A new report from the Organisation for Economic Co-operation and Development (OECD), Ten Questions for Mathematics Teachers… and How PISA Can Help Answer Them, organizes key findings from the Programme for International Student Assessment (PISA) 2012 and the Teaching and Learning International Survey (TALIS) 2013 into a set of questions teachers can use to guide their instruction and move students to deeper learning.
The 2012 PISA focused on mathematics and the results indicated which countries had the highest- and lowest-performing students in this subject. Alongside the exam, students completed a background questionnaire with information about themselves, their home and school environments, and their learning experiences, particularly in mathematics classes. The OECD’s TALIS surveyed teachers worldwide for information about the number of years they had been teaching, their teaching methods, and the learning environment of their students, among other topics.
Using data from PISA and TALIS, the new OECD report explores many of the questions teachers may have about how best to achieve deeper learning in mathematics classrooms. For example, the report asks, “Should I encourage my students to use their creativity in mathematics?” For this question, the OECD report examines how teachers can use elaboration strategies to encourage students to make connections among mathematics tasks; link learning to prior knowledge and real-life situations; and solve problems in different ways by developing analogies and examples, brainstorming, and using concept maps. These strategies help students understand new information in mathematics and retain it over the long term. They also align with several research-based teaching practices, such as implementing tasks that promote reasoning and problem-solving and facilitating meaningful mathematical discourse, supported by the National Council of Teachers of Mathematics in its landmark publication Principles to Action: Ensuring Mathematical Success for All. Data from the OECD shows that students who use these kinds of elaboration strategies have greater success solving more complex problems.
“Regular opportunities to engage such practices not only supports deeper learning of mathematics but regularly answers the oft heard student chant of ‘when are we ever gonna use this stuff,’” said Francis (Skip) Fennell, professor emeritus and project director of the Elementary Mathematics Specialists and Teacher Leaders Project at McDaniel College, past president of the National Council of Teachers of Mathematics, and a panelist at the Alliance for Excellent Education’s (Alliance’s) recent webinar on the new OECD report.
The OECD report also explores another common question that teachers have: “Are some mathematics teaching methods more effective than others?” To answer this question, the report examines various cognitive-activation strategies, such as providing students with problems that engage them in questioning, summarizing, and predicting when solving problems. The data shows that students perform better when teachers use such strategies.
Unfortunately, not all students receive this kind of instruction. The OECD data shows that disadvantaged students have less exposure to both applied and deeper levels of mathematics, but stresses that teachers should “not shy away from challenging mathematics topics.” The report notes the following:
All students, regardless of their ability or socio-economic background, should be challenged in mathematics. While your students may not grow up to become mathematicians, they still need to know how to reason mathematically to be successful in later life. Be sensitive to the fact that challenging mathematics problems can increase anxiety in lower-performing students. Offer extra support for those students, but don’t avoid difficult topics or problem solving altogether.
“All students should be exposed to and engaged in high-quality mathematics activities which challenge them every day,” stated Fennell. “That said, ongoing professional learning and opportunities for teacher collaboration and support must be provided, at the elementary, middle, and high school levels, to not only promote but also to ensure curricular adaptations, use of activities, and resources which engage and support all students.”
Robin White, a second panelist at the Alliance’s webinar and a mathematics instructional support teacher in Howard County (Maryland) Public Schools, asked, “How can we accomplish these things?” White stressed the importance of collaboration as a professional practice and efforts to overcome potential obstacles, such as the lack of time that teachers have to work with each other and with new solutions, such as virtual or digital mediums.
“We must, on a daily basis,” Fennell added, “find ways to engage students in the many contexts of mathematics that provide a source of interest to them as well as a means to deepen their understanding of it.”
Abner Oakes is the director of outreach and strategic partnerships for policy to practice at the Alliance.
About Deeper Learning
Trends in the economy mean that the fastest-growing jobs are those that require problem solving and critical thinking, while those that require only routine manual skills will be in decline.
A 2012 report by the National Research Council concluded that deeper learning competencies—the ability to apply knowledge to new situations—are associated with better life and work outcomes.
Understanding the Need
On the 2012 Programme for International Student Assessment (PISA), a test that measures students’ abilities to apply their knowledge to real-world problems, U.S. fifteen-year-olds were 26th of 34 industrialized countries in mathematics.
Only 5 percent of U.S. low-income students performed in the top quartile on PISA, less than the proportion in other industrialized countries.
Deeper Learning in Schools
A 2014 study by the American Institutes of Research found that students in deeper learning schools graduated from high school and attended selective colleges at higher rates than comparable students in non-deeper learning schools.
A hallmark of deeper learning schools is the emphasis on encouraging students to take responsibility for their own learning, according to Monica R. Martinez and Dennis McGrath, the authors of Deeper Learning.