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LEWISBURG, Pa. — Lynn Breyfogle, professor of mathematics and director of the Writing Program, talks about Common Core State Standards for mathematics, and writing.
Q: You are the chair of a task force of the Association of Mathematics Teacher Educators working on issues related to the implementation of the Common Core State Standards. What are the standards and why are they important?
A: The Common Core State Standards Initiative is a state-led effort to establish a shared set of educational standards in language arts and mathematics, spearheaded by the National Governors Association for Best Practices and the Council of Chief State School Officers. As of today, 46 states and territories have adopted them.
The CCSS are not national standards, nor are they a national curriculum. According to the U.S. Constitution, education is a state right, and the Federal Government cannot directly impose educational policy. Certainly the Federal Government can impose its influence by creating programs like No Child Left Behind that tie Federal monies to education. However, even with No Child Left Behind, it was up to the individual states to create and determine their own measuring sticks. These measuring sticks are wildly different from state to state.
Educators and policy makers have been arguing about creating national standards for decades. Philosophically I am opposed to national standards, but practically speaking we must have some sort of accepted set of understandings about what mathematics should be taught and at what grade level. If you look at countries whose students in eighth grade have scored the highest on the TIMSS studies — Singapore, Japan, Hong Kong, and Taiwan — they all have national standards. There needs to be some sort of common language and consistency across the states, for the kids' sake, especially those who find themselves frequently uprooted and transient populations.
The CCSS is not the end of the discussion; it is really the beginning. It will be a living document that will be revised and refined as we continue to learn and research how children best learn mathematics.
My role as chair of this task force is to help other mathematics teacher educators, who prepare future teachers and provide professional development to current teachers, develop materials and resources for math teacher educators to use to educate their students about CCSS and its implications.
Q: How would you describe the state of U.S. math education?
Certainly we can always make it better; I don't think it has gotten worse. If you look at the Trends in International Mathematics and Science Study (TIMSS) of 2007, we're in the top 10 of countries who have participated in the study. In 1995, we were 24th of the countries that took it.
We have work to do to improve our mathematics education. The area I would like us to focus on is quantitative literacy rather than basic skills. People are not generally quantitatively literate. I really worry about individuals' personal financial choices, for example, when they do not understand the mathematics behind credit cards and mortgages.
In K-12 education, we are too focused on the mathematics for preparing students for college; what we need to focus on are the more quantitative elements of mathematics — concepts within statistics like appropriate graphical representations, or in algebra like the idea of compound interest and functions related to compound interest.
It's possible to investigate the financial aspects of mathematics within algebra courses in high schools, but often these examples aren't used. Historically, students see mathematics as a dichotomy of school math and real-world math. Very often, the research shows, as soon as kids enter a math classroom, they are no longer thinking about real-world math. They've disconnected school math from real math.
Q: In your work with education majors here at Bucknell, you are teaching future mathematics teachers how to teach mathematics. What are the most important skills or pedagogical methods a new math teacher must have to be successful?
A: We talk about teachers developing a set of knowledge called "mathematical knowledge for teaching," which is not strictly content knowledge, or strictly pedagogical knowledge, or even pedagogical content knowledge. It is a set of knowledge that allows a teacher to not only understand the content she is teaching, and how she should teach it, but also to understand how her students might be thinking about it, be able to analyze the students' thinking, and pose counterexamples or develop on the spot additional problems to challenge or press students' thinking.
For example, if a teacher wants to help students understand what is happening in the product 1 ½ x 2/3, she needs to be able to think about appropriate and inappropriate models she might use — area models, set models or measurement models. She has to think about what models would be best to use in this situation and what problems exist with the various models. She must anticipate the students' misconceptions and help to guide their thinking.
Most importantly, I want to help develop in future teachers an attitude and propensity toward them developing their own mathematical knowledge for teaching. There is not enough time during the classes they have with me for me to dump everything they need to know into their heads, but if I can help them to understand what kind of knowledge is important, they can be life-long learners and continually develop their professional knowledge.
It is also important, especially for future high-school teachers, to recognize that mathematics is a growing body of knowledge. Much of what they will be teaching is the same that they experienced; however, new mathematics is created and understood each year and may show up in the high school classroom.
Q: You are also the director of the Writing Program; what's the connection between mathematics and writing?
A: The director of the Writing Program is a rotating faculty position, and some people find it odd that this post is held by a mathematician. Bucknell's program is a writing- across-the-curriculum model in which we are committed to our students learning to write effectively, no matter their discipline.
Writing is an important skill in which all college graduates should be competent. No matter what profession one enters, written communication will be a part of his responsibilities. Whether it is composing memos to clients and colleagues or business reports to stockholders or even letters home to parents, writing will be a part of the job. Developing concise and well-crafted writing with clearly articulated arguments takes years to develop, which is part of the reason we require students to take three writing intensive courses.
The writing program is more than focusing on a final product. It is about helping students to understand that writing is a process and when they read a journal article or research study or book, they recognize that much planning, revision and editing took place in addition to the composing.
Writing is also an important way to learn content. Research shows that during the process of writing, a learner can understand more if they have tried to articulate their thoughts in writing. So writing to learn is an important part of any class, no matter the content. Even in mathematics, we use writing to learn so that students fully understand what they're supposed to be learning.
Interviewed by Kathryn Kopchik
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