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 chooses 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.
5 thoughts on “On the desire to push kids ahead”
A responder asked, “But what about when parents see taking Calculus early as a method to improve their child’s college admissions chances?”First of all, on some level, improving college admissions chances is behind most parents’ concerns about acceleration. Parents may say that they want their children to “not be bored” or “to be more challenged,” but really, parents want to be able to help their child demonstrate in the college admissions process, that he is better than other students, and parents (possibly subconsciously) think that advocating for accelerated math is the way to do this. Second, if this is truly the parent’s main concern, it is also short-sighted. I’m actually not against putting students in advanced courses in high school. I have done this, many times. But I have done this for students who are exceptionally cognitively mature, and I have purposely waited until a child is 14 or 15 instead of 11 or 12. If a parent needs to overly advocate with me, it is because their child is likely not ready for the acceleration, and should I back down from my stance, I am offering no gift to the student in terms of “college admissions support.” Because our math sequence will just be too hard for this student, the student is likely going to really struggle and get much poorer grades than he might have taking math with his peers. In the end, the parents’ over-advocation ends up hurting the child’s overall mathematical growth, power, skillsets, and confidence, and also ends up hurting his college prospects (that is if we believe that college prospects are directly correlated to GPA).
More and more university math profs complain that for many if not most students, earlier calculus is counterproductive, as it results in students with a superficial knowledge of calculus, and with weak understanding of the algebra prerequisites. See, for one, this guest post by a professor from Penn:https://blog.mathed.page/2016/02/more-calculus-less-understanding.html
[…] In my view, acceleration by one year can work for many students, and in fact it is a good idea for all concerned —but we should beware of willy-nilly hyper-acceleration. Many parents lose perspective on what is in the best educational interest of the child. (“If many students are taking Algebra 1 in eighth grade, then by God my son should take it in seventh grade!” This turns into an unwinnable arms race.) I have warned about the dangers of that sort of thinking and presented alternatives in this article: Hyper-Acceleration. See also this guest post by a private school teacher On the Desire to Push Kids Ahead. […]
I always feel these stories on hyper-acceleration are too one-sided, so I will share my story. I grew up in a small, rural town in the Midwest and graduate in ’89. At the time, Algebra was taught in 9th grade and there was no Calculus in the curriculum. Students who were accelerated in math would take Calculus at the local liberal arts college. I was (and still am) very interested in math. By the end of 6th grade, I had been accelerated by 1 year, working independently of the rest of my class. I was placed into 8th grade math class for my 7th grade class. My recollection was it was a rather boring year for math, but my father did sign us up for a computer class at the local college where we learned to program in BASIC during the school year (it may have been the year before). We ended writing a payroll program for his small business that was used until 2020. I was fortunate that the summer after 7th grade, my local college was participating in the Midwest Talent Search. I was able to take Algebra over the summer. It was taught by a college professor, and it was fantastic. So in 8th grade, I was taking Honors Geometry (10th grade class) at the high school. It wasn’t very challenging, but proofs were a lot of fun. In the summer, I took a computer class and learned to program in Pascal. In 9th grade, I was taking Adv Algebra II/Trig and my father signed me up for precalculus via correspondence via Northwestern University. This allowed me to take Calculus in 10th grade at our local college where I continued to take classes through the rest of my high school. During this whole time, I had a partner in crime who accelerated with me. The camps that I continued to attend at different universities let meet other bright and passionate students in math, English and other subjects. I was quite fortunate that I had supportive parents (with the means to support my passion), supportive schools (high school and college), and supportive teachers!
Share the positive stories of gifted math students from your career and let’s talk about supporting everyone!
I have a gifted child who is finishing Calculus 1 at 9yo. I have seen plenty of bad faith actors running interference to this educational outcome for a variety of reasons. All things equal when she turns 18 and is sitting in a dorm room with her same IQ doppelganger, who was not accelerated, there will be profound lifelong differences in their ability and usefulness to society. Depth before novelty can be a hamster wheel and novelty before depth can create gaps in their skills or understanding. There are far more hamster wheels in public education than kids with so called “gaps” in their knowledge.
The blog puts forth the unfair standard that students should not forget skills or concepts from various grades. I have seen plenty of instances where professional teachers and recent graduates get embarrassed because my daughter decided to take the lesson in a slightly different direction. All math teachers prepare and revisit material – I have had to train my daughter to be careful not to embarrass an unprepared teacher. Spiral the curriculum if there are concerns of loss or lack of depth but hold these accelerated kids to fair and reasonable standard you would hold to yourself.
The arguments put forth in the blog are directed at acceleration policy for an averaged cohort of accelerated kids. Those kids requiring acceleration are required, per various state laws, to be highly individualized. Although it would be easier to speak in general terms the decision to hyper accelerate is highly individualized. For each child the real work must be done through IQ, achievement testing and the childs choice to determine what is best for a child.
In these blogs I have seen the word “equity” and plenty of reference to the California Math Framework. This policy effort is based on oppressed/oppressor narrative ideology and not the individual well being of a particular advanced student. Conflation of poor performing children with the individualized considerations of the advanced student is reason to doubt the arguments being put forth are for the well being of the accelerated child and not a diversity, equity and inclusion scheme.
The most important consideration missing from all this is the child. What does the child want? Provided they ace the SAT PLEASE leave them alone or give them what they want.