Encourage Your Daughter, Your Son, and Their Teachers to Understand and Enjoy Math. They’ll All Thank You Later.
Whether you’re a student, a teacher, or a parent, the key to understanding—and enjoying—math is about conceptual understanding and practice
By Nigel Green, Vice President of Personalization and Kelly Urlacher, Senior Curriculum Designer at DreamBox Learning
As a former professional musician and educator, and a former elementary school teacher, we found the recent New York Times piece, “Make Your Daughter Practice Math. She’ll Thank You Later,” and, in particular, author Barbara Oakley’s comparison of learning math to learning to play an instrument, a very interesting read. However, she misses a few critical points.
While we agree with Ms. Oakley’s statement that math is essential, we know that it is the understanding of mathematics, not just the practice of it, that makes it “sine qua non.”
Readers of Professor Oakley’s article might be tempted to think that practice is more important than conceptual understanding and enjoyment of math for girls. If that’s true, why bother spending time on understanding? The truth is that both are equally important.
As any sports coach will tell you, it’s not how much you practice that counts, it’s whether you are practicing the right things. Practice alone does not make perfect. Taking Professor Oakley’s analogy further, few if any guitar teachers would instruct students to simply practice putting their fingers repetitively in certain positions without the student understanding why they were doing so. They teach each chord and skill in context. Usually, the context is a song or piece well-known to the student so they learn and practice the chords based upon some initial understanding. In addition, the students grow to understand that certain chords are most commonly used in certain keys. Over time they understand they can use different finger and string positions to make the same chord, but one that fits the feel of certain pieces better. The fun comes from the feelings of accomplishment of being able to play the piece yourself, and by playing with others.
Now imagine if a teacher instead decided that the best way for a student to learn was to simply memorize and mimic finger positions, without any context as to where they fit into the plan of becoming a musician. What if the teacher decided the next week to move on to learning a piece that the student has never heard and without mastering where their fingers had to go from the week before. (Perhaps the student practiced, but without adequate supervision and correction she possibly practiced and ingrained what are now bad habits. The teacher follows this pattern and now the once-hopeful musician is struggling to remember the chords from week one and the song from week two. Feeling motivated yet?)
When raising and educating young human beings there are rarely simple causes or solutions to the problems that arise. If there were, parenting would be easy and teachers would follow the same proven approach that works for all students. While replacing conceptual understanding with more practice may seem an appealingly simple solution, it is one that fails to take into account the large quantity of research that points to wider, more impactful, and occasionally more subtle, influences that can adversely affect the math proficiency of some girls.
Writing in “Unlocking Children’s Math Potential: 5 Research Results to Transform Math Learning” Jo Boaler, Professor of Mathematics Education at Stanford University describes decades of research on student ‘mindset’ by Carol Dweck, Professor of Psychology at Stanford University, as having “more impact on educational practice than any other research volume I know.” In her research Dweck found, amongst other things, that high achieving girls with a fixed mindset – a belief that some people are innately smart and some are not, versus a growth mindset where the more you learn the smarter you become – tended to avoid more challenging work where they might not be immediately be successful. Dweck also found that gender differences in schools are only found among fixed mindset students.
What causes this fixed mindset, particularly in otherwise well performing girls? What can we do correct this? In questioning over 800 teachers Professor Boaler found the most commonly cited reason was grouping students by some implied ability. For example, the “high performing” vs. “not” groups. But other, more subtle factors can also cause students to self-select into what they perceive to be a lower performing group. An article published in the Proceedings of the National Academy of Sciences of the United States of America clearly shows the effect that an educator’s unease with math can have on students, particularly young female students. Children are more likely to emulate the behavior and attitudes of same-gender vs. opposite-gender adults. With the majority of primary teachers being female, any math anxiety they may exhibit therefore imprints more strongly onto the girls in the class.
The problem of how math anxiety affects student performance is significant enough that the best math programs are specifically designed to address this in their students. Sadly, few go the extra mile by also offering ways to correct what often heavily influences these students: a teacher’s fixed mindset. By addressing the needs of both the student and the teacher, we can develop growth mindsets for math in both students and teachers and overcome this often subtle obstacle whose affects can last a lifetime.
To help develop a growth mindset in math, as in music, students need both conceptual understanding and practice. All students deserve to experience coherent learning pathways in math that build a solid foundation and confidence in numeracy and problem-solving skills. Both the conceptual understanding and procedural fluency are significant components of effective mathematics pedagogy as proven by learning science. It’s imperative to utilize a pedagogy that combines big ideas, models, and strategies into a conceptual framework that allows students to investigate the why and make sense of big ideas, before ever reaching the procedural fluency component, or the how. Fluency and practice should be within the context and beauty of mathematics, not the sole focus.
At DreamBox, we design our platform to support this growth in students and teachers. We provide practice via both repetition with adaptively increasing complexity and difficulty within and across lessons. Practice is embedded as students are developing conceptual understanding by building upon previous lessons and skills to create broader, deeper and more specific understanding.
All musicians practice. But practice alone will not make you a musician, or a confident mathematician. If we encourage our daughters, and our sons, and their teachers to think, problem solve and engage deeply in mathematics, the joy and understanding will follow. They’ll thank us, and so will future generations.
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