For nearly one hundred years the basic structure of high school mathematics has changed only a little, not because it is working so well, but because there are powerful forces with a vested interest in maintaining the status quo.
For most students, most of the time, the required journey from Algebra 1 to Geometry to Algebra 2, and onward to Precalculus and Trigonometry, is devoid of interest, much less excitement.
It is mired in an out-of-date curriculum that not only fails to stimulate but also increasingly exacerbates inequity by closing off options and failing to prepare most students for the realities of citizenship and work in the twenty-first century.
And content is only half the battle. Even updated, invigorated content will fall flat and continue to be underperforming unless it is accompanied by equivalent invigoration in our teaching, our assessments, and our use of technology.
The status quo is no longer acceptable.
8 Excuses Perpetuating the Status Quo
We don’t ignore the need to change because we don’t care about our students. In fact, we care deeply about our students, but we are convinced our hands are tied and we think, “Who are we to challenge the status quo?” or “Is it worth taking on the battles that significant change would entail?”
So, with the best of intentions, we make excuses. We find reasons not to change and we excuse away a clearly underperforming status quo.
Here are eight of these excuses—some strong, some excruciatingly weak—that we must confront in order to change high school mathematics for the better.
Excuse #1: They don’t have basic skills
Everywhere we work we hear, “How can we do anything different when so many of our students have such extraordinary gaps in skills?” When we probe, we are told about ninth graders who don’t know their multiplication facts, who can’t do long division, and who are lost with anything involving fractions.
However, in most schools we are talking about no more than 20 percent of the students with deficiencies of this magnitude. Given that 20 percent of our students, on average, perform at an advanced level, we argue that this leaves the middle 60 percent, for whom this excuse is inappropriately applied.
It is not because of skill gaps that this middle 60 percent are not learning enough; it is more likely because the mathematics they are being taught and how it is being taught just do not meet their intellectual or emotional needs. There is definitely a need for intensive interventions—but a large proportion of our students should be able to succeed given opportunity, experience, and effort.
Excuse #2: They just aren’t motivated
If we are honest with ourselves, most high school students have little reason to be motivated by most of the high school algebraic-centered mathematics. Look at the endless parade of mindless worksheets with nary an application nor a reason for students to feel the need to learn these skills.
Not convinced? Consider how many lessons and days we allocate to solving linear equations before our students ever need to create an equation and then solve it in a meaningful context. Where does this approach generate motivation? It only reinforces a mindset of “just tell me what to do to get the right answer.”
Instead, we could launch the functions unit with the story of getting a speeding ticket in Vermont:
- We start by telling students that, not that long ago, the fine in Vermont was $4 for every mile over the 65-mph speed limit—plus a $10 processing fee.
- We ask what students notice and how they can understand and represent this situation.
- We work together to convert the words to a graph, identifying where the 4, the 65, and the 10 would appear.
- We ask what the driver and the police officer might be interested in knowing.
- We then relate the speed to the fine and unleash students to find such things as the fine when you were going 86 miles per hour or the speed you must have been going if your fine was $74.
- We add a constraint that the maximum fine is $200 and ask about the speed at which it no longer matters.
- We change to another state with different parameters and explore and compare the tables and graphs that emerge.
With realistic examples like this, motivation is rarely an issue with nearly all high school students.
Excuse #3: I’ve got to prepare them for the tests
There is no question that tests like the SAT, the ACT, and the AP exams exert extraordinary pressure. We fear to deviate in any way that might jeopardize our students’ opportunity to succeed on these exams.
However, even now we are not adequately preparing students for these tests! (In fact, we teach a lot of content that never appears on these exams.) If you’re a high school math teacher, click here to take a sample SAT exam or here for a sample ACT exam. Next, link the test items with what you teach and what you don’t teach (or emphasize).
Look at the content you currently teach that is nowhere found on these tests. Then examine the tested content that is only skimmed over in your classes at best. Then look at the thinking and reasoning—more than procedural knowledge—required by many of the test items and that are not typically reflected in our instruction.
Excuse #4: It’s what the colleges demand
Many postsecondary institutions around the country have engaged in serious efforts to reform their math requirements.
Colleges are now offering new pathways in areas like statistics and quantitative reasoning for students with interests outside the STEM disciplines. These postsecondary reforms have paved the way for reconsidering the mathematics required for college admission, as well as the mathematical preparation high schools provide. It is time for high schools to develop pathway options that much more appropriately prepare students for a postsecondary world that branches into a broad spectrum of careers for which calculus is not needed
Excuse #5: There just isn’t enough time
Correct! Unless you have a locked-in minimum of 60 minutes per day for each of four years of high school mathematics, you and your students are being set up!
The standard 45- or 47-minute (or even 42-minute) period per day or the 90-minute block every other day do not provide the time needed to accomplish what we are being asked to do. When we hear complaints about what the high school mathematics department isn’t accomplishing and are told that the teachers have a 45-minute period for math each day, we have already identified a major reason for the achievement problems!
Excuse #6: My textbook guides what I do
An effective mathematics curriculum is driven by a coherent set of standards or expectations.
The curriculum should be supported, not driven, by instructional materials. The standards, and unit assessments that are aligned with those standards, should guide what we do. Handing over that responsibility to textbooks is not professional and doesn’t serve our students.
Excuse #7: I don’t have the technology I need
When our smartphones—ubiquitous devices in the hands of more than 90 percent of high school students—have free calculators and access to free apps and sites such as Desmos, then access to technology essentially stops being a problem. If we work around destructive cell phone bans, appropriate technology can be available for nearly all students.
This situation also means that we have no excuses not to expect access to and use of powerful technology in our classrooms and on our tests. We should not limit access to smartphones because a few students might abuse them. Restricting these devices because they can disrupt and distract suggests that the mathematics being taught needs to be far more relevant and motivating
Excuse #8: I don’t have the training
This is an entirely legitimate excuse, albeit a highly problematic one.
Teachers cannot do what they can’t envision or don’t understand. Moreover, teachers need collaborative structures such as course committees and collegial visits to share ideas and give and get feedback. Professional isolation remains the single greatest obstacle to the quality and improvement of instruction.
• • •
As you reflect on this list, consider: Which excuses are most familiar to you? Which ones apply to your school or district? What other excuses for not changing have you encountered? How can we respond practically so that excuses like these don’t become obstacles to change?
To learn more about Invigorating High School Math visit Heinemann.com.
Steve Leinwand is Principal Research Analyst at American Institutes for Research in Arlington, Virginia and the author of Accessible Mathematics and Sensible Mathematics, and coauthor of Developing Numerical Fluency. Steve served as Mathematics Supervisor in the Connecticut Department of Education for 22 years and is a former president of the National Council of Supervisors of Mathematics. In 2021, he was awarded the National Council of Teachers of Mathematics' Lifetime Achievement Award.
Eric Milou is Professor of Mathematics at Rowan University in Glassboro, NJ and co-author of Daily Routines to Jump Start Math Class and EnVision Math A|G|A. Eric served as President of the Association of Mathematics Teachers of New Jersey and on the Board of Directors of the National Council of Supervisors of Mathematics.