# But That Won’t Prepare Them for College!

**Matt Larson**, NCTM President

April 26, 2017

For perhaps the first time in our history there is clear and growing consensus concerning what constitutes effective mathematics instruction, kindergarten **through college**.

The monolithic nature of college mathematics instruction, dominated by lecture and summative exams, is changing.

Instructional strategies and classroom environments that have been recommended by NCTM at the K–12 level for at least two decades are in the process of being advocated for and adopted for college mathematics instruction. In 2016, the Conference Board of the Mathematical Sciences (CBMS) issued a statement on *Active Learning in Post-Secondary Mathematics Education*. In this statement the authors wrote that*Classroom environments in which students are provided opportunities to engage in mathematical investigation, communication, and group problem solving, while also receiving feedback on their work from both experts and peers, have a positive effect on learning. Teaching techniques that support these activities are called active learning methods … we call on institutions of higher education, mathematics departments and the mathematics faculty, public policy-makers, and funding agencies to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classrooms.*

These recommendations are consistent with the research-informed instructional strategies in *Principles to Actions*. The presidents of 15 professional mathematics and mathematics education organizations endorsed the statement, including the American Mathematical Association of Two-Year Colleges (AMATYC), the American Mathematical Society (AMS), the American Statistical Association (ASA), the Mathematical Association of America (MAA), and the Society for Industrial and Applied Mathematics (SIAM).

The CBMS statement was based on research supporting the efficacy of active learning techniques across the STEM disciplines as well as a number of other reports that recommend a transformation in postsecondary mathematics instruction, including the 2015 MAA report *A Common Vision for Undergraduate Mathematical Sciences Programs in 2025* and the 2013 National Research Council Report *The Mathematical Sciences in 2025*.

At the 2017 Joint Math Meetings, the MAA released draft components for discussion from its forthcoming *Instructional Practices Guide*. Although what was shared at the conference was incomplete and preliminary in nature, I was struck by the topics addressed, which included:

- Fostering Student Engagement
- Selecting Appropriate Tasks
- Collaborative Learning Strategies
- Just-in-Time Teaching (a formative assessment technique)
- Developing Persistence/Grit in Problem Solving
- Inquiry-Based and Discovery Learning
- Communication—Reading, Writing, Presenting, and Visualizing
- Error Analysis of Student Work
- Use of Technology
- Building Procedural Fluency from Conceptual Understanding
- Classroom Discourse
- Assessment Practices (formative and summative)
- Design Practices (Instructional Planning, which includes a discussion of the value of professional collaboration)

In addition, the authors of a recent article in the *Notices of the AMS* argued that “mathematics faculty need to be well informed about active learning and related topics,” need to be provided with examples of active learning strategies, and need to have common concerns with implementation addressed (Braun, Bremser, Duval, Lockwood, & White, 2017).

Although our labels may differ in some cases, it is clear that the draft MAA *Instructional Practices Guide* and the research-informed recommendations found in *Principles to Actions* have much in common. Are these instructional practices in place in every postsecondary mathematics course? Of course not, but neither are they in place in every pre-K–12 mathematics classroom.

This consensus exists because the research literature is clear: Greater student learning results from classroom instruction where students are engaged in problem solving (in addition to building conceptual understanding and procedural fluency), where students are discussing mathematical ideas, and where students are doing mathematics and their teachers are collaborating and using assessment to guide instruction. And perhaps more important, these strategies are consistent with equity-based instructional strategies that support our work in reaching each and every student.

In February, NCTM held another successful Effective Teaching with Principles to Actions: Implementing College- and Career-Readiness Standards Professional Development Institute. The content of the Institute focused on supporting teams of teachers and administrators in implementing the recommendations outlined in *Principles to Actions*.

Institute time was allocated for teams to work together and interact with experts to answer questions and collaboratively support participant efforts to implement what they learned at the Institute in their schools and districts. Nearly everyone in attendance was already a strong supporter of the six principles and recommended action steps in *Principles to Actions*, but many teams expressed a similar concern: “How do we respond to colleagues who say that if we implement these recommendations, we won’t be preparing students for college?” It is a question I am sure you have heard a colleague ask at one point or another in response to some recommended reform.

In my own experience as a K–12 district math curriculum specialist, more than a few teachers expressed real concern that some standards-based instructional reform would “not prepare students for college because no college professor would ever use such a practice.” You may have shared similar concerns at some point in time; we likely all have. I want you to know that this concern, while not uncommon, rests on a number of questionable assumptions.

This concern frames the primary purpose of pre-K–12 mathematics instruction as preparation for college—including preparation for the assumed instructional practices of college mathematics professors. First, the purpose of teaching and learning mathematics in grades K–12 extends well beyond a narrow preparation for college and careers—a topic I will address in a future President’s Message.

A second and increasingly less certain assumption embedded in the “that won’t prepare them for college” concern is that college mathematics instruction is singularly characterized by lecture and summative exams. The evidence is clear that college mathematics instruction is in the process of undergoing a fundamental shift in favor of active learning and student engagement.

I encourage you to review the reports and recommendations mentioned in this post and to continue to collaborate with your colleagues to implement these practices in your own classroom, school, and district. And the next time someone says to you that some practice “isn’t what students will do in college,” make sure you share with them the evidence that postsecondary mathematics instruction is beginning to change in ways that are consistent with long-standing recommendations at the K–12 level. As K–12 teachers of mathematics, we certainly don’t want to prepare our students for a past that is in the process of changing and will increasingly no longer exist.

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Kwesi Yankey- 5/9/2017 8:05:57 AMThanks for your help for this year conference. This is one of the best. We need more help for international math educators. Africa math teachers need help.

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W Gary Martin- 5/2/2017 9:01:57 PMMatt, Thanks for this article.

These are exciting times.In four decades in the profession, this is the closest I have seen to a consensus between K12 and Higher Ed about what is important in mathematics teaching and learning. NCTM's engagement with the math community has been an important part of making this connection.We really need to capitalize on this opportunity by beginning dialogue at all levels -- starting with faculty at universities and colleges and faculty at the high schools which send them their students. Articles like this, as well as some of the others Matt references, can be a great starting point for discussion. Another good article comes from the Proceedings of the National Academies of Science -- Freeman et al., 2014 -- showing the benefits of active learning across the STEM curriculum. The time for excuses is gone, we can do better!

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John Wenger- 5/2/2017 5:02:14 AMI have been retired for almost 15 years now, and I taught in a two year college. I have almost no background in education courses of any kind. However, it has always been my opinion that what students need (especially poorly prepared students coming from high school to college) is more time on task, regardless of what methods you use to teach them. I also believe that it won't happen because no one will spend the money to make it happen. Sad, but trtue.

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Kathy Redmond- 4/30/2017 9:07:19 AMAs an elementary curriculum specialist, coach, principal, and most importantly, kindergarten teacher, this is wickedly awesome news! I am SO excited to hear about the shift in secondary education. I am working diligently, standing tall on my soapbox, to do the same in elementary classrooms. However, the excuse that our ineffective instructional practices in elementary schools are for the purpose of preparing our kids for instructional strategies to come, is completely unsound. Let's say that secondary education never changes... it is still our responsiblity to create classrooms where students learn solid mathematics. If we do that successfully, our darlings will be ready for whatever comes next! Here's to growing all students to exceed expectations!!

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Chris Kalmbach- 4/28/2017 3:37:52 PMThe news that NCTM's work and advocacy is starting to have impact at the college level is fantastic news! Thanks for sharing!

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Kristine Lindeblad- 5/4/2017 12:01:32 PMOf course I see you here! :-) Let's talk about this sometime

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Rick Wandler- 4/28/2017 3:01:25 PMThank you, Matt. This is indeed exciting news.

Referring back to MAA recommendations, students at all levels should build procedural fluency from conceptual understanding. We should strive to unveil the beauty and creativity of math, including calculus, in a manner that makes sense to students. Doing so would enable students to synthesize and apply appropriate math tools to get at the real issue...solving problems and communicating those solutions in a clear and convincing manner (.."convince yourself, convince a friend, convince a skeptic". Mathematical Mindsets, Boaler, pg 87) . While I recognize the need for teaching procedures (lecture), that need should not occur at the expense of sense-making. Sense-making should occur both in and out of the classroom through a robust exchange of ideas. I know that way back when I attended college we had lectures but we also had extended labs where reasoning/problem solving took place.

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Corey Andreasen- 4/28/2017 1:53:50 PMI think there's another point that was left out. "Prepare them for college" doesn't necessarily mean "Give them the same experience they'll have in college." First, those experiences vary greatly. Secondly, I've said half-jokingly, "If I want to give kids what I experienced in college, I should do a poor job of teaching and base the grade on two tests!" (I understand that "do a poor job of teaching" sounds like a dig, but is really more of a commentary on the lack of time college professors have to actually teach.) The best preparation for college is to make sure students know the content as well as possible. That means we need to use good teaching methods regardless of what they'll experience in college. I'm glad to hear that colleges are moving in the direction of more effective practices as well, but that isn't (to me, anyway) the reason to teach well in earlier schools.

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Janie Merendino- 4/27/2017 1:52:23 PMFinally I am hearing back up from such worthy educators! As a mathematics curriculum specialist I fight the fight for using these active learning strategies. Here in my own state of WV we now have a legislature that wants to throw out our standards- just as we are seeing change in elementary students' understanding of mathematics. I fight the fight of teach inergrated math in the high schools because colleges do not align with that. Maybe now those institutions of higher ed will wise up and change! I used to teach a course called developmental math at our local university. But i quit because they wanted it to be taught all lecture and use of a software program requiring tons of procedure practice and kids were getting credit but they still knew no more about math than when they got there! I had a conversation with a local house delegate and he came to see the benefit of teaching for understanding however he then said, " teachers need to be more vocal about this"- as if we have the time! This article and the ones mentioned will help!

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Art Bardige- 4/27/2017 11:41:27 AMMatt while I share your enthusiasm I am not sure I share your confidence. But I would like your thoughts on whether there is any concensus on the curriculum that colleges should be teaching or the skills they require K-12 to deliver. This current curriculum does not, I believe, prepare students for the work or life they will be entering. It does not prepare or enable them to handle the technology or the problems of the digital age.

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W Gary Martin- 5/2/2017 8:46:15 PMArt, There is a lot of discussion around this issue at the undergrad level in the documents Matt mentions in his article, about how to address the lack of preparation you mention. Of course, it's a long journey to enacting these recommendations. I will say that sessions on active learning are very well attended at various undergrad math conferences. As the 2012 PCAST Report famously stated, "If math departments don't do a better job teaching, we'll find someone else who can." OK, to be honest that's a bit of a paraphrase. :)

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Art Bardige- 5/4/2017 4:56:47 PMGary, Most of the discussion in these reports has to do with pedagogy and process and not content. The word technology appears often but the word spreadsheet almost never. Yet, the world our college students need to get ready for uses spreadsheets for both business and for STEM applications. Are we preparing our students for that world, for using that technology, for solving problems in a new way. For example, spreadsheets are function machines that focus almost exclusively on discrete quantities, yet most of the algebra and calculus we teach students is continuous. What would math education look like if we designed it for the jobs of the future and not the past?

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W Gary Martin- 5/9/2017 9:39:16 AMI couldn't agree with you more! In fact, see this article I cowrote with Eric Hart on discrete modeling.

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Tracey Knerr- 4/27/2017 9:29:02 AMThis is indeed fabulous news!

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Janet Herrelko- 4/26/2017 11:48:04 PMWhile our university mathematics department tries to use active learning, most do not have the pedagogical training to know how to do this effectively. The issues that arise due to poor implementation cause the upper level instructors to keep using lecture. As a university professor with two decades of high school teaching background, I know how active learning reaches the majority of students to grow their critical thinking and problem solving. Active learning takes planning and time to create. It is encouraging to read how many of you at the university level do employ pedagogical content methods that grow mathematicians. Now we need the ambition to grow university mathematicians into teachers rather than instructors.

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Janie Merendino- 4/27/2017 1:51:02 PMI hear you Janet! I was a teaching fellow at our local university for 2 years and I was charged with re writing the syllabus for our one 3 hour math methods course for elementary teachers. I did But, when it went to the math dept for verification they tore it apart. Those professors thought how you dare to take out truth tables and proving the cartesian product? I had the cartesian product in the syllabus buit just as it related to teaching multiplication and derived fact strategies! I cant wait to send this to them!

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Rita Kottmeyer- 4/26/2017 8:47:18 PMI have been a professor of mathematics at Lindenwood University for nearly 27 years. We have traditional age college students, and we also have working adults getting undergraduate and graduate degrees. I've had my PhD in math since 1973 and have seen many changes in education. One thing is certain. Mathematics and Quantitative Literacy should be taught from the perspective of student needs, not from an aged set of lecture notes. No matter what the age of the students, you cannot get their attention until you spark their interest.

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Jeanne Lazzarini- 4/26/2017 6:56:46 PMThis is very important good news for me to pass along to the K - 12th grade teachers that I coach in mathematics instruction ! I often I hear (from both teachers and parents) that all the interactive, exploratory, engaging active learning that students get prior to college will go out the window once they are in college. Now I have great evidence that this is not the case anymore!

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David Spangler- 4/26/2017 6:12:20 PMMany universities are moving towards providing more online classes -- including math methods classes going totally online. I am interested in hearing from folks about their view as to whether or not active learning as described here by NCTM can REALLY occur in a totally online environment.

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Janie Merendino- 4/27/2017 1:51:42 PM## Reply processing please wait...

Jason Libberton- 4/26/2017 4:44:41 PMI suggest that another erroneous assumption is that teaching in a lecture-based format WILL prepare them for success in college. I think we've tried that approach long enough to conclude that it works for a small minority--a minority that would likely succeed in those college classes anyway.

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Gloria Mitchell- 4/26/2017 10:03:08 PMExactly what I was thinking. Most college-age students can sit still and listen when this is required. But can they reason mathematically and represent their ideas about mathematics? Can they draw on a range of problem-solving strategies? Can they ask worthwhile questions? Are they curious? Do they have experience with mathematics as an engaging, enjoyable subject that is worth learning about? Even if all college classes were composed of lectures, it's by no means certain that a high school diet of lectures would prepare students to succeed in them.

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John Golden- 4/26/2017 4:43:29 PMThere is no better preparation for college than deep understanding. In our university's math classes, active learning is the expectation. So if a high school teacher were worried about mode of instruction, that might be the style for which to prepare. Granted, we hire for great teaching, but in applications for our search this year there was more evidence than ever before that actual teaching is becoming common in colleges across the country. Even R1 research schools run teaching seminars for graduate students. Add in the hope that there are some future STEM professionals among your high school students and there is a great need for them to start learning how to problem solve.

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Michael Wiernicki- 4/26/2017 4:18:43 PMMatt,

This is fantastic! It's exciting to hear that the post-secondary math world is making the shift and that practices are changing. This is definitely something to share across our district, as I've heard the "that won't prepare them for college" argument. I'm especially hopeful for the college students who will gain an appreciation for math through the sense making and inquiry they engage in as they learn "college math."

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