This is a guest post by Rachel Chou, Math Department Chair at Menlo School in Silicon Valley. I wrote about this topic on my Web site, under the title Hyper-Acceleration. You’ll see that Rachel addresses a particularly acute version of this problem, given the fact that she is in a private school in a region where hyper-acceleration is deeply embedded in the culture of privileged parents. Even if the situation at your school is not as extreme, you might get some ideas from Rachel on how to discuss this non-confrontationally with pushy parents or the administrators they pressure.
On the desire to push kids ahead
– by Rachel Chou
“We were disappointed to hear that the 6th grade wasn’t leveling. We had hoped that Monica would be on the same path as her older brother Brian.” This was a comment made to me in passing, by two parents new to the 6-12 independent school where I work. These two lovely parents, were already concerned about whether or not their 11-year-old daughter would be exposed to Calculus by the 11th grade. 6th grade had only begun two weeks prior. Their feelings and sentiments are normal though. Many parents at independent schools were themselves both serious and successful students. At any given point, if their children are not on a particular path to “be the best,” to be “ahead of everyone else,” they start to get nervous. These parents are well-meaning. They love their children, want the best for their children, and worry when a child gets “off-plan” on the way to this measure of success. While the parents that I interact with are almost always kind, well-meaning, and have their children’s best interests at heart, their concerns and desires are often short-sighted.
Should we choose a school because it brags that it “gets all kids through” Algebra 1 in the 7th grade?
At my independent school, as a matter of philosophy and practice, we do not have students study a traditional Algebra 1 course in 7th grade followed by Geometry in 8th grade. I’m particularly unimpressed with middle schools that brag, “We get all 7th graders through Algebra 1!” Normal or even advanced adolescent cognitive development does not leave a child ready to deeply understand the topics in a traditional Algebra 1 sequence. When middle schools brag about this, it means that they are teaching a course titled Algebra 1, but that they are necessarily altering the content and cognitive demand of the tasks being included, in an effort to make the material accessible to younger students. Or worse, they are not altering the cognitive demand of the tasks being included, and instead are running a course that is predicated on teaching students to be docile memorizers of routines, but not mathematically thoughtful and powerful thinkers. I don’t want my own child in a class where she is learning to do Algebra. I want her in a class in which she is being exposed to meaningful learning experiences, which have an effect on her overall ability to deeply understand Algebra.
Absolutely no one choose a pediatrician because he brags, “I get all babies walking by 12 months old!” We accept that the normal age at which babies learn to walk is somewhere between 9 and 18 months of age, and the children who gain this skill on the latter end of the scale are no less athletic or physically capable children. We also certainly do not believe that when a child begins to walk is any reflection of the pediatrician caring for him.
Meanwhile, the parents who might think that their child is particularly advanced might choose a middle school because it is bragging that it gets all of its 7th graders thru Algebra 1; however, this is also very short-sighted. Remember that this course must be targeted at the average cognitive maturity of a 7th grader. If I thought my child was unusually precocious, such a course would necessarily defeat my purposes.
“But I just don’t want my child to repeat a class!”
At our school, half of the incoming 9th grade students come from outside middle schools. Many of these middle schools do allow the acceleration mentioned above. We tell parents that we base placement on what a student knows and can do and not on the names of courses they may have taken. In practice, while 20 to 30 of our incoming ninth graders have taken a course called Geometry, we place only 2 – 4 of them in Honors Algebra 2 as freshmen. Parents often worry if their children have taken Geometry in middle school, that they will be “repeating” something in our Geometry class, and yet, exactly no one, has ever called my history colleagues asking if their children can skip 11th grade US History for the reason that “Their child studied US History in 8th grade.” We somehow accept that kids can look at the problems of history with a more thoughtful lens when they have reached an older age. The same is true for Geometry topics. As a matter of fact, students who have studied geometry in their 8th grade years report little to no advantage over their peers who haven’t. Often, they are at a disadvantage because their ability to handle algebraic abstraction is less well-developed specifically because they studied Algebra 1 when they were not yet cognitively mature enough to understand it.
When might we allow some acceleration?
It may sound somewhat contradictory that we allow advanced placement in our high school and not our middle school, but this is a thoughtful choice, not an accident. It is not our department’s belief that all students can acquire mathematical understandings or power at the exact same rate, but it is our belief that picking children out too early for advanced acceleration provides students with very little gain, and can lead to unwanted consequences. I offer the following analogy: The tallest child in the class in 6th grade is not always the tallest child in the class in 10th grade. (They haven’t gotten any shorter! Their friends just grew taller!) We accept and understand that children hit their physical growth spurts at very different ages. This is also true of cognitive growth spurts, though it is far less obvious to non-teachers. A child might be particularly mathematically precocious in sixth grade, and might be closer to the average by tenth grade. This child has not grown less capable or intelligent, but rather her friends have simply caught up! The point here is that there is a real danger in separating out children at a young age for active acceleration. They might handle the extra challenges in the 6th grade, but if they end up in a situation in which they are hitting Precalculus in the tenth grade, they are often not ready for the cognitive demands of the class. And all a school has succeeded in doing in this case is accelerating a child to a place of frustration. These students often report that they “loved math when they were little” but that “they no longer do now.” That can’t be our goal as parents or as educators.
On trusting the knowledge of practicing educators.
Not surprisingly, when I speak to parents at open house events and inform them that it is common for 20 to 30 of our admitted students to seek an Algebra 2 placement, but only a small few actually are placed there, the parents immediately assume that their child will be one of these “select few.” This makes lots of sense. First, as parents we are biologically predisposed to believe in our kids and think they are generally awesome. Second, there is the issue of sample size. The average parent at my school has a sample size of 1 to 4. The parents with 3 or 4 kids will think their best math student is “incredibly brilliant” and needs more than what the grade-level curriculum has to offer. But the educator who is making placement decisions typically will have a sample size of about 2,000 students. Math educators have a far better ability to understand where a particular student fits in terms of their cognitive maturity as compared to their peers, and parents would be wise to heed the advice of the math educators caring for their children.
Why are we trying to race toward calculus?
Back to the story of the two parents concerned about their 6th grade daughter’s eventual 11th grade math placement. Another point worth mentioning is the odd belief in this country that K-12 mathematics is a race toward studying calculus. First, there is so much interesting mathematics for kids to study that is not a pre-requisite for studying calculus. Students are typically quite drawn to discrete math topics such as probability, combinatorics, elementary graph theory, number theory, sorting algorithms, and the list goes on. If we view a traditionally taught calculus course as the only end goal of a K-12 math sequence, we might leave such interesting and mind-stretching topics out. Why? Instead of lobbying your local school or your private school to accelerate your child toward Calculus, consider advocating that math curriculums include more depth, more open-ended tasks, and more discrete math topics.
Second, and possibly conversely, why are we waiting so long to get to calculus exposure? Students need not have formally studied continuous math topics such as advanced trigonometry, exponential and logarithmic functions, polynomials and the like to appreciate calculus concepts. A thoughtful geometry teacher might guide her students to find a “slope-computing formula” (the derivative!) of the function which represents the top-half of a circle, by applying understandings of how a tangent line intersects the radius of a circle. Similarly, included in either a geometry course or an introductory programming course, students might write code to compute the area under curves by breaking the area into skinny slices. How many of us actually integrate by hand, unless we are ourselves teaching calculus, or training students for the next integration bee?
No child’s mathematical journey is the same. As teachers, in any single classroom, we are charged with furthering the mathematical growth of a wide variety of needs. The thoughtful teacher sets up her curriculum so that students can learn, grow, and deepen their mathematical thoughtfulness and creativity at varying levels within the same classroom. It is time to stop believing that the best thing to do for our children is to advocate that they advance through a sequence of math courses at an accelerated pace.