Standards, how did we get here? A history lesson in collaboration
by Nancy Sattler
When I was in graduate school in the 1980s, getting a master's degree in mathematics education, my professor had us review the National Council of Teachers of Mathematics (NCTM) draft standards. As it was my first time being exposed to standards, I was eager to read about them, and apply those standards to my own teaching as a mathematics teacher at a two-year college. In 1989, NCTM developed the Curriculum and Evaluation Standards for School Mathematics, followed by the Professional Standards for Teaching Mathematics (1991) and the Assessment Standards for School Mathematics (1995). The curriculum standards called for greater emphasis on conceptual understanding and problem solving informed by a constructivist understanding of how children learn. After completing my masters’ degree and being hired full time at Terra Community College, my goal became clear. I wanted my students to be critical thinkers and problem solvers.
In the early 1990s, the AMATYC leadership formed a task force on distance education. I was appointed the chair. Some members of the task force were enthusiastic about teaching at a distance while others were more hesitant and were fearful of what could happen to their teaching load because of distance learning. The task force created a white paper on Distance Education, a precursor to the first Distance Learning Position Paper. Over the years, the position paper has been revised, with the latest revision made in 2019 (https://amatyc.site-ym.com/page/GuidelinesPositions). It advises faculty to maintain high standards and use research-based practices.
In 1995, AMATYC released its first standards document, Crosswords in Mathematics (https://amatyc.site-ym.com/page/GuidelineCrossroads), which emphasized desired modes of student thinking and guidelines for selecting content and instructional strategies. Three sets of standards were developed in the context of the calculus reform movement and NCTM’s initial standards. These standards were intended to revitalize the mathematics curriculum preceding calculus. It also aimed to stimulate changes in instructional methods so that students would be engaged as active learners in relevant mathematical tasks. The Standards for Intellectual Development addressed desired modes of student thinking and included problem-solving, modeling, reasoning, connection with other disciplines, communicating, using technology, and developing mathematical power. The Standards for Content provide guidelines for number sense, symbolism and algebra, geometry, functions, discrete mathematics, probability and statistics, and deductive proof. The Standards for Pedagogy recommend the use of instructional strategies: teaching with technology, interactive and collaborative learning, connecting with other experiences, multiple approaches, and experiencing mathematics. The document was a collaborative effort with members of the National Steering Committee from the American Mathematical Society, the National Council of Teachers of Mathematics, Mathematical Science Education Board, and the American Association of Community Colleges.
In 2000, NCTM used a consensus process involving mathematicians, teachers, and educational researchers to revise its standards with the release of the Principles and Standards for School Mathematics, which replaced all preceding publications. The new standards were organized around six principles: equity, curriculum, teaching, learning, assessment, and technology; ten strands which included five content areas: number and operations, algebra, geometry, measurement, and data analysis and probability; and five processes: problem-solving, reasoning and proof, communication, connections, and representation. Principles and Standards was not perceived to be as radical as the 1989 standards and did not generate significant criticism. The new standards have been widely used for textbook creation, state and local curricula, and current teaching trends.
Originally written in 2005, endorsed by the American Statistical Association (ASA), and revised in 2016, The Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report (https://www.amstat.org/asa/files/pdfs/GAISE/GaiseCollege_Full.pdf), offers six recommendations for teaching introductory statistics at both two- and four-year institutions: (1) teach statistical thinking. Teach statistics as an investigative process of problem-solving and decision-making. Give students experience with multivariable thinking; (2) focus on conceptual understanding; (3) integrate real data with a context and purpose; (4) foster active learning; (5) use technology to explore concepts and analyze data; (6) use assessments to improve and evaluate student learning. The report also includes suggested learning objectives for introductory statistics courses.
In 2006, Beyond Crossroads: Implementing Mathematics Standards in the First Two Years of College (http://beyondcrossroads.matyc.org/doc/PDFs/BCAll.pdf) was written and released by AMATYC. It was reviewed by the American Mathematical Society Committee on Education, American Statistical Association/AMATYC Joint Committee on Statistics, Mathematical Association of America, National Association of Developmental Education and the National Council of Teachers of Mathematics. It was considered bold and visionary and included a set of Implementation Standards: Student Learning and the Learning Environment, Assessment of Student Learning, Curriculum and Program Development, Instruction, and Professionalism. The document called on faculty to continuously improve by being student-centered and providing an active learning approach guided by research in learning theory. Faculty were reminded to use technology to enhance conceptual understanding using research-based strategies. Distance Learning was addressed for the first time in an AMATYC standards document. Faculty were advised to provide access and equity for all students and utilize effective instructional design practices when developing and implementing distance learning courses in mathematics. I was a section writer for this document.
By 2009, schools across the country had adopted various standards, with each state having their own definition of proficiency. This lack of standardization was impetus for the development of the Common Core State Standards. The K-12 standards in English language arts and mathematics, created and adopted in 2010, detailed what students were expected to know and be able to do by the time they graduated from high school. Content standards and standards for mathematical practice were developed (http://www.corestandards.org/wp-content/uploads/Math_Standards1.pdf). Teachers were involved in the standards by serving on work groups and feedback groups, while state teams were created to provide regular feedback on the standards. I was part of the Ohio team and later became a member of the Ohio Educator Leader Cadre to promote the Common Core State Standards (CCSS) and the Common Core Assessments (CCA). In the past 10 years, various states have created their own version of the CCSS and have continued to update them on a cyclic basis, but the eight standards for mathematical practice (http://www.corestandards.org/Math/Practice/) are widely accepted. Those standards include: Make sense of problems and persevere in solving them; Reason abstractly and quantitatively; Construct viable arguments and critique the reasoning of others; Model with mathematics; Use appropriate tools strategically; Attend to precision; Look for and make use of structure; and Look for and express regularity in repeated reasoning.
In 2015, the Mathematical Association of American published its 2015 CUPM Curriculum Guide to Majors in Mathematical Sciences (https://www.maa.org/sites/default/files/CUPM%20Guide.pdf), a follow-up to the guide published in 2004. The MAA relied on response groups to offer feedback to the document. This group consisted of members of the Conference Board on the Mathematical Sciences: American Mathematical Association of Two-Year Colleges, American Mathematical Society, American Statistical Association, Association of State Supervisors of Mathematics, Association for Symbolic Logic (ASL Committee on Logic Education), Association for Women in Mathematics, Casualty Actuarial Society, Society of Actuaries, Society for Industrial and Applied Mathematics, and Society for Mathematical Biology. The focus of the guide is on curriculum with some mention of pedagogy. Topics include calculus, linear algebra, data analysis, preparation for graduate education, and beyond the curriculum. I was able to read the draft document and respond to it.
Also in 2015, the Mathematical Association of America called together members of 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) to focus on creating a common vision for modernizing undergraduate programs in the mathematical sciences. Each of these five societies had published curricular guides, some written without intense collaboration with the other associations, each sending the message that the status quo was unacceptable. A Common Vision for Undergraduate Mathematical Sciences Programs in 2025 (https://www.maa.org/sites/default/files/pdf/CommonVisionFinal.pdf) examined these guides to identify common themes and articulate a coherent vision of undergraduate programs in the mathematical sciences that all five associations would endorse and disseminate. The ultimate goal of Common Vision was to galvanize the mathematical sciences community around a modern, cohesive, vision for undergraduate programs. The document called on members of the mathematical sciences community to (1) update curricula, (2) articulate clear pathways between curricula driven by changes at the K–12 level and the first courses students take in college, (3) scale up the use of evidence-based pedagogical methods, (4) find ways to remove barriers facing students at critical transition points (e.g., placement, transfer) and (5) establish stronger connections with other disciplines. I was a member of the Common Vision 2025 Conference Working Group.
First published in 2016, and revised in 2019, GAIMME: Guidelines for Assessment and Instruction in Mathematical Modeling Education (https://www.siam.org/Portals/0/Publications/Reports/GAIMME_2ED/GAIMME-2nd-ed-final-online-viewing-color.pdf), was a collaborative effort of the Consortium for Mathematics and Its Applications (COMAP) and the Society for Industrial and Applied Mathematics (SIAM). This document includes three guide levels: early grades, high school, and undergraduate. It defines mathematical modeling and discusses the teaching of mathematics through modeling.
In 2018, AMATYC's newest document, IMPACT: Improving Mathematical Prowess And College Teaching, was published (https://cdn.ymaws.com/amatyc.site-ym.com/resource/resmgr/impact/impact2018-11-5.pdf). This document built upon AMATYC’s first two standards documents and created four pillars of PROWESS: Proficiency, Ownership, Engagement, and Student Success. Of note is an entire chapter devoted to research, providing a blueprint for faculty. Collaboration on the document was evident with members of the National Advisory Council hailing from the American Mathematical Society, Association of Mathematics Teacher Educators, Carnegie Foundation for the Advancement in Teaching, Charlies A. Dana Center, National Association for Developmental Education, National Center for Developmental Education, National Council of Teachers of Mathematics, National Council of Supervisors of Mathematics, Transforming Post-secondary Education in Mathematics, and TODOS: Mathematics for ALL. Along with Mary Beth Orrange, I co-chaired the writing of this document.
Standards are in place to guide faculty in the teaching and learning of mathematics. Because of my interest in standards, and the changes that have occurred since I began teaching as an adjunct faculty in 1983, I am a firm believer in professional development for faculty. This can be done by taking part in discussions either in person or on-line, such as those on IMPACTLive! (https://my.amatyc.org/home), reading scholarly newsletters and journals such as AMATYC News (https://amatyc.site-ym.com/page/AMATYCNews) and MathAMATYC Educator (https://amatyc.site-ym.com/page/MathAMATYCEducator), attending webinars either pre-recorded or live (https://amatyc.site-ym.com/page/Webinars) and by attending professional conferences such as the AMATYC National Conference (https://amatyc.site-ym.com/page/Conferences). The Fourth Annual National Math Summit (https://thenoss.org/event-3821542) is another opportunity for professional development. The summit is jointly sponsored by AMATYC, National Organization for Student Success (NOSS, formerly NADE), Carnegie Math Pathways, Charles A. Dana Center, Mathematical Association of American, and Paul Nolting. This is truly a collaborative effort bringing speakers from these entities together to share their expertise on such topics as active learning, affective characteristics, assessing student success, co-requisite models, equity, high-quality mathematics pathways in the first two years, mathematical rigor, multiple measures of placement, and supportive learning environment. I have had a part in the planning of the National Math Summits and look forward to attending and hearing about these topics. Whether the summit is held virtually or in person, it is sure to be a worthwhile event!
The status quo is unacceptable. As faculty, we need to be aware of updated standards, the research that has occurred, and best practices that can be used in teaching mathematics. We need to be life-long learners and adjust our teaching methods based on best practices and research.
How familiar are you with any of the standards documents that I have discussed? What questions do you have?
I look forward to reading your comments this month as the spotlight shifts to standards.