classes are leveled, the high kids just end up getting all procedural knowledge because they are good at memorizing strategies and knowing when to plug them in. They rip through the material without necessarily going deeper. On paper, these kids can do the procedure, but inside their brains, they don’t deeply understanding the math. This may be benefiting the parents who can say their child is a year ahead in math, because this is what our culture values, but it is not benefiting the child who is missing fundamental number sense or the ability to think critically about math.
PowerPlus Tutoring is grateful to Marlo Shumway for her time and appreciates her insights and knowledge on this topic. Due to requests from several parents, we are looking forward to having another Q and A session with Marlo in the very near future. If you have questions or comments that you would like me to include in my next interview, please contact me at Lizzie@powerplustutoring.org.