Math Stagnation in High School
Math Stagnation in High School
Thursday, August 27, 1 p.m. Eastern time
Recent results from the nation’s premier test of academic skills show a perplexing trend: U.S. students at early grades have made slow, steady progress in math, but high school students’ test scores remain mostly flat. Why are students’ scores stagnating in the upper grades? Have there been improvements to early-grades math curriculum or teaching that are not being carried through to older students? Or are students’ difficulties with certain topics, like algebra, standing in their way?
Related Story: “NCLB Found to Raise Scores Across Spectrum” (June 17, 2009)
Henry S. Kepner, president, National Council of Teachers of Mathematics
Susan K. Eddins, educational consultant and former teacher, Illinois Mathematics and Science Academy
Sean Cavanagh, assistant editor, Education Week, will moderate this chat.
|Math Stagnation In High School||(08/27/2009)|
|12:25||Web Person: Casey: Today’s chat, Math Stagnation in High School, is open for questions, so please start submitting them now. The chat will begin at 1 p.m. Thank you for joining us.|
Our chat today focuses on an important issue in math. Educators and policymakers have been concerned about the slippage, and stagnation in U.S. students’ math performance as they move through the K-12 system. This trend can be seen in the recent results from the National Assessment of Educational Progress. Math performance among 9- and 13-year olds have generally increased slowly and steadily since the 1970s. But the progress isn’t there among 17-year-olds – scores in 2008 were pretty much what they were in 1973.
What factors could be contributing to this poor performance at the high school level, and what can be done about it? Two guests have joined us today to discuss this trend.
One of our guests, Hank, will be joining us shortly. Susan, why don’t you begin by introducting yourself.
|1:02||Sue Eddins: Hi, I am Sue Eddins. I taught high school mathematics in Illinois for over 30 years, during which time I helped develop mathematics curriculum materials and participated in several extra-curricular activities involving mathematics standards and assessment. Since retiring from the classroom a few years ago, have been working part time as a consultant in math education with the focus again being on student expectations as exemplified in standards and assessment.|
|1:04||Sean Cavanagh: Susan, I’ll pose this first question to you. It relates to a pretty basic issue -- finding a job, and getting into the high school classroom with the necessary certification.|
|1:04||[Comment From David Love]|
I have a B.S. in Mathematics, but not in math.ed., and am still heavily in debt with student loans. I have a couple of years’ experience teaching math at a local community college as an adjunct on an emergency basis. I understand that there is supposed to be a shortage of math/science teachers in various parts of the country. Are there schools or other institutions which would help me to obtain the requisite certification to teach mathematics?
|1:05||Sue Eddins: David, several years ago I taught in a program to provide alternative certification for folks in your position or those who wished to change careers but had a good math/science background. Many colleges and universities offer such a program so I would encourage you to look in your area for that sort of thing.|
|1:06||Sean Cavanagh: Hank, thanks for joining us. Can you introduce yourself to readers?|
|1:06||[Comment From hank Kepner]|
President, NCTM; professor of mathematics education, Univ. of Wisconsin-Milwaukee; taught middle, high school math 12 years - Milwaukee, Iowa City; Program Officer, NSF 5 years. Also president, National Council of Supervisors of Math and Assoc. of Math Teacher Educators.
As a second comment to David, I would say that I preferred folks who were going to teach high school to have a math degree rather than one in education.
|1:07||Sean Cavanagh: Thank you. I’ll pose this question to you, Hank, from Mark, about the National Math Panel.|
|1:07||[Comment From Mark]|
The National Math Panel spoke to a need to focus on proficiency in K-8 for fractions, whole numbers, measurement and some aspects of Geometry and Measurement. Which publishing companies have responded the best to this recommendation? How will the national math standards support this recommendation?
|1:08||Sean Cavanagh: Susan, why don’t you take on this one from Bob?|
|1:08||[Comment From Bob]|
ACT’s The Forgotten Middle makes the claim that “Eighth-grade students’ achievement has a larger impact on their readiness for college by the end of high school than anything that happens academcially in today’s high schools.” What does this tell us about what to do with high school students who enter behind in math? And do you believe that students’ fates are basically sealed by eighth grade?
|1:08||hank Kepner: A follow up to David and Sue: Although where a degree is granted within an institution of higher education is a matter of history. Many colleges have high school teachers graduate “in education” but they have the equivalent of a math major on that campus.|
|1:09||[Comment From Cathy in ND]|
Why is that elementary teachers seem more willing than secondary to adapt to research in pedagogy?
|1:10||Sean Cavanagh: Hank, here’s a question for you from Cathy.|
|1:10||Sean Cavanagh: Sorry, see above, Hank.|
The National Math Panel recommendation is well-known and highlighted in most programs. I would make the case that the challenge is on helping students understand the conceptual reasons why fractions work that way along with estimation skills. Unfortunately, too often stress in the classroom may be on formula and skill manipulation without connections to meaning and sense of results.
|1:11||Sue Eddins: It seems to me that at least part of the problem is that many capable students are able to be relatively successful in math through the early grades by learning discrete facts. Moving into middle school, learning conceptually becomes increasingly necessary and many students tend to fall apart at that level. Nothing is “sealed” about the fate of a student, but unlearning habits of how one learns provide an additional challenge.|
|1:12||Sean Cavanagh: Sue, here’s another one related, related to motivation.|
|1:12||[Comment From Jeff Weld]|
Seems the stagnation coincides with studies suggesting a decline in interest and motivation among youth in developed nations particularly, such as USA and Japan in comparison with Nigeria and Thailand. How might changes in the way we prepare math teachers (or offer professional development) contributed to a decline in interest among students, if that might be causal? Thanks.
Which of these standards should an American education policymaker give the most weight to, when considering strategies to improve the quality of US high school math lessons?
Knowledge/skills needed for good-paying job
Curriculum used by high-performing foreign nations
Curriculum/teaching strategies of top U.S. states
|1:13||Sue Eddins: I concur with Hank’s response about the National Math Panel. Rote learning is a problem. In terms of materials books currently have a lot of work on fractions, but a different kind of work will be needed if students are to truly understand the math behind their operations.|
|1:13||hank Kepner: In a continuation of the rational numbers conversation, the returning to reasoning and estimation needs to revisited every year - not just as rules but through use and student talk with peers and the teacher. Most errors on fractions repeat themselves when even the best students are challenged with rational expressions.|
While our guests delve into questions from our audience, I’ll remind readers of news that is occurring on one front related to this discussion. The National Governors Association and the Council of Chief State School Officers are leading an effort to draft common academic standards in language arts and math, as we’ve reported. The first phase of this project is focusing on older students, and the skills they need for college and the workforce success. Here’s a story we wrote on an early draft of the standards:
A revised draft is expected to be put forward by NGA and CCSSO in mid-September. I’ll pose this to readers: What impact, if any, will the standards effort have on high school students’ math performance?
|1:14||[Comment From Rob Foshay]|
I’d like to explore the Algebra problem. Do kids crash & burn in Algebra because of the way the subject is defined, the way it is taught, or because they don’t have the prerequisites?
|1:14||Sean Cavanagh: Hank, can you respond to Rob’s question about algebra?|
|1:14||Sue Eddins: Jeff, I do think that high school students have increasing demands on their time and it is difficult to engage them fully in learning. I worry that we are developing a culture that rewards “getting through” rather than the level of respect for deeper learning so prevalent in at least the Asian countries.|
|1:15||Sue Eddins: Again, Jeff, preparation of teachers needs to focus on a rich and deep understanding of the mathematics studied in high school. A number of recent publications - such as one by Zal Usiskin and Dick Stanley - point the way on this and are definitely worth looking into.|
|1:16||Sean Cavanagh: Sue, here’s a question from Anne Clark about foundational math.|
|1:16||[Comment From Anne Clark]|
How much of the trouble students have with Algebra and higher math can be attributed to a lack of fluency with basic computation - addition, subtraction, multiplication, and division?
|1:18||Sean Cavanagh: Hank, a couple years ago, NCTM published Curriculum Focal Points, which sought to bring more focus to elem/middle grades math. I understand you’re now working on a high school project. Can you please describe it for our audience?|
hank Kepner: To Rob: All of your observations are part of the challenges. It takes students exposure and discussion in getting comfortable with variables having the same meaning as specific numbers over students life before algebra. E.g.,
Also, there is often a serious gap between solving equations and comfort in creating equations that represent a phenomena in society. (Math modeling)
|1:18||Sue Eddins: Again, I think that the answer is that the way many students learn how to do math is some rote formula that is not digested by them but repeated from being shown “how” not “why” to so something, Procedures learned that way are easily forgotten - I think about all the dates I knew at one time to get an A in history! We need to have students learn the foundational ideas as concepts and understand where the procedures come from if they are to transfer to higher level content.|
|1:19||Sean Cavanagh: Sue, I’ll direct this question about “hands-on” math, or the lack of it, at the HS level, to you.|
|1:19||[Comment From David Love]|
I remember elementary school math being much more ‘hands-on’ with items being physically counted/wieghed/measured. In high school, all of the hands-on instrumentation (geiger counters, volt/ammeters, pH meters, etc.) was conducted in natural/physical sciences classes but math class was limited to textbook and lecture learning. Might this difference in teaching style result in a reduction of learning?
|1:21||hank Kepner: The NCTM will be releasing a focus on high school later this month: The mantra is: Students should be making sense of mathematics and reasoning mathematically every day in class. When they are learning a new rule or procedure, are we ensuring that students are trying to understand how that is connected to the mathematics they already know? |
Too often, students see their goal is to memorize the rule or procedure of the day!
Sean Cavanagh: By way of background for our audience:
Last year, Achieve, a Washington policy organization, released the results of an Algebra 2 test, given to students in a dozen states. Achieve officials said the test was designed to be demanding – more so than many state high school tests, which present 9th or 10th grade math material. Perhaps not surprisingly, students struggled on the exam – the top-scoring state produced a score of 35 percent correct. Mastery of algebra 2 is widely regarded as being important to success in college.
Achieve is a part of the American Diploma Project Network, an effort to align standards, tests, and graduation requirements across states.
|1:22||Sue Eddins: David, I think that having more “hand-on” math in high schools is an excellent idea and I agree that it would be great to have more high school teachers comfortable with that. We do need to remember,however, that moving into conceptual understanding is key in order to master high school content so conclusions need to be made after the hands-on experience. Also, the instruments can change. Graphing calculators, while not exactly hand-on have provided an invaluable visual tool for math exploration.|
Hank, I will direct this question to you (though Sue, feel free to chime in). I have written about the interest among some academic scholars, high school teachers, and others, to create more high school math options for students. Some say that high school students are not given enough high school math options, particularly late in high school. Their schools basically give them the option of taking pre-calculus or calculus, as seniors (even if they don’t plan on majoring in math in college) or the option of being put in an unchallenging senior-year math course. Some say U.S. schools need to create more senior-year alternatives – such as statistics, challenging applied math, discrete math.
Should U.S. schools be focused on adding more high school math options for students? And how realistic is it to think that U.S. high schools can offer these alternatives?
|1:24||Sean Cavanagh: Comment from reader Jeff Weld, on national standards:|
|1:24||[Comment From Jeff Weld]|
In response to Sean’s question about the Ntl Stds and impact-- I think well-formulated, research-based standards are a logical and fantastic start. But that is all they can be, requiring, of course, buy-in among practitioners. And that has so much to do with the workplace milieu-- a supportive, informed administration, plentiful opportunities for professional enrichment, and perhaps most importantly, students and parents aware of and supportive of teaching and learning models and methods that may not look like what they (parents) thought of math back in the day, but embrace and support in acknowledgment of the professionals’ know-how and of the changing times.
I know that you asked Hank, Sean, but am also going to post an answer about an increase in high school options, I think that it is an excellent idea. With the new common standards that are about to come out from NGA and CCSSO, there will be a more common definition of what is a baseline for all students by the end of high school. Once students have achieved that level, many will have a year or two to take other courses and right now AP Statistics and STEM courses are about the only alternatives. Other courses at a comparable level would be wonderful, letting students see how math is used in art, music, finance, and so on.
|1:30||Sean Cavanagh: Thank you - just curious -- of the alternative senior-year math courses, do you have a particular favorite, Sue?|
|1:30||Sue Eddins: Jeff brings up very good points. Once standards are agreed upon and the implications for K-12 are spelled out - the timeline by the way for that phase is the end of this year - there needs to be an entire support system for learning and professional development. Unfortunately, no one pays attention quite often until an assessment drives them to it. That is also part of the plan. I will say, however, that many higher ed and professional organizations have been part of the review groups for the national standards and have at least indicated a desire to work on the areas you raise. Local level issues are harder.|
hank Kepner: We have had a narrow focus for progressing in high school mathematics toward the Calculus. While that is of particular importance for those likely to pursue engineering and the hard sciences, it is not the only choice for others - journalism, social sciences, arts, humanites.
I challenge all of us - should a student not planning to take Calculus be enrolled in “Precalculus” or a better choice of rigorous math topics?
|1:31||Sean Cavanagh: Hank, just to follow-up with you. Wouldn’t adding more course options in high school create a financial/staffing burden on schools? And can you suggest any way around that?|
|1:33||Sue Eddins: In response to Sean’s question about alternative upper level courses. I have seen some nice outlines for financial courses and for function-based courses that use functions and/or geometric constructs from particular fields - running a business, architecture, building trades come to mind. I also like problem-based courses that could focus on a community issue but emphasize the math that can be used to|
Actually, the expanded courses may only be a burden in that more students would stay in mathematics longer - based on more motivation/interest, and possible success.
With the narrow curriculum we have had, many students leave math sooner than they might if they had more personally challenging options. Today, we have many students leave math early, or fail a filter course - often repeatedly. Both of those have financial costs.
|1:34||Sean Cavanagh: Thanks, Sue. Here’s a question I’ll direct to you from Marion, about the impact of standardized tests.|
|1:34||[Comment From Marion]|
The teaser for this chat summed up the possible reasons high school students are lagging as follows: “Have there been improvements to early-grades math curriculum or teaching that are not being carried through to older students? Or are students’ difficulties with certain topics, like algebra, standing in their way?” But I think there is another much more prevelant possibility, and that is that with the huge pressure for children in early grades to score well on standardized tests, teachers in the elementary levels are increasingly teaching “recipe math” (“Just learn the steps to get the right answer” with or without real understanding) so even though students are scoring sufficiently well to ‘pass’ the standardized tests they are not developing a real foundation on which to build in high school. (They don’t really “know” what we think they know in the lower grades.) As I see it, the more pressure that is put on standardized test scores, the worse this problem gets. Could you please comment?
|1:35||Sue Eddins: We have a local district that has specialized programs farmed out to the various campuses and they all involve some upper level courses that look at the math needed for the field. The ones I know about are working with handicapped and elderly services and one that deals with culinary arts.|
|1:36||Sean Cavanagh: Hank, I believe Rob is asking you a follow-up about NCTM’s high school project and it’s impact, if any, on NCTM’s standards. Can you respond?|
|1:36||[Comment From Rob Foshay]|
Thanks, Hank. Will we see this change of emphasis in the national standards? In the accompanying tests? What about in the textbooks/curricula/technology we adopt?
|1:39||Sue Eddins: Marion brings up a point that I am concerned about. Good curricular materials have been developed at all levels over the past decade, but I think that their usage in the early-grade has caught on and that the various programs have more in common than is the case with the high school materials. On your second point that standardized tests are getting in the way. I tend to agree in general that we are losing the goal of real learning to the goal of “getting through”. I mentioned this earlier and I think it applies even more broadly than in the testing, but it certainly applies there as well. They are learning how to do well at the moment and sometimes at least sacrificing te learning that will lead to understanding in the future.|
|1:41||Sean Cavanagh: Sue -- Lisa has a follow-up question for you about the training she’s receiving in a credentialing program, and practical classroom math skills.|
|1:41||[Comment From Lisa B.]|
Regarding Sue’s comment “preparation of teachers needs to focus on a rich and deep understanding of the mathematics studied in high school” and the need for hands on math: I’m currently in a credential program, and while I find the topics of the courses interesting and somewhat helpful, I feel I would benefit much more from discussions on HOW to teach specific math concepts. Am I just in the wrong program?...or can I expect to learn these skills elsewhere? If my program does not provide this experience, what resources should I be looking into to get it?
|1:42||[Comment From Doris Alvarez]|
Is it possible to receive a copy of the transcript?
Rob: Great question. While there are no guarantees in a policy world, we are working hard to push in that direction. An early version of the Common Core State Standards document provided strong reference and some examples of tasks that would expect students to model mathematical data, communicate their reasoning and answers - often in contextual problems.
|1:42||Sue Eddins: Since I have been the writer for the national math standard, I also want to weigh in on Bob’s question. The strongest agreement among members of the Working Group writing these standards has been that we describe mathematics in such a way that teachers and students will view it as coherent and connected - in need of sense-making rather than regurgitation of facts and procedures. It will be interesting to see whether others think we have at least succeeded in describing math in that way.|
|1:42||Sean Cavanagh: Doris -- the transcript will be online at www.edweek.org.|
|1:44||Sean Cavanagh: Hank, here’s a question for you from Jeff, following up on the caculus/trig discussion.|
|1:44||[Comment From Jeff Weld]|
Would we be in a rush to abandon Trig and Calc and such for most all of our students if these courses were taught in an active, investigative, applied (design, build, explain) mode that would likely make them more appealing to more students? Otherwise one might wonder if we’re not erecting filters... sealing fates, perhaps.
|1:45||Sue Eddins: Lisa, I don’t think that you are just in the wrong program, but I might suggest that you look up some of the materials that I referenced before - sorry, but I don’t have titles at my fingertips - and bring them to one of your classes for discussion. In all honesty, none of us really learned the “how"until we got into a classroom. A mentoring program, if done well, often is the best source for this kind of experiential learning beyond student teaching.|
|1:46||Sean Cavanagh: Sue, you’re involved with the writing of the “Common Core” standards effort. Can you address Anne’s question?|
|1:46||[Comment From Anne Clark]|
Is the NGA/CCSSO writing group concluding that the H.S. baseline will end with Geometry?
hank Kepner: Revisiting a piece of an early question of student fluency with facts and computational skills, let me present three thoughts:
Second, fluency with whole number work should have a heavy estimation skill with it. Often work-sheet sequences do not provide or even support such a critical skill
Third, our use of technology is a major component here. For a high school student who might be “weak” in messy calculations, strategic use of technology may allow that student to continue making mathematical process while getting sharper with necessary computation. (I don’t do paper-pencil subtraction to “do my checkbook.” I use a spreadsheet or Quicken. Both allow me to focus my human thoughts on real issues.
|1:49||Sue Eddins: Jeff, I don’t think that we would be erecting filters for students by not giving them calculus provided we have given them a solid base through the level described by Achieve’s ADP document or the about-t-be-released Common Core Standards. Some student may just want to go another direction. I do think we do a disservice to students who complete that work prior to 12th grade when we offer no attractive alternatives to the STEM track. We want students to remain in math all through high school - there is strong evidence that this in and of itself has a tremendous impact on student success. The calculus is not the only possible valuable direction in my opinion.|
|1:51||Sue Eddins: Anne,I would say that the algebra, functions and modeling currently in those standards go beyond what is typically found in an Algebra 1 course or even a second year integrated program so, while Geometry will be expected, at least some Algebra 2 level topics and some statistics and probability not currently found in an Algebra 1/Geometry sequence will be expected.|
Sean Cavanagh: Thanks Sue.
Hank, this may seem like a broad question, but can you give us your thoughts on “integrated” math, and the role it can play in as schools seek to improve HS lessons.
|1:51||[Comment From LaJanneice Sylvester]|
Hello, I work in math publishing and we produce a high school integrated mathematics curr., however, many educators do not seen very keen on this idea, why is that?
|1:54||[Comment From Doris Alvarez]|
I am working with some cognitive scientists about what brain research can tell us about abstract learning such as is found when students begin the study of algebra. Does anyone have any resources that address this issue?
|1:54||Sean Cavanagh: Having covered the National Math Panel’s discussions, I know that they delved into various issues surrounding cognition and math. Check out the backgroud reports from the sub-groups that go with the panel’s main report.|
Sean Cavanagh: Here’s the link, Doris:
|1:55||hank Kepner: Jeff: Your question is a good one. However, for most college students one can argue that there more important mathematical topics to learn than Calculus. Its a priority question for a student’s time and energy. A societal question related to mathematics: for a person to be mathematically literate in our culture, how would we prioritize statisitcal decision-making and certain components of trig? I don’t say make an all-or-nothing choice, but rather a reasoned decision. |
I might note that the large number of newspaper journalists that I talk to all over the country about mathematics would have benefitted from more statistical reasoning than others.
Your point about “shutting doors” is a major concern, but mathematics is having a bigger and bigger foundation for use throughout disciplines - and they don’t have the same foundational sets.
|1:56||Sue Eddins: I also will respond to LaJanneice’s comment. There is a lack of familiarity and comfort with integrated programs on the part of many teachers. Part of that may come from the wide range in the types of integrated curricula that came out of the NSF program to develop such curricula. In many cases, teachers become concerned when the math is not readily evident in a format they are used to. That is not really a good excuse, but it may answer the question to some extent.|
Sean Cavanagh: To follow up on Hank’s points about calculus, check out this Rutgers University professor’s thoughts on HS students’ lack of preparation and interest in it:
|1:59||Sean Cavanagh: Sue -- Any thoughts on how to bring more specialization in math to middle school math classes (Question from Todd)?|
|1:59||[Comment From todd]|
In our schools, we’ve seen history, english, etc. teachers being responsible for teaching math in the junior high schools, so by the time we get the kids in high school, they’ve lost interest in math and the math skills they once had.
|2:00||Sean Cavanagh: Hank -- one more for you about “tracking.”|
|2:00||[Comment From Ceil H]|
What impact does “tracking” or homogeneously grouping play at the high school level?
|2:01||Sue Eddins: Todd, this comes to the issue of certification and differentiated pay. Many districts pay high school teachers more so teachers in high-demand areas tend to gravitate there leaving those certified more broadly in education to teach the middle school courses. While all elementary certification requires some math, it is often minimal and state requirements haven’t changed enough in the face of shortages in qualified math and science teachers - at least in many districts.|
hank Kepner: In this country, “integrated math” has been a flash point for debates. In the range of programs that are available, most have a reasonably common target level of attainment by the end of a third year of high school mathematics.
Whether integrated or Alg 1-Geom-Alg 2, the opportunity to make mathematics rich, exciting, and connected is our challenge. Do we have tasks that make the math a sensible experience TO THE STUDENT - not only the teacher.
Looking at an IB curriculum as well as the high school level of mathematics internationally, they have various takes on “integrated math.” Essentially, only in the US is there a rigid Algebra 1 - Geometry - Algebra 2 course sequence. If that is sequence you have, I must ask - do your students experience data analysis, visualization in both 2- and 3-d worlds, and making conjectures on the content frequently?
|2:03||Sue Eddins: To further respond to Todd’s concern about loss of interest by the time students get to high school math: some of that might be helped if high school math folks could get involved with middle school math contests and such. Just a thought.|
On tracking, at the high school level, after a base level of algebra (including modeling), geometry, and data analysis, there are significant options of highly rigorous mathematical study that students can accomplish. Different directions should be related to student-parent-teacher discussion about options for students’ careers.
The traditional “Tracking” negative occurs when a student is not allowed to go in a direction. Not easy, but we have to help students make critical decisions in their lives.
Sean Cavanagh: Thanks, Hank.
That’s all the time we have for today’s chat, folks.
I want to thank Hank and Sue for all of their insights. To see an archive of the chat, visit EdWeek’s site at www.edweek.org.