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Curriculum Matters: Language and Math

Updated: Apr 7, 2023

An important aspect of my work is helping young people make good decisions about their high school courses. Each year of high school provides more flexibility and choice, which is (I hope) exciting, and also can present some dilemmas.


In the brave new world of expanded test-optional and test-free policies, rigor of curriculum and performance over time are highly significant factors in admission review across a spectrum of institutions, paired with demonstrated community impact.


Generally speaking, it has always been true that college admission offices want to see students taking the most appropriate next level of rigor in each of the core academic areas as they move through grades 9-12. Those core subjects are English, Math, Science, History/ Social Studies, and Language Other Than English (LOTE.)


When I use the word "appropriate," I mean that students should consult teachers and counselors and take the next course in the progression that they are most prepared for. Questions around these choices seem to arise most frequently when we are discussing math. It is tempting to want to jump ahead in this discipline, in order to get to more advanced levels as a senior. Mathematics builds on a progressive foundation of skills and knowledge to prepare students for the next level. You learn skills from Algebra that lead in to PreCal/ Analysis and then Calculus, while also incorporating an understanding of Geometry that informs those more advanced courses.


Jumping over a course, or trying to get ahead with an abbreviated summer course, sometimes works, and also often leads to students getting "stuck," and needing to reset and go back to review fundamental concepts before they can proceed (or worse, a disastrous grade!) Sometimes, though, strategies to get ahead can work. Way back when I was in high school, the structure of my high school curriculum meant that I had to double up on Geometry and Algebra 2 as a sophomore in order to get on a Calculus track, and fortunately those were manageable courses to take concurrently. I advise students to make curricular decisions carefully, and to err on the side of success and solid comprehension of skills to be built upon through high school into college. Education is a continuum.


Balance is key when planning the following year's courses. Yes, it's important to challenge yourself, but taking on too many intensive courses with a high homework load can backfire. As with every topic related to high school growth, preparation for college, and eventual college application, it's important to know you're building a record, and to show that you took on increasing levels of rigor, but, especially in grades 11 and 12, it's important to choose which areas you're going to take on at the most intensive level-- be it through AP, IB Higher Levels, or just moving through a subject that you find particularly challenging. You also need to allow time for your interests beyond the classroom-- and allow for one class worth of light homework in junior spring and senior fall to manage searching and applying to colleges!


Admission Bias in the Math Curriculum

In my 20 years advising students in making high school choices and applying to college, the emphasis on Calculus as a marker of a rigorous curriculum has grown progressively stronger.


A quirk of the unusual approach to admission review in the US, often referred to as "holistic," is that there is a culture of admission preferences and bias that exists across admission offices, even among different categories of colleges and universities. The kind of personal narrative writing that tends to be valued in essays is a particularly American phenomenon, for example. While in the UK, you write a focused personal statement on your intended course of study and your preparation and aspirations for it, here, a story about lessons learned from a failed attempt to make a soufflé could be an admission officer favorite. A student of mine admitted to CalTech to study jet propulsion wrote an essay on chicken nugget day in his high school dining hall that was very well received.


The preference for Calculus on a high school transcript is a product of a similar admission office bias. Let's be honest: there are a lot of great folks working in college admission, and few of them have a background in education or pedagogy. Oddly, admission prerequisites aren't usually determined by the professors who teach the admitted students. Preference for things like style of essays, Calculus, and a narrow view of test scores are learned in the admission office.


A lot of college professors I've talked to at a lot of places actually disagree with this preference for Calculus. It's frustrating to tell students to avoid Statistics, if it's offered at their school and it interests them. However, if students haven't had Calculus by senior year, making the decision to go from PreCal to Stats as a senior course can lead to a different set of admission outcomes. So, for better or worse, the best advice about Stats, which is a practical discipline that is relevant to many fields of study, is usually to take it after Calculus (if you have the somewhat unusual chance to take Calc in 11th grade), or else to take the two concurrently in senior year.


However, there are movements under way to question this Calculus bias. A group called Just Equations released a report called Calculating the Odds: Counselor Views on Math Coursetaking and College Admissions.


Here's a summary and quote:


As long as calculus remains overvalued in college admission, students without access to it can be at a disadvantage in the college application process. This report underscores this inequitable dynamic by highlighting the support and guidance about math course selection from counselors at schools with an emphasis on college planning. Anderson and Burdman make a compelling case for strategies to slow the “race to calculus” and empower students in their math pathways.

“It is deeply problematic that college admission offices—many of which are entirely unaware of how actual math content, sequencing, programs work—use calculus as a benchmark for college admission. It’s one of the most frustrating things about the process.” — High school counselor

The 74 published this story on Calculus bias, the disconnect between admission priority and teaching/ learning reality, and the impact on lower income students at less-resourced schools.


A couple of key quotes from the piece:

“A background in calculus is certainly helpful — and many colleges do expect it for students pursuing STEM degrees — but research shows that deeper mastery of prerequisites for calculus is more important than calculus itself,” Baker said. “High school students should not rush through the curriculum to take the course. And even most selective colleges can support students who didn’t have access to calculus in high school.”
“The focus on calculus in high school is a vicious cycle that needs to stop: It’s inequitable and will not lead to a stronger body of college applicants or a stronger society,” she said. “It will lead to more of the same and delay 21-century advancement that relies on data and technology.”

I hope that these efforts to educate and re-calibrate admission offices are successful, and like other advisors to high school students, I'll be keeping an eye on this conversation with great interest.


"Foreign Language," aka LOTE, On the High School Transcript

The question of how much of a language to take in high school is a close second to math concerns.


It has been true as long as I have been in admission and counseling that 3 years of language in high school is a standard recommendation, and a prerequisite at many colleges. If you take the time to look at recommended admission prerequisites on admission websites, you'll find that many selective colleges "recommend" a full 4 years. The difference between "required" (usually 2 or 3 years) and "recommended" (usually 3 or 4 years) can be confusing-- it's generally advisable to take admission office recommendations as very strong encouragement, if not actually a de facto requirement.


FAQ: What about language courses I took in middle school? Usually language prereq is assessed independently of language study prior to high school, or the level achieved.


At many colleges, even though language is a stated prereq, it can often be waived for purposes of admission, if the student is adding another academic course into their schedule-- like doubling up in a subject, or taking something like Computer Science. Still, usually this "waiving" of a prereq comes with a notation of a "deficiency" that needs to be satisfied before college graduation.


Over the last 10 years, more high school students seem to choosing to take fewer years of language. I have this conversation with students frequently. It hits a little close to home for me-- my undergraduate degree is in Spanish, I did work towards a graduate degree in Spanish Literature, and my bilingualism has enriched my life beyond measure. I count among my closest lifelong friends folks from Mexico and Spain that I would not have met without that pursuit and time spent abroad.


I also understand that learning language in the high school classroom is not ideal. Immersion is the key to fluency, and I grew up in a bilingual community, which gave my high school classmates and me an advantage.


My time in graduate school in the mid-90's gives me another perspective on this: I taught Spanish classes at University of North Carolina-Chapel Hill and University of Texas-Austin.


At both places, I taught essentially the same class: a one-semester recap of Spanish 1 and 2 topics for students who, by virtue of having just 2 years under their belt in high school, or a placement exam, needed to take a level 3/ intermediate course in order to satisfy the university's graduation requirement. If they had been away from Spanish a year or more, they often felt unready to jump into level 3, and so my class was, effectively, a prerequisite for a prerequisite! It was something they needed to get through in order to take the class that would actually satisfy their graduation requirement.


This class was a lot of fun for me to teach. The fast pace and the fact that the students were not seeing this material for the first time allowed for geeking out on some of those topics that need to be mastered to get past the beginners' plateau: Por/ Para, Preterite/ Imperfect, Indicative/ Subjunctive. (If you ever want to see me draw visual illustrations of these concepts, I'm happy to oblige.) It was kind of a bummer, though, that one more high school class could have kept these students from having to take my review course.


Recently, Andy Borst, Director of Undergraduate Admission at University of Illinois- Urbana/ Champaign (UIUC), tweeted out some interesting insights into language study and admission outcomes in UIUC's pool.


I recommend following Andy, who has stated his intent to offer transparency and insights into how decisions are made at his public flagship: https://twitter.com/AndyBorstUofI


This graphic Andy shared tells a clear story:



"Most students admitted to UIUC (66.2%) took 4 levels or more of a language other than English. 36.5% took more than 4 levels, 85.3% took 3 or more levels, and 98.5% took 2 or more levels."

As Andy points out in an insightful thread, as his admission office moves away from testing emphasis, levels of LOTE taken in high school are shown to correlate directly to first-year academic performance, so in turn those levels achieved are influencing admission offers. He also points out that, much like in the case of Calculus, there are equity and access barriers here that can penalize lower-income students and those at less-resourced schools. Also: students whose first/ household language is not English might fairly be looked at a little differently as far as expectation of learning a THIRD language in high school.


There's a clear takeaway, though, for most students currently making decisions about 11th and 12th grade: take 3, if not 4, years of Language Other Than English.

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