Originally published in TEACH Magazine, May/June 2018 Issue
By Adam Stone
There are indications that student math scores are slipping. Although the picture isn’t entirely clear, and while the situation is far from calamitous, it’s evident that at least some students are having a hard time making the numbers add up when it comes to standardized math assessments.
Educators point to a number of reasons why the trend lines may be pointing downward. The issue may lie at least in part with the tests themselves: perhaps classroom work hasn’t caught up to changing assessments and evolving expectations.
Others suggest the problem may be inherent to the subject matter. “Learning math is really hard,” says Dr. Kevin R. Chandler, Assistant Professor of Mathematics and Head of the Math Lab at Beacon College in Leesburg, FL.
“To do a simple addition problem such as two plus five, a student must first know what both two and five mean, what it means to add, and the meaning of equality,” he says. “They must be able to understand how the numbers relate to each other and how the mathematical process of adding works. They then have to apply this knowledge and understanding to determine the correct answer. We then give the student a story problem which requires two other higher-order thinking skills: analysis and synthesis. That is expecting a lot of a child.”
How hard is it, really? To get a sense of where the issues may lie, we’ll take a look at some recent news about math scores, and then dive into a range of suggested solutions from educators.
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The Trend Lines
In the big picture, numerous indicators suggest a decline in math scores.
In fall 2017, Ontario’s Education Quality and Accountability Office sparked concern with its news about student proficiency in mathematics. Only half of Grade 6 students were meeting the provincial standard in math, while only 44% of Grade 9 students in applied mathematics did the same. The Toronto District School Board has since announced that just 28% of Grade 9 students in applied mathematics met the provincial standard.
National news from the U.S. is no more heartening. Between 2011 and 2015, math scores on the National Assessment of Educational Progress declined in 20 states. (That slide may be in check, though. On the 2017 assessment, 48 states showed no significant change in their Grade 8 math scores compared to 2015.)
The most recent stats from the Program for International Student Assessment, or PISA, showed that in math, the U.S. scored 470, below the international average of 490. Average scores ranged from 564 in Singapore to 328 in the Dominican Republic.
State and local figures are no more encouraging. The number of third-graders who met or exceeded state expectations on Massachusetts’ new standardized test MCAS 2.0 fell by more than 20 percentage points last year, with smaller drops in other grades. In the St. Paul Public Schools district, only 35.5% of students scored proficient or advanced on the math portion of the Minnesota Comprehensive Assessments, a 2% drop from the previous year. It was the fourth straight year of declines for students in Grades 3–8.
The news is hardly encouraging, but educators say there is much that can be done in the classroom to boost student test scores and to elevate students’ overall understanding of mathematical concepts.
Tips and Tools
In its guidance to top-achieving schools, known as Blue Ribbon Schools, the U.S. Department of Education encourages a strong focus on thoughtful curriculum development.
“Curriculum content and standards Blue Ribbon Schools use are coherent, focused, and demanding mathematics curriculum that reflect the logical and sequential nature of mathematics,” the Department notes. “Students move from mastering basic computational skills and number concepts to more complex ideas and mathematical reasoning, including problem-solving. Schools expect students to know math concepts and be able to apply them in a variety of settings. All teaching is aligned with district and state standards in mathematics.”
This strong structural approach at the top level should help to drive positive classroom outcomes. State and local governments, too, can play a role in helping boost scores. New York state for instance, has been steadily increasing the number of questions it releases to the public from its standardized tests. In 2017, the state made public 75% of the questions from the Grade 3–8 math tests. By allowing teachers and parents to review questions and answers, the state aims to boost educators’ ability to steer student progress.
While these top-down initiatives can help move the needle, experts say, even more can be done at the classroom level.
Amber Gentile, EdD, Assistant Professor of Teacher Education at Cabrini University, encourages K–12 teachers to look beyond the next exam. “Teachers feel pressured to cover set topics and materials due to standardized testing. As a result, they may find themselves ‘teaching to the test.’ The trend seems to be a very regimented and prescribed teaching of math,” she says.
This approach “does not lend itself to generalizability or a deep conceptual understanding. We need to remember the true goals of math, which should be about learning deductive reasoning, being prepared for further learning of advanced math and science concepts, and being able to understand the information around us in life.”
How do we get to this new orientation? Gentile says it is up to the teacher to establish a mode of instruction that focuses on developing the student’s own problem-solving skills.
“Rather than the current practice of providing students with a formula and then having them apply it to a specific problem, we should be teaching students to figure out how to solve a problem, having them figure out the formulas,” she said. “Teach students how to think conceptually and how to deduce what is needed to solve problems.”
Frank Milner is President of Tutor Doctor, a worldwide in-home tutoring company. He offers several strategies for boosting math proficiency:
- Consider the student’s point of view: Before trying to take control of a problem, teachers should first listen to their students regarding the situation. Ask the student if they are feeling stressed or overwhelmed, or what they are struggling with in particular. Often times, having a conversation with a student can identify factors causing a negative performance. Through dialogue and asking questions, teachers can create a more focused plan that addresses their student’s academic problems.
- Focus on mastering one topic before moving onto the next: A math curriculum is designed in a sequence that has topics build upon one another into more complex topics. Algebra leads to Geometry, which is then followed by Trig and Pre-calculus. Therefore, if a student is having a problem with a topic, continue working with them on that one topic until they’ve gotten a grasp of it and can work problems successfully. Only then should they move onto another subject.
- Be open to making mistakes: While we all want a perfect score on an exam, students learn the most when they have a setback. Mistakes require us to examine our work to find out where an error occurs and learn what steps are needed to correct it. Educators can help in this process by showing students where things went wrong and turning it into a learning experience.
At St. Mark’s Episcopal School in Fort Lauderdale, FL, Principal Kathleen Rotella acknowledges math can be a steep hill to climb. “You are always going to have some students who struggle with math. It may not come as easily as other subjects, for some students,” she says. But there are things teachers can do to help the stragglers along.
“You need to have support from home,” she notes. “Get the parents engaged. If a mother is cooking she can go through the measurements with the child. Math is all around us in our day-to-day tasks, and teachers can encourage parents to have those conversations with their children.”
Collaboration at the classroom level is another key to success. Rotella’s Grade 6–8 teachers routinely get together to review test scores and student progress. If Grade 7 students are missing key concepts, the Grade 6 teacher can beef up that part of the curriculum, and the Grade 8 teacher can be ready with remedial materials if needed.
Finally, Rotella says, teachers can look to adjust the ways in which they approach the subject on a macroscopic level. Rather than rush to solutions, educators need to slow math down, stretch out the process in order to give students room to find their way.
“Teachers can ask more ‘why’ questions. Instead of immediately giving students the answer, you want to ask leading questions and give them time to work it out,” she says. “We sometimes jump in too quickly as teachers, wanting to help the child get to the answer, but they first need time to understand what the question is asking them. They need time to work out the problem for themselves.”
Adam Stone is a seasoned journalist with 20+ years’ experience. He covers education, technology, government, and the military, along with diverse other topics.
