澳门跑狗论坛

Amid falling student scores and renewed debates about how the subject should be taught, math is in the spotlight once again.

The pandemic, which affected student learning across the board, had particularly devastating effects in math. Experts agree that supporting students in the subject will require time, money, and additional services like tutoring. But exactly what instructional approaches are likely to move the needle is the subject of decades-long debate.

The field is littered with enduring pedagogical disagreements. Among them:

• Whether teachers should spend more time explicitly teaching math procedures and content, or give students more time to puzzle out problems on their own;
• How to balance procedural knowledge, fluency, and conceptual understanding; and
• When鈥攊f ever鈥攊t makes sense to group students by ability in classrooms.

Those core disagreements are not easily resolved, in part because perspectives about explicit teaching vs. an inquiry-based approach map onto larger philosophical arguments about the purpose of education鈥攁nd in part because researchers in math education and cognitive science fields often come to different conclusions about what best practice should look like.

See Also

Open image caption

Close image caption

iStock/Getty Images Plus

Mathematics California Adopts Controversial New Math Framework. Here's What's in It

Sarah Schwartz, July 12, 2023

•

10 min read

Remove Save to favorites

As part of our coverage of math education, 澳门跑狗论坛 wanted to shed some light on where these divisions come from and why. To understand more about how teachers are prepared to teach math, the EdWeek Research Center surveyed a nationally representative sample of 373 postsecondary math and math education instructors in June and July of this year. Of this group, 126 taught only math courses, 142 taught only math education courses (typically as part of teacher education programs), and 105 taught both.

(The Bill & Melinda Gates Foundation provided financial support for the survey. EdWeek designed the instrument and maintains sole control over articles informed by the results.)

While K-12 teachers learn new content and techniques over time, this university education forms the foundation of their knowledge base鈥攁nd just as significantly, their philosophy of education.

This first of three stories on these survey results explores how math and math education professors shape their courses: Which scholars do they introduce to students? What documents do they rely on? And what topics and practices do they cover with aspiring teachers, and expect them to master?

In sum, the results show that programs teach a mix of strategies鈥攂oth explicit and more constructivist. They seem to rely less on empirical research than on textbooks and other materials; and special education gets less attention than some advocates would like. All of those findings are likely to raise fresh questions about whether programs are using the right recipe.

The experts who show up on math professors鈥� syllabi

When asked about which math scholars鈥�, experts鈥�, or practitioners鈥� work instructors introduce to their students, Jo Boaler topped the list, with 36 percent of math education and math instructors naming her.

Boaler, a professor of education at Stanford University, is a major figure in the math education world. Her work focuses on developing students鈥� math mindset鈥攈elping students see themselves as 鈥渕ath people鈥� who are capable in the subject鈥攁nd promoting equity in math classrooms.

鈥淚 would imagine that I鈥檓 high on the list because I have spent the last 10 years getting mathematics education out through the website YouCubed,鈥� said Boaler, referencing a Stanford hub for math activities, lessons, and teaching guidance. (An earlier EdWeek Research Center survey, of K-12 math teachers, found that no one source, including YouCubed, was dominant in teachers鈥� use of instructional materials.)

鈥淧articularly we wanted to get out the newer science that was out at that time that any student can get anything, and teachers should not promote the idea that some students don鈥檛 have a math brain,鈥� Boaler said.

Boaler has a devoted teacher following, and she recently served as part of the writing committee for the new California Math Framework, which in general reflects many of her ideas about math. But she also , who argue that she has overstated research findings to promote teaching methods that are not evidence-based. Boaler has pushed back against these claims.

About a quarter of respondents listed names not included on the list of response choices. In open-ended responses, several survey participants named historical mathematicians rather than math education scholars: Fibonacci, Brahmagupta, Euclid, Carl Friedrich Gauss, Leonhard Euler, and Ren茅 Descartes were all listed as examples. (Respondents to this question included both math education instructors and math professors who taught at least some future teachers.)

Still, many answers included well-known textbook authors, some of whom are or were also university professors, such as John Van de Walle, whose book Elementary and Middle School Mathematics: Teaching Developmentally was cited several times in open-ended survey responses. That finding makes sense given that many university instructors use textbooks or other instructional guides in their courses, said Sarah Powell, an associate professor of special education who studies math instruction at the University of Texas at Austin.

But it鈥檚 also a figure that gives her pause. 鈥淏ooks typically don鈥檛 undergo any peer review,鈥� she said.

This is in contrast to research articles in scientific journals, which go through a rigorous peer review process. In research universities, publishing in journals matters for career advancement, Powell said. It鈥檚 a factor that鈥檚 considered when academics are up for tenure. Writing a book often doesn鈥檛 carry the same weight.

鈥淭here鈥檚 this disconnect between what鈥檚 expected in research-heavy positions and what鈥檚 expected in other positions,鈥� she said. 鈥淢any people who write books don鈥檛 have a heavy research agenda.鈥�

Documents that inform math education courses

In addition to math education scholars, university instructors also use some core documents to inform their classes.

Many of these have direct classroom relevance. When asked what foundational documents they use to inform their courses or introduce to their students, 77 percent of math education instructors said that they used the Common Core State Standards or state-level standards. Seventy-four percent said they used publications from the National Council of Teachers of Mathematics. The teacher professional organization is the largest math education organization in the country, and that math learning 鈥渋s maximized when teachers focus on mathematical thinking and reasoning.鈥�

But other practice-oriented resources weren鈥檛 as popular. Only 16 percent of instructors said that they used the What Works Clearinghouse Practice Guides in math from the Institute of Education Sciences, the U.S. Department of Education鈥檚 research wing. The practice guides are based on empirical evidence, weighted toward random-assignment studies with control groups.

It鈥檚 a figure that troubled Nicole McNeil, a professor cognitive psychology who studies math learning at the University of Notre Dame.

鈥淚t鈥檚 the best thing that they could use in my opinion,鈥� she said, of the guides. 鈥淚 don鈥檛 know why it is that IES hasn鈥檛 seemed to be able to crack through the PK-12 space to be seen as a leader, as a place for guidance. But to me, in our tutoring program, that鈥檚 what we use. That鈥檚 our No. 1 thing. Because it鈥檚 so well-resourced.鈥�

The guides are written by researchers and outline best practices for specific grade levels, such as how to increase algebra knowledge in middle and high school students, or how to support problem-solving among 4th through 8th graders. They also include recommendations for interventions for struggling students.

When IES first started releasing these guides, they were focused heavily on findings from cognitive science and experimental psychology, rather than from the field of math education, which could have alienated researchers in that discipline, McNeil said. That鈥檚 since changed somewhat, but there鈥檚 still a 鈥渄isconnect鈥� between the fields, she said. 鈥淭he world of education and schools of education haven鈥檛 yet connected up with that world of experimental psychology, math cognition.鈥�

Other math educators weren鈥檛 as surprised to see that the What Works Clearinghouse practice guides didn鈥檛 top the list. 鈥淐lassroom teachers usually do not interact a lot with research,鈥� said Kyndall Brown, the executive director of the California Mathematics Project, a professional development network.

鈥淭hey might get it secondhand from someone who鈥檚 writing about the research. Very seldom are teachers reading journal articles or research articles,鈥� he said.

For Brown, guides and documents from organizations like NCTM are a viable alternative, he said: 鈥淸Teachers] are much more likely to read something like that than to read an actual research article.鈥�

Translating research into practice is a notoriously complex process for teachers and professional organizations.

How instructors use class time

Math education professors spend a large chunk of time working with future teachers on the skills they鈥檒l use in the classroom. The most commonly practiced strategies were using multiple representations, connecting new math content to prior knowledge, and explicitly modeling math skills and strategies.

Seeing that other practices were further down the list was 鈥渆xtremely disappointing,鈥� said Afi Wiggins, the interim managing director of the Dana Center, a math research and technical assistance organization at the University of Texas at Austin.

Wiggins would have wanted to see future teachers get more practice with what she described as 21st century skills鈥攊tems such as identifying and responding to misconceptions in math knowledge, and connecting math content to students鈥� personal or cultural knowledge. 鈥淭hat research has been out there for many, many years as critical to helping students learn,鈥� Wiggins said.

Teachers noted that the survey responses could obscure important differences in how these skills were taught. Take using multiple representations, for example, which was the most commonly cited answer.

Often, teachers are taught to show these representations with manipulatives. But the efficacy of manipulatives depends on how teachers use them, said Brian Bushart, a 4th grade teacher in West Irondequoit Schools in New York.

Sometimes, manipulatives can help show why math works the way it does and create an 鈥渁ha鈥� moment. But they could also lead to more confusion. Ideally, he said, teachers need to know: How do they prepare and coach a class so that the core math idea arises from use of manipulatives?

Math professors also reported frequent use of another strategy: productive struggle.

Productive struggle is the idea that math learners can benefit from puzzling out difficult problems, sometimes without much teacher prompting, even if it causes some discomfort.

鈥淢ore recently math educators have been trying to support classroom teachers to really get students engaged and share their thinking,鈥� said Brown. 鈥淚t makes sense to me that math educators would be modeling these kinds of strategies for their students to be able to take back into the classroom.鈥�

Productive struggle is also a key component of math education courses at Stanford, where instructors prepare teachers to use this approach in the classroom, said Boaler.

But productive struggle is hard to do well, because it鈥檚 based on finding the right level of challenge for each student, said Powell. 鈥淚f you鈥檙e doing that in a classroom of students, you cannot have one activity that meets all students exactly where they are and moves them forward.鈥�

Preparation for supporting student needs

The survey also asked teacher educators how much time they spent preparing future teachers to work with students who struggle in math, and students with math learning disabilities.

Fifty-eight percent of instructors said they spent up to a quarter of their course covering math learning disabilities.

鈥淥ne to 25 percent is not an amazing number,鈥� said Tara Warren, a math instructional coach in the Santa Monica-Malibu Unified school district. 鈥淏ut I thought it was better than it has been in the past.鈥�

The percentages didn鈥檛 surprise Wiggins, of the Dana Center. When she took math methods courses, she remembers them focusing extensively on creativity, but not as much on differentiated learning for students who might need more help or who have a learning difference. She did learn about differentiation, but in separate courses.

鈥淭hings are isolated,鈥� Wiggins said. 鈥淲hen I learned about differentiated instruction, it wasn鈥檛 in the context of content.鈥�

Approximately 5 to 7 percent of students have dyscalculia, a processing disorder that makes it harder to learn math, particularly how number symbols represent quantity. Many other students struggle more generally with math.

Powell, who studies special education, said the results about math disabilities didn鈥檛 surprise her either. 鈥淢any people draw a line in the sand for special education vs. general education,鈥� she said.

But the responses to a question about students who struggle more generally disappointed Powell. When teacher educators were asked what percentage of their courses they spent teaching educators to teach students who struggle with math, about half said less than 50 percent, and half said more than 50 percent.

Data from the National Assessment of Educational Progress show that the majority of students in this country struggle with math, she said, referencing students who scored below proficient on the test.

鈥淭hey鈥檙e spending less than 50 percent of their time thinking about how to support the majority of students who are in U.S. classrooms,鈥� said Powell. 鈥淚t doesn鈥檛 really match the percentage of students in the United States.鈥�

Data analysis for this article was provided by the EdWeek Research Center. Learn more about the center鈥檚 work.