A Reflection on 25 Years in Mathematics Education
By NCTM President Linda M. Gojak NCTM Summing Up, April 1, 2014
Twenty-five years ago NCTM released Curriculum and Evaluation Standards for Teaching Mathematics, which presented a comprehensive vision for mathematics teaching, learning, and assessment in grades K–12. Other significant publications, including Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics continue to identify what we believe students should know and be able to do throughout their school mathematics experience.
Since this is my final President’s Message, I thought this would be a good time to look at what the mathematics education community has accomplished since 1989 and the challenges that we must continue to address.
Teachers in the Classroom
Accomplishment: The focus on the importance of mathematics education has grown over the last 25 years—faster than at any other time since the Sputnik era. The focus on STEM at the federal level, the development of standards led by the National Governors Association and Council of Chief State School Officers, and conversations among mathematicians, mathematics educators, and mathematics leaders have generated partnerships and projects that have the potential to radically improve mathematics education for our students.
Challenge: We must be certain that this information and these opportunities include classroom teachers and reach teachers in the classroom. While the focus on mathematics education is to be applauded, little will change if it doesn’t have an impact on the work we do with our students.
Accomplishment. Teacher preparation has increased in rigor and accountability. Credential and licensure requirements have become more stringent. Those interested in teaching can enter the profession by multiple pathways.
Challenge: We continue to have a shortage of qualified K–12 mathematics teachers. Too often elementary teacher preparation does not provide ample coursework to provide preservice teachers with the deep knowledge of mathematics content and pedagogy necessary to provide their future students with the mathematical foundation and productive disposition needed to ensure success in middle and high school mathematics courses. In many colleges and universities, methodology courses for future middle and high school mathematics teachers are not specific to mathematics teaching. A lack of focused work in building pedagogical content knowledge is likely to encourage teaching the way that we were taught rather than experiencing research-based effective teaching and learning practices that contribute to student success. As a variety of pathways for entering the profession continue to become available, guarantees for high-quality teachers must be in place. Too many teachers enter the classroom ill prepared to teach mathematics well through no fault of their own.
Accomplishment: Although many of us recall taking a learning theory course in our preparation, the direct connection between cognitive science and its implications for howwe teach children mathematics has become much more explicit in the past 25 years, influencing teaching materials, research in mathematics education, and classroom teachers. We now have a better understanding of how children make connections among mathematical concepts, and we can use that information for more meaningful instruction.
Challenge: Too many students continue to be taught through traditional show-and-tell methods to teach mathematics. The belief is that if students don’t get it the first time, we should show it bigger or explain it louder. Or perhaps show them another trick so that they will remember how to, say, divide fractions. Moving to teaching mathematics including rich tasks, developing thinking strategies, and making connections takes time, as well as ongoing high-quality professional development for teachers. We must find the financial resources and time to offer classroom teachers such opportunities. An additional challenge is that parents often do not understand the significance of teaching strategies based on cognitive science. Many did not learn mathematics this way and cannot help their children with what they consider “new math.” It is incumbent on us to find ways to provide parents with information and experiences so that they understand the significance of developing student thinking through meaningful experiences in mathematics. We must make it a priority to work collaboratively with parents to ensure the success of their children.
Accomplishment: Over the last 25 years, the quality of resources for teaching mathematics has improved. Curricular materials that are aligned with standards and apply what we know from cognitive science continue to be developed and updated. Advances in technology, including graphing calculators, tablets, and computer software, has affected what we emphasize in mathematics instruction and increased the importance of student reasoning and opportunities to make sense of mathematics.
Challenge: The quantity of resources has also increased. The Internet provides us with thousands of mathematics education resources. Technology has changed how we teach and what we teach, and efforts to align textbooks and resources with standards are pervasive. As educators we must make informed decisions about the teaching resources we choose. Claims that materials are aligned with the Common Core State Standards do not ensure that they are. Availability of materials on the Web is not a guarantee of quality. Teachers and students should thoughtfully consider when and how to use technology. Publishers must make a broad effort to provide teachers with the best possible resources for teaching. Teachers must recognize and demand high-quality textbooks and resources. We must realize that teachers are not curriculum developers. We cannot overestimate the importance of selecting materials that connect conceptual and procedural understanding.
Accomplishment: Classroom teachers recognize the importance of good research in mathematics education. The link between higher education and K–12 mathematics education has become stronger. Partnerships between classroom teachers, mathematics educators, and mathematicians, supported by private and publicly funded grants, continue to grow in number and impact.
Challenge: Although many classroom teachers participate in partnerships with their colleagues in higher education, even more do not have such opportunities. We must find ways to ensure that the important work and results of such partnerships reach more mathematics educators. We must continue to recognize and nurture the development of teacher leaders who continue to work in the classroom but who also have the potential to influence the work of their colleagues and the education of students.
This column brings me to the end of my term as president of NCTM. I want to thank everyone for his or her support over the past two years. It has been exciting, invigorating, and challenging. I think back to my early years in the classroom, and I am reminded of the incredible influence that NCTM had on me as a young teacher and continues to have on me today. I encourage all of you to get involved with NCTM and with your local Affiliates, and that you become active in mentoring your colleagues. Together, we will make a difference for our students!
Some final thoughts …
B. F. Skinner famously said, “We shouldn’t teach great books; we should teach a love of reading. Knowing the contents of a few works of literature is a trivial achievement. Being inclined to go on reading is a great achievement.” With apologies to Skinner, as mathematics educators we might say, “We should not just teach mathematics, we should teach a love of mathematics. Knowing the content of some mathematics is a trivial achievement. Being inclined to see the beauty in mathematics and to go on doing mathematics are great achievements.”