An esteemed faculty member in my school, Allise Vicens, was kind enough to share a recent OpEd piece written in the New York Times. This article emphasizes the need for girls (and boys) to practice math nightly. According to the author, the focus on conceptual mathematics (i.e. the Chicago school of math) has been largely proven not to increase test scores, lifelong devotion to careers that utilize math, or even feelings of success in math. Despite this understanding, conceptual mathematics persists as a popular approach to math education in the US. The author of this piece believes that it is precisely this focus on "the fun" and the concepts that takes away from the need for students to really practice and become fluent in the language of math.
I think we need to have both. I know this sounds like having your cake and eating it too, but concepts alone do not provide enough of a framework for all students to be able to extrapolate what to do in every situation. Conceptual approaches do not account for the more concrete thinker. Conceptual approaches do not address all learners in the classroom. Conceptual approaches alone lack a vital element.
I think we need to have both. I know this sounds like having your cake and eating it too, but concepts alone do not provide enough of a framework for all students to be able to extrapolate what to do in every situation. Conceptual approaches do not account for the more concrete thinker. Conceptual approaches do not address all learners in the classroom. Conceptual approaches alone lack a vital element.
Anyone who wants to learn a foreign language needs to practice learning vocabulary and practice actually speaking the language. So too, in order to perfect your math ability, you need to actually do math. The author also explains that there is a big difference between understanding how to play an instrument and actually playing it. While I do think there is a merit to understanding what you are doing, a stronger focus needs to be on the practice of doing.
The author also explains that focusing so much on making math fun detracts from providing students with the skills and experiences needed to practice enough to become masters in the subject. While I am all for having embedded in lessons parts that evoke curiosity, discovery, and intrigue, I find a focus on fun to the detriment of providing students with real learning experiences to be a problem with many "popular" education fads. Ultimately, practice will make perfect and while you can certainly come up with creative ways for children to practice, not every child will find every moment of class fun. I actually think that is a teachable moment. ( I might suggest though that truly meaningful education provides students a love of learning that surpasses just one simple experience one day in a classroom.)
Math is not the only subject where repetition and practice matters. This year we are spending a lot of time as a team delving into our writing curriculum. Something I have noticed is that in following the Judith Hochman approach, our school has been rightfully scaffolding the teaching of writing a five-paragraph essays. Traditionally, third grade has been the year we teach one paragraph writing. In fourth grade, traditionally we teach four-paragraph essays writing. By the end of fifth grade, students are expected to have mastered the basic five-paragraph essay. The goal was for children to have a clear understanding of the concept of essay writing, but also for them to have explicit direct instruction in how to do so.
I agreed with the approach, but I felt the specific expectations per grade level were limiting. While I do believe there is tremendous merit to any scaffolded approach where basic skills are retaught with new skills are added on each year, I think our students can do more writing. In looking at national and international standards, we now expect our third graders to write three-paragraph essays. We now expect our fourth graders to write four to five paragraph essays (albiet not nearly as fleshed out as in the older years) and we now expect our fifth graders to write five-paragraph essays. The reason for this is simple. The more students practice writing and the more they write, the better writers they will be. The "longer" they write, the better they will be.
Malcolm Gladwell writes about the 10,000 hour rule. He explains that in order to be truly great at anything, to become a master, you need to dedicate 10,000 hours of your time invested in practice. Practice is not glorious. You do not always reap immediate rewards. It is important to teaching our students to relish in the satisfaction that will come from sustained effort. The critical component here is that success will not always come immediately. This lesson is a glorious gift we need to give all children. It is a lesson of perseverance.
Somewhat related to what I have just written above is an understanding that through the practice of a discipline, the student will acquire a new language- the language embedded in that discipline. There is a dialogue that can only take place between the student and the subject when the student has mastered that language. It is the language of background knowledge, of the basics within that subject and understanding of how that subject functions as a whole. Hence, it is always important when designing lessons in any subject to not only think about engagement, but engagement in what. The "what" matters. It is what makes a subject different from another and valued as a discipline.
Math is not the only subject where repetition and practice matters. This year we are spending a lot of time as a team delving into our writing curriculum. Something I have noticed is that in following the Judith Hochman approach, our school has been rightfully scaffolding the teaching of writing a five-paragraph essays. Traditionally, third grade has been the year we teach one paragraph writing. In fourth grade, traditionally we teach four-paragraph essays writing. By the end of fifth grade, students are expected to have mastered the basic five-paragraph essay. The goal was for children to have a clear understanding of the concept of essay writing, but also for them to have explicit direct instruction in how to do so.
I agreed with the approach, but I felt the specific expectations per grade level were limiting. While I do believe there is tremendous merit to any scaffolded approach where basic skills are retaught with new skills are added on each year, I think our students can do more writing. In looking at national and international standards, we now expect our third graders to write three-paragraph essays. We now expect our fourth graders to write four to five paragraph essays (albiet not nearly as fleshed out as in the older years) and we now expect our fifth graders to write five-paragraph essays. The reason for this is simple. The more students practice writing and the more they write, the better writers they will be. The "longer" they write, the better they will be.
Malcolm Gladwell writes about the 10,000 hour rule. He explains that in order to be truly great at anything, to become a master, you need to dedicate 10,000 hours of your time invested in practice. Practice is not glorious. You do not always reap immediate rewards. It is important to teaching our students to relish in the satisfaction that will come from sustained effort. The critical component here is that success will not always come immediately. This lesson is a glorious gift we need to give all children. It is a lesson of perseverance.
Somewhat related to what I have just written above is an understanding that through the practice of a discipline, the student will acquire a new language- the language embedded in that discipline. There is a dialogue that can only take place between the student and the subject when the student has mastered that language. It is the language of background knowledge, of the basics within that subject and understanding of how that subject functions as a whole. Hence, it is always important when designing lessons in any subject to not only think about engagement, but engagement in what. The "what" matters. It is what makes a subject different from another and valued as a discipline.
I have heard this debate many times in my career. I will never forget the social studies department head who questioned why children needed to know the causes of World War II when they could look them up online. Yes, absolutely they could, but like a foreign language there is a vocabulary of history, of civilization we want our children to be aware of (even if more broadly) throughout their lives. As a former AP teacher, I would have found it very disturbing for my students to walk out of my class not knowing that 6 million Jews had died during the Holocaust or that the Nazis believed in racial superiority. Simply knowing how to find something, or do something, is important, but without background knowledge, you often cannot even know where or what to look for.
Concepts matter. They will always matter. Concepts frame the skills and the content, but alone concepts are hollow without skills and content. I stand for a concepts plus approach.
Concepts matter. They will always matter. Concepts frame the skills and the content, but alone concepts are hollow without skills and content. I stand for a concepts plus approach.
