This is a two-part series: Read Part 2
Robert Berry disagrees with the notion that – similar to drinking milk – kids either love or hate math.
The University of Virginia’s Samuel Braley Gray Professor of Education believes children enter the world as “emergent mathematicians, naturally curious, and trying to make sense of their world using mathematical thinking.”
The problem, according to Berry, is maintaining that curiosity, rather than suppressing it. He studies how teachers can foster such curiosity, as well as the national policy shifts and equity issues that impact how children are taught.
“Children’s experiences in mathematics must nurture and strengthen the curiosity and joy that they naturally bring to their learning and observations of the world,” he said. “Children are inquisitive and need teachers to be equally as curious about their mathematical observations, questions and insights.”
Too often, Berry said, children’s math experiences at the early childhood and elementary school levels are reduced to rote knowledge and skills.
“I believe that children do not hate mathematics; they may hate their experiences with mathematics that do not allow them to investigate their curiosities and experience joy,” he said.
In the first of a two-part series, UVA Today caught up with Berry, of UVA’s Curry School of Education and Human Development, to take a deeper dive into the subject.
Q. Do we have any idea how today’s kids in elementary school are performing in math relative to recent generations?
A. The National Assessment of Educational Progress is given every two years to a representative sample of students in the United States in grades four, eight and 12. Since 1990, the average mathematics score on “the Nation’s Report Card” has gone up 27 points at grade four. However, the trend has been relatively flat since 2009. In grade eight, we see a similar trend; since 1990, the average mathematics score on the Nation’s Report Card has gone up 19 points, but has been relatively flat since 2009.
Although the NAEP results are a cause for concern, we must view these results in the context of reforms over the past 30 years. What impact have reforms during this period had on mathematics teaching and learning? The significant gains were made during a period when specific funding was provided by the Dwight D. Eisenhower Mathematics and Science Education Act. This national policy and funding supported professional development for teachers to build mathematics content knowledge and to improve mathematics teaching practices.
I believe that the shift from the supports provided by the Eisenhower funds to the 2002 Elementary and Secondary Education Act, better known as the No Child Left Behind Act, had an impact on NAEP scores. The No Child Left Behind law brought educational reform with the premise that sanctions and accountability measures tied to funding would improve outcomes. No Child Left Behind assumed that solutions to issues of student achievement required increased accountability with a focus on testing. For many students, such a solution reduced instructional strategies to focus on rote knowledge covered on standardized tests and dissociation from higher levels of mathematics content and practices supportive of critical thinking, problem-solving and mathematical reasoning.
Q. Have the ways we’re teaching kids math changed over the years? If so, how?
A. Yes, teaching has changed over the years. Over the past 50 years, there have been advancements in research on mathematics teaching and learning, leading to shifts in curricular materials and teaching practices. The National Council of Teachers of Mathematics has identified a core set of eight research-informed effective teaching practices. Rather than discussing all eight practices, I will highlight some big ideas embedded in the eight practices.
Effective teaching of mathematics:
- Engages students in solving and discussing tasks that promote mathematical reasoning and problem-solving and allow multiple entry points and varied solution strategies.
- Engages students in making connections among mathematical representations (pictures, manipulatives, technology, words and numbers) to deepen understanding of mathematics concepts and procedures and as tools for problem-solving.
- Facilitates discourse among students to build a shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.
- Builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.
These ideas are a shift from focusing on memorization. Mathematics is more than getting an answer quickly. Effective mathematics teaching engages students in explaining why their answers make sense and why the strategy they used is appropriate.
Further, effective teaching situates mistakes and struggles as opportunities for growth in learning. Mistakes or struggles are not a sign of low intelligence. They are a normal part of learning. When teachers engage students in struggling productively, students are likely to develop deeper understandings of mathematics.
Q. Equity issues in children’s math education has been a big focus of your work, particularly pertaining to African American children. What have you found those issues to be? How big of a problem do you consider this to be?
A. Black children experience the following conditions in mathematics: a) reduced access to advanced mathematics courses; b) routine exposure to rote decontextualized learning, with little engagement in activities that promote reasoning and position mathematics as a tool to analyze social and economic issues, critique power dynamics and build advocacy; and c) less access to qualified teachers of mathematics who both understand mathematics deeply and understand black children’s cultural and community context genuinely to give them access to mathematical knowledge.
The cumulative effect of these conditions on black children’s attainment in mathematics constrains achievement to disproportionately low proficiency. Much of my work considers issues of race, racism, context, identity and social conditions as salient variables that impact the mathematical experiences of black children.
Q. Is it still considered OK for kids to use their fingers when they’re doing simple arithmetic?
A. It is more than OK for children to use their fingers in mathematics. Fingers are probably one of our most useful visual aids when engaged in mathematical concepts. My colleague, Jo Boaler, from Stanford University, discussed the use of fingers in mathematics in an article in The Atlantic. She stated, “The need for and importance of finger perception could even be the reason that pianists, and other musicians, often display higher mathematical understanding than people who don’t learn a musical instrument.”
In my work, I find that finger use is important for young children to anchor numbers around 5 and 10. For example, the number 7 can be understood as 5 and 2 more, as well as 3 less than 10. These anchors can be understood by using fingers.
By anchoring numbers around 5 and 10, it supports decomposing and composing numbers to build number strategies. Another example, 8 + 6 can be thought of as (5 + 3) + (5 + 1). Through decomposing 8 to 5 + 3 and 6 to 5 + 1, students can add the fives then add on the 3 and 1 to get 14. Such development is important for building understanding and development of strategies; thus, the use of fingers can be foundational to this development.
Next, Berry will offer tips for parents to help their kids find more joy and success in math.