*In this monthly column, we speak with a notable member of the mathematics education community about their work and their perspectives on the teaching and learning of mathematics. This month, we had the pleasure of speaking with Steve Leinwand, who we look forward to welcoming this fall as a SUM Conference 2017 keynote presenter.
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*Steve Leinwand** is a Principal Research Analyst at the American Institutes for Research (AIR) and has over 35 years of leadership positions in mathematics education. He currently serves as mathematics expert on a wide range of AIR projects that focus on high quality mathematics instruction, turning around underperforming schools, evaluating programs, developing assessments and providing technical assistance. Leinwand has spoken and written about effectively implementing the Common Core State Standards in Mathematics, differentiated learning, and “What Every School Leader Needs to Know about Making Math Work for All Students.” In addition, Leinwand has overseen the development and quality review of multiple-choice and constructed response items for AIR’s contracts with diverse states. *

*Before joining AIR in 2002, Leinwand spent 22 years as Mathematics Consultant with the Connecticut Department of Education, has served on the National Council of Teachers of Mathematics’ Board of Directors, and has been President of the National Council of Supervisors of Mathematics. Steve is also an author of several mathematics textbooks and has written numerous articles. His books, *Sensible Mathematics: A Guide for School Leaders in the Era of Common Core State Standard*s and *Accessible Mathematics: 10 Instructional Shifts That Raise Student Achievement*, were published by Heinemann in 2012 and 2009, respectively. In addition, Leinwand was the awardee of the 2015 National Council of Supervisors of Mathematics Glenn Gilbert/Ross Taylor National Leadership Award for outstanding contributions to mathematics education.*

*First things first, thank you for taking the time for this conversation! *

*With over 35 years of leadership positions in mathematics education that span consulting, evaluation, program development, research, and more, you have surely observed many changes in curriculum, pedagogy, assessment, and philosophy in the area of mathematics teaching and learning at the primary and secondary levels. *

*In your view, what are we doing better today in the area of mathematics education, in comparison to 35 years ago?*

I am very optimistic and believe that nearly every aspect of the teaching and learning of mathematics is better than it was 35 years ago. In terms of curriculum, particularly in Grades K-8, we have moved from fragmented, repetitive and overwhelmingly skill-based mathematics to fewer and clearer standards, and more teachable mathematics based on coherent progressions that significantly eliminate duplication. In terms of instruction, we have moved from worksheet and practice-driven teaching-by-telling to more problem-driven, activity-driven learning-by-doing. And every year reveals important shifts in assessment away from primarily multiple-choice assessment of skills to far more open-ended, constructed-response assessments of a balance of skills, concepts, and applications. It’s not just my optimism or seeing things through rose-colored glasses: rather, these changes are reflected in consistently higher scores on a range of reliable measures of student achievement. Back in 1990, only a dismal 13 percent of US fourth graders were deemed proficient or above on the National Assessment of Educational Progress. In 2013, this had grown significantly to 42 percent! This is still far short of where we need to be, but it is certainly clear evidence of real change and improvement.

*And where do you see there being greatest room for improvement?*

[No longer just frills or add-ons, collaborative structures and coaching must be seen as essential components of a system where our goal of high levels of mathematics for all students can be met.

*The National Council of Teachers of Mathematics’ (NCTM) *Curriculum and Evaluation Standards for School Mathematics *(1989) and, then, the *Principles and Standards for School Mathematics* (NCTM, 2000) have been major drivers of changes in the teaching and learning of mathematics in the past, and are still influential today. As Alan Schoenfeld (2004, p. 266) wrote, “none of the authors or others involved in the production of the [1989] *Standards* had any idea of what the ultimate magnitude of the response to their document would be,” and yet they spurred “a highly creative design process during the following decade” (p. 268) as a “‘standards movement’ took the nation by storm” (p. 269), setting in motion changes to curriculum, pedagogy, and materials across the country—and indeed, the continent, influencing as they did the Western and Nothern Canadian Protocol (WNCP).*

*What do you see as being the greatest drivers of change in mathematics education today, and in the coming decades?*

I see four powerful levers or drivers of change in mathematics education: all, resources, tests and technology.

*all.*This push from some to all, and its implications for curriculum and instruction is a prime driver. Second, the internet and the amazing range of free, or essentially free, resources – many of very high quality – have also resulted in significant change and improvement. I have been overjoyed by the use of three-act lessons [first introduced by California teacher Dan Meyer –

*Ed.*], Desmos activities, great tasks, virtual manipulatives, and much, much more to improve student access to and engagement with mathematics. Third, our tests seem to get better every year and also drive change and improvement as constructed-response replaces multiple-choice and computer-adaptive replaces fixed-form paper-and-pencil. Finally, when any 15-year-old can use his or her smartphone’s calculator and a free download of Desmos, we have changed the game from expensive graphing calculators and web-based applications requiring internet access to readily available tools that, when used appropriately, change what math is important and how best to teach this math for understanding. Coupled with the power of display that emerges from interactive white boards and document cameras, technology is the fourth critical driver of powerful changes in teaching and learning.

*In Leinwand (2009, par. 1), you suggest that “a strong K-12 mathematics program [is] at the heart of America’s long-term economic viability,” given that long-term economic security and social well-being are linked to sustained innovation and workplace productivity, which in turn rely on high-quality education in the areas of literacy, mathematics, and science. *

*And yet, with the proliferation of technology, it is clear that the world does not need human calculators solving artificial problems that can be computed in milliseconds by a pocket calculator or smartphone. *

*If this is the case, what kinds of skills and habits of mind can students develop during their mathematics education that are relevant and necessary in the modern world, and how has mathematics curriculum and pedagogy changed—or should change—to emphasize these skills?*

My touchstone for what is non-negotiable for preparation for the 21st century world of work and effective citizenship is the first four Standards for Mathematical Practice delineated in the Common Core. That is, when *all *students can persevere and solve problems, reason quantitatively and mathematically, model with mathematics and most importantly, construct viable arguments and critique the reasoning of others, we have truly prepared our students for an ever-changing and increasingly complex world. Every mathematics lesson and every mathematics assessment must be planned and implemented with these four practices in mind. If there are no problems to solve in a lesson, if students are not asked “why?” or “can you convince us?” to construct an argument and demonstrate reasoning, and if the lesson is essentially about how to find an answer without understanding, then we know we are *not* preparing our students with the skills and understandings and practices they really need.

*You have spent some time studying high-performing education systems around the world (e.g., Singapore; Ginsburg, Leinwand, Anstrom, & Pollock, 2005) in an effort to unearth high-impact practices in mathematics education.*

*In a nutshell, what can North America learn from the mathematics education programs in countries such as Singapore?*

What we learned in our study of Singapore’s impressive mathematics program was very simple: First, there is high quality to each of the components of their program, and second, there was strong alignment among each of these components. That is, Singapore Math is not just a textbook, a philosophy, or a system of assessment. Rather, K-6 mathematics in Singapore is based on a clear and coherent set of standards, strong instructional materials, and effective teaching supported by impactful professional development, and is held together with high quality assessments, where each of these components is carefully and closely aligned with the others. Our study of Singapore math helped to influence the Common Core Standards movement in the US with a much more coherent set of standards and higher-quality, aligned assessments. The market has since provided increasingly aligned curricular materials.

*And which aspects of these programs do *not* transfer well—due to cultural differences, or otherwise—to mathematics education programs in North America?*

Where there remain gigantic gaps between Singapore and North America is in the domain of teacher recruitment, training, induction, and support.

However, where there remain gigantic gaps between Singapore and North America is in the domain of teacher recruitment, training, induction, and support. In Singapore, teacher trainees are paid throughout two years of intensive training in both mathematics and the teaching of mathematics (granted, Singapore is a city-state about the size of Chicago). Singapore teachers then serve as interns during an intensive year of induction, only observing their colleagues and co-teaching. Even during their second year in schools, Singapore teachers are very closely supervised and mentored, finally becoming independent practitioners in their third year, during which they now mentor first year teachers. Obviously, there is a lot that we in North America have to do to begin to replicate practices like this.

*You have often discussed the importance of coherence and alignment in mathematics curricula between goals, materials, instruction, assessment, and so on (e.g., Leinwand, 2009, 2012). As you write in Leinwand (2012, par. 7), in the context of presenting strategies to improve an underperforming mathematics education program: “You need a coherent and aligned curriculum that includes a set of grade level content expectations, appropriate print and electronic instructional materials, with a pacing guide that links the content standards, the materials and the calendar.”*

*You have also, however, applauded the growth of online resources available for teachers, such as Dan Meyer’s **three-act tasks**, Andrew Stadel’s **Estimation 180 lessons**, and more (Editorial, 2015). Many of these resources have been developed by individual classroom teachers or consultants, rather than teams of curriculum developers.*

*Is there a tension here—that is, a tension between a desire for coherence and the (ever-increasing) diversity of readily-available resources? Is coherence possible in the digital age, where teachers pull together content from a variety of resources (high-quality or otherwise) during their lesson planning*

Since no one resource is likely to align perfectly with the selected standards, it is entirely appropriate to carefully pick and choose from the growing wealth of on-line resources.

*Lastly, our readers are likely aware that you will in Saskatoon this November to present as a keynote speaker at our very own Saskatchewan Understands Math (SUM) Conference. (We can’t wait!) We don’t want to spoil the surprise, but could you give our readers some insight into what you will be discussing during your sessions?*

I have been blessed to have been asked to give between five and ten such keynote talks each year. Accordingly, since I tend to get bored faster than anyone in my audience, I have tried to create a new keynote or major talk each year that I massage and revise over several months and then retire from my repertoire. This year’s theme is designing lessons that incorporate the eight Mathematics Teaching Practices presented in NCTM’s Principles to Actions. So my SUM talk will explore and model a lesson development process that includes goals, tasks, representations, discourse, questions, fluency, struggle, and evidence, all rolled up into an accessible process that supports effective teaching.

*Thank you for taking the time for this conversation. We look forward to continuing the discussion at SUM Conference 2017!*

*Ilona Vashchyshyn*

**References
**Editorial: Steve Leinwand’s bets online math resources. (2015, October 19).

*Heinemann.*Retrieved from http://www.heinemann.com/blog/leinwand-qa-10-19/

Gingsburg, A., Leinwand, S., Anstrom, T., & Pollock, E. (2005). *What the United States **can learn from Singapore’s world-class mathematics system (and what Singapore can learn from the United States): An exploratory study.* American Institutes for Research.

Leinwand, S. (2009, January 5). Moving mathematics out of mediocrity. *Education Week. *Retrieved from http://www.edweek.org/ew/articles/2009/01/07/16leinwand.h28.html

Leinwand, S. (2012). Building a sustainable foundation for a successful turnaround in mathematics, or behind the curtain at Hazelwood East Middle School. Retrieved from http://steveleinwand.com/wp-content/uploads/2014/08/Behind-the-Curtain-at-Hazelwood-East-Middle-School-Final-Draft.docx

National Council of Teachers of Mathematics. (1989). *Curriculum and evaluation standards for school mathematics.* Reston, VA: Author.

National Council of Teachers of Mathematics. (2000). *Principles and standards for school mathematics. *Reston, VA: Author.

Schoenfeld, A. H. (2004). The math wars. *Educational Policy, 18*(1), 253–286.