Good afternoon and welcome to this month’s chat with NCTM President Cathy Seeley, who will be answering questions on her most recent President's Message, “Using Research to Improve Teaching.”
Our first question is from
Research or reactionary? It would appear that many decisions for curriculum are made by overreaction to issues or situations, such as low test scores, parent complaints, etc., rather than on good education principles. If we looked at research and NCLB what would it say about having all students reaching their grade level of performance? Someplace in the last year or so I read that most educational research was flawed in one direction or another to prove the point of the researcher. So even though NCLB is probably statistically impossible to reach who looked at the research when writing the law? So I would pose three questions: Who is going to check the research to make sure it’s correct? If there is good research why haven’t those in political arenas encompassed that research when writing legislation? Third, with good research available to educated people who represent us on board and in Congress, will they listen or still be reactionary because it gets votes?
Wow. Good questions. Your points emphasize the importance of educators working with policymakers to make sure that they have access to good information and current research findings. I think this can happen at the national level, with NCTM taking a leadership role in disseminating information. The Research Briefs and Research Clips being generated by NCTM this summer should help in this arena.
I would also encourage you and others to share appropriate findings with your particular Congressional representative and Senators, as you establish a relationship with them with you being viewed as a resource in mathematics teaching. It helps to reach out to such policymakers on a regular basis so that when they have to react quickly, they can call on you or have ready access to information. Communicating with a level of language that is accessible is very important in these settings. Again, as the Council’s Research Briefs and Clips are generated, these should be very helpful.
Is there research supporting that more time spent in math class or a second math class increases learning for the struggling learner?
Available research tells us that time is important, but how we use the time we have may be more significant. At some point, fatigue, motivation, and other factors may interfere with the potential benefits of spending more time on mathematics. In responding to questions, I’ll try to include specific citations when I can. The transcript posted after the chat may include more citations.
In terms of overall time spent on mathematics, several studies support the benefits of spending more time on mathematics. The 2001 National Research Council publication, “Adding It Up: Helping Children Learn Mathematics,” suggests that significant time should be devoted to daily mathematics instruction in every grade of elementary and middle school. Further, we know that there is a positive relationship between total time allocated to mathematics and general student performance (Handbook of Research on Improving Student Achievement (1999). Second Edition, Gordon Cawelti, Editor. p.118). Similar findings were reported following the 2000 National Assessment of Educational Progress (NAEP): The average scores of fourth and eighth graders generally increased as the amount of instructional time increased (The Nation’s Report Card: Mathematics 2000, NAEP, 2001).
In terms of the nature of the time spent, we can look at the 1999 TIMSS video study. In that study, Australia, Hong Kong, Japan, the Netherlands, and Switzerland [all higher performing than the U.S.] devoted more time, on average, to studying new content (ranging from 56 to 76 percent of lesson time) than reviewing previous content. In the U.S. there was no detectable difference between the average percent of lesson time devoted to reviewing previous content and studying new content—53 and 48 percent of lesson time, respectively (Highlights from the TIMSS 1999 Video Study of Eighth-Grade Mathematics Teaching, National Center for Educational Statistics, USDOE, March, 2003).
With the number of students that are placed in our classrooms, the limited resources we are given, and the number of non-English speaking students, it has become necessary to track students in math. This is the only way that we are able to ensure that the needs of all our students are met.
These are challenging times for teaching, especially as we strive for teaching every student high-level mathematics. I would respectfully disagree, however, that tracking is the only solution. In fact, there are examples of schools that have worked to maintain heterogeneity while raising expectations for all students. In particular, I can refer you to a charter school in San Diego called High Tech High. I would also encourage you to explore research conducted by Jo Boaler and her colleagues over several years at schools near Stanford University where she is on the faculty. Boaler has several publications related to the use of what she calls “equity-based teaching practices” in mathematics for diverse groups of students in low socio-economic settings. I know there are other examples as well, but these are the most familiar to me in support of not tracking. The main point is that when students are actively engaged in challenging and interesting mathematics problems, they can often deal with language difficulties and other gaps as they talk through the problem with other students.
What does the latest research say about the effects of calculators, particularly graphing calculators, on student comprehension of mathematics?
Research on calculators continues to show that students’ problem-solving skills and conceptual understanding can be positively affected when teachers use calculators in meaningful ways. Students’ learning of computation does not suffer as a result of calculator use. Common sense tells us that calculator use has to be part of a balanced program where students also develop their pencil-and-paper skills and, especially, their mental math skills.
A couple of sources of research syntheses with respect to calculators follow:
A Meta-Analysis of the Effects of Calculators on Students’ Achievement and Attitude Levels in Precollege Mathematics Classes. By: Ellington, Aimee J., Journal for Research in Mathematics Education, Nov.2003, Vol. 34 Issue 5, p.433, 31p, 10 charts; (AN 11122911). Also, Texas Instruments has published a research summary related to calculators on its Web site.
With the number of standards-based math classrooms increasing, how do we address the disconnect between what and how we teach and the continued use of summative assessments? How can we encourage our teachers to infuse formative assessments to inform learning for everyone when often these assessments are not valued by parents, schools, and the government?
The emphasis on demonstrating Adequate Yearly Progress and the prevalence of large-scale assessments that rely on multiple-choice items present particular challenges to teachers trying to teach for understanding as well as proficiency. However, even more significant than the tests themselves is the overemphasis on preparing for tests at the expense of effective mathematics teaching that we see promoted in some communities. I still believe, however, that if we teach math in the ways we know work, our students will do fine on tests, even those that seem too low-level or somewhat inappropriate. At the same time, we have a long way to go in learning how to construct appropriate large-scale tests and, as you observe, in infusing appropriate assessments as part of the learning process. I encourage you to reach out to the community through family nights and inviting folks into your classroom to see what kind of mathematics and assessment you are promoting.
How much evidence does research provide supporting a discovery-learning approach in the mathematics classroom?
Discovery learning is not a term commonly used in documents of the Council or in current research reports. There is some confusion with respect to terms that are sometimes applied to particular teaching approaches, including discovery learning, constructivist teaching, hands-on learning, new math, etc. It may be more useful to look at descriptions of what is being called for in certain documents, rather than trying to fit these descriptions into particular labels. For the purposes of research, instructional approaches are not universally effective or not effective; they are more or less effective for helping students achieve particular goals in particular settings. Certainly some types of teaching approaches involve students more extensively in their learning than others, but the key is engaging students in their learning, regardless of the approach a teacher uses. It is not so critical whether students “discover” everything for themselves but it is critical that students are allowed to do some genuine mathematical work on their own. If teachers do all the work and students are left only to copy and imitate and practice what the teacher has done, they are less likely to make sense of the material, remember it later, or transfer it to new situations.
Whether a teacher employs a discovery-type approach to learning or direct teaching or any other approach isn’t as important to student learning as the learning tasks students engage in. Looking at classrooms in the United States and in other countries that tend to be high performing in mathematics, Hiebert and Stigler have found, through a careful analysis of the TIMSS data, that the most important thing with respect to student learning is the nature of the learning task students engage in. Students need to be mentally engaged in a challenging and worthwhile mathematical task that emphasizes the conceptual aspects of the mathematical topic and promotes the formation of mathematical connections if they are to learn skills with meaning and be able to use those skills to solve problems. Students need to be encouraged to think and persist with respect to the mathematical task, and the teacher should refrain from stepping in too early to provide students with answers or tell them exactly what steps they should use. Rather, the teacher can support students by asking them questions that guide them toward mathematical learning. This can be effectively done in a range of instructional settings from the most student-centered to the most teacher-centered.
In addition to the TIMSS analyses by Stigler and Hiebert, a 1999 review on engagement and motivation in the Journal for Research in Mathematics Education may be helpful: “Motivation for Achievement in Mathematics: Findings, Generalizations, and Criticisms of the Research,” JRME, Middleton, J. A. and Spanias, P. A., January 1999, 30(1), pages 65–88.
The following citations were added after the live online chat:
Fawcett, H. P. (1938). The nature of proof: A description and evaluation of certain procedures used in a senior high school to develop an understanding of the nature of proof. New York: Teachers College, Columbia University.
Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29, 41-62.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American Educational Research Journal, 30, 393-425.
Inagaki, K., Hatano, G., & Morita, E. (1998). Construction of mathematical knowledge through whole-class discussion. Learning and Instruction, 8, 503-526.
I am working on my Ed.D. at UCLA and want to do a case study of several urban elementary schools with similar demographics but different test performance. I want to examine the mathematical community of learning that exists at the different schools to see if particular factors exist at one type of school and not at the other. I will be examining formal and informal professional development, how test data is used, both horizontal and vertical collaboration, the interaction of the administration, math coach, and teachers, etc. I hope that as a result of identifying the critical factors a possible check list for improvement can be developed to help low-performing schools chart a course to success in mathematics. The NCSM sessions and numerous research articles are providing lots of ideas and suggestions, yet schools are still having trouble. How do we get the information to the schools in a way that they embrace the ideas?
This sounds like a great effort! It is challenging to present usable capsules of research about what we know in a way that practitioners can apply it. The Council is undertaking a significant initiative in Linking Research and Practice. The first round of results should be available by late this summer, involving Research Briefs and Research Clips that address some of what you are looking at. I might also call your attention to a study conducted in Texas a few years ago, with which I am familiar: Expecting Success: A Study of Five High Performing, High Poverty Schools (2002), available from the University of Texas Charles A. Dana Center (utdanacenter.org; look for Reports).
I also think that visits to successful schools can sometimes help, provided that the visiting educators view the school they are visiting as similar to their own.
New Bedford, Massachusetts
It is imperative that research in mathematics be highly aligned with state mathematics curriculum and standards. The materials that a primary teacher uses daily must enable the students to become proficient in mathematics.
I welcome research-based materials in our schools.
You are absolutely right that research has to be relevant to expectations for what we want our students to learn. We have a responsibility to share the research we know and to build and disseminate materials and programs around what we know.
I think my biggest challenge in implementing a research-based curriculum is time management. A lot of the research-based practices seem to take up a lot of time; time that teachers don’t seem to have. Any suggestions you can give would be helpful.
You have identified the factor that is the most universal barrier cited by teachers in improving their teaching the way they might like—having enough time. It isn’t so much about managing the time as about viewing it differently and rethinking curriculum. I would view many excellent practices and effective strategies not as an expenditure, but rather as an investment. When we teach for lasting understanding, it takes longer. But when students learn something and understand it at a deep level, they are much more likely to remember it and not to require the relentless annual reteaching that has become part of our culture.
In order to do this, we cannot view the mathematics curriculum as a list of 40 to 80 separate things, as we recently discovered in comparing state standards. Rather, there has to be some prioritizing and some clustering around the most important ideas. This helps students in at least two ways—they can better see the connections among mathematical ideas and skills, and also we can make more efficient use of time by teaching a group of related concepts, ideas, and skills together through rich and engaging tasks that call for more than superficial attention.
The bottom line is that we have to make choices about where our time is best spent in order to help students learn.
Below are two similar questions for which Cathy will provide one answer:
I find that researchers use a vocabulary that does not communicate or is not understandable to the average teacher. What can be done to make these presentations and studies more comprehensible for non-researchers?
The main difficulties I find in translating research to practice in the classroom are that teachers are too busy to read research papers, and the presentation of most research is not attractive to teachers.
The challenge many of us have faced is that researchers often communicate in a language for other researchers, and teachers don’t have the time or interest to read lengthy research reports that may not be immediately usable. This is why one of the most important directions for NCTM is to focus on Linking Research and Practice. To do this, we must produce concise, readable Research Analyses, Research Briefs, and Research Clips (kind of like Research ABCs). The Council is beginning this work this summer, and I hope to see it continue as an ongoing effort. Just as important, we need to find ways to communicate from practitioners what questions they most need answers to.
Across the board in mathematics education, we have to find ways for these two communities—researchers and practitioners—to each understand the other better. And we also need to grow and develop the group of people whose interest lies not necessarily within either of these communities, but rather in the connections between them.
As in every field, it seems that you can find research to support virtually any position. These days, most mathematics materials from the big publishers are billed as “research-based” and this is probably true, perhaps depending on how one defines “research.” It’s similar to the way that many foods are now labeled as “lowfat” even if they are otherwise unhealthy! While research is important, I wonder if the whole idea of true research-based practice has already been pre-empted by empty jargon.
This is a perceptive observation. The term “research-based” clearly means different things to different people. I would suggest that, as with food products, we had better read the label, and “Let the buyer beware.” NCTM has an opportunity to set the bar high with respect to reporting sound research in usable ways.
I am a university professor in the early childhood and elementary education department. I will be teaching both an undergraduate course titled “Methods of Teaching Elementary Math,” and a graduate course titled “Math in the Elementary School” for the first time next semester. Does anyone have any suggestions to get the students enrolled in these courses jazzed up about reading and using the research in mathematics teaching? Are there any must-read articles that I should assign my aspiring math teachers?
We’ll put this question out for other responses as well, but a few suggestions follow.
The 2001 book, “Adding it Up, Helping Children Learn Mathematics,” from the National Research Council, is a good, contemporary source of research-based information.
A couple of NCTM sources intended for teachers are: Lessons Learned from Research (NCTM, 2002) 3. Putting Research into Practice in the Elementary Grades (NCTM, 2001)
Also, while not a research source, a motivating book for preservice and new teachers is NCTM’s “Empowering the Beginning Elementary Teacher,” which is a nice motivator.
I am from Ontario and we are asking schools to do the same thing—look at data and use it to drive your planning and instruction.
In your article, I hear you saying two things: look at data and decide where you need to focus your attention, and then look at research and decide how you will change. I see the problem as being vast. My team members want to bring together lots of research related to improving achievement in mathematics. For example, information about the need to change the culture of mathematics instruction (in our North American culture) to be more like the Japanese model of teaching (structured problem solving), information about the importance of focusing the learning in the classrooms on what the students are doing, information about what elements need to be addressed to effect large-scale change and the information about how to plan for learning occasions for collectives.
We want to change a whole system of education with about 1.2million students. I think we know what works for math education now. We have several models of excellence. However, supporting a whole system of teachers to change the way they view instruction is a big task. We need to find new ways to embed learning about research into the teachers’ daily work so they begin to learn differently and change because they like it better and they can see that the learning is better for the children.
This is indeed a big task. I am optimistic that we can produce Research Briefs and Clips, as described in an earlier response, that can help, but we also need to continue to provide the best examples we can of research-based practices, whether from our own country/countries or from outside. We also need to provide many avenues for exchanges between practitioners/teachers and researchers. This is a critical priority for the Council and the profession, in my opinion.
The largest obstacle in the implementation of mathematical reform is the overwhelmingly large wall between higher and public education, which precludes widespread professional development based upon research-validated practice. In locales where such walls are being torn down, real reform can be seen because the folks in public education and the folks in higher education talk to each other work together as equals.
Your point is excellent. Unfortunately, too many good efforts at high school fall apart when students move into very traditional postsecondary programs.
The ideal situation is where colleagues from higher education work in true collaboration with secondary educators. I think we need to call on our higher education colleagues who are working with schools and also doing reform efforts at the university level to share what they are doing with others at the same level. We need to hear more voices from the postsecondary world, and we need to establish partnerships built on mutual respect for the expertise of each partner.
Thank you for your participation in today’s live online chat with Cathy Seeley. The next online chat with Cathy will be at 4:00 p.m. EDT on Tuesday, May 24. See the NCTM News Bulletin and the NCTM.org home page for the President’s Message that will be the subject of the chat.
Thanks for your interest in this important topic. I appreciate your interest in and your efforts to inform teaching by what we know from research. I’m optimistic that as a profession, we can make great gains in this area as we bring the research community and practitioners into collaborative efforts to improve mathematics teaching and learning.