Thursday, April 21, 2011

Lecture-Style Presentations Lead to Higher Achievement in Math and Science

Harvard Study Shows that Lecture-Style Presentations Lead to Higher Student Achievement

Widely-used problem-solving pedagogy as implemented in practice is

not as effective for raising achievement levels

Cambridge, MA – A new study finds that 8th grade students in the U.S. score higher on standardized tests in math and science when their teachers allocate greater amounts of class time to lecture-style presentations than to group problem-solving activities. For both math and science, the study finds that a shift of 10 percentage points of time from problem solving to lecture-style presentations (for example, increasing the share of time spent lecturing from 60 to 70 percent) is associated with a rise in student test scores of 4 percent of a standard deviation for the students who had the exact same peers in both their math and science classes – or between one and two months’ worth of learning in a typical school year.

These estimates are based on the actual implementation of teaching practices that the researchers observe in practice. Thus, while problem-solving activities may be very effective if implemented in the correct way, simply inducing the average teacher employed today to shift time in class from lecture style presentations to problem solving, without concern for how this is implemented, contains little potential to increase student achievement. On the contrary, the study’s results indicate that there might even be adverse effects on student learning.

Guido Schwerdt, a postdoctoral fellow in Harvard’s Program on Education Policy and Governance, and Amelie C. Wuppermann, a postdoctoral researcher at the University of Mainz, Germany, conducted the study. A research article, “Sage on the Stage,” presenting the study’s findings will appear in the Summer 2011 issue of Education Next.

The researchers used data from the 2003 Trends in International Mathematics and Science Study (TIMSS). Their sample includes 6,310 students in 205 U.S. schools with 639 teachers (303 math teachers and 355 science teachers, of which 19 teacher both subjects). In addition to test scores in math and science, the TIMSS data include information on teacher characteristics, qualifications, and classroom practices. Most important for the analysis, teachers were asked what proportion of time in a typical week students spent on each of eight activities, and the authors’ methodology focused on three of these activities — listening to lecture-style presentations, working on problems with the teacher’s guidance, and working on problems without guidance — as a “good proxy for the time in class in which students are taught new material.” They divide the amount of time spent listening to lecture-style presentations by the total amount of time spent on each of these three activities to generate a single measure of how much time the teacher devoted to lecturing relative to how much time was devoted to problem-solving activities.

Schwerdt and Wuppermann observe that in recent years, a consensus has emerged among researchers that teacher quality “matters enormously for student performance,” but that relatively few rigorous studies have looked inside the classroom to see what kinds of teaching styles are the most effective. Their study of teaching styles finds that “teaching style matters for student achievement, but in the opposite direction than anticipated by conventional wisdom: an emphasis on lecture-style presentations (rather than problem-solving activities) is associated with an increase — not a decrease — in student achievement.” They report that prominent organizations such as the National Research Council and the National Council of Teachers of Mathematics, for at least the last three decades, have “called for teachers to engage students in constructing their own new knowledge through more hands-on learning and group work.” The emphasis on group problem-solving instructional methods has been incorporated into most U.S. teacher preparation programs, and the authors found that teachers in the study’s sample allocated, on average, twice as much time to problem-solving activities as to lecturing, or “direct instruction.”

The researchers recognize that a key challenge in studying the effects of teaching practices is that “teachers may adjust their methods in response to the ability or behavior of their students,” perhaps relying more on lectures when assigned more capable or attentive students. To address these concerns, they “exploit the fact that the TIMSS study tested each student in both mathematics and science,” which allowed them to compare the math and science test scores of individual students whose teacher in one subject tended to emphasize a different teaching style than their teacher in the other subject. They found that in both math and science, the positive relationship between lecture-style methods and test score gains was maintained. The estimated .04 standard deviation impact of a greater emphasis on lecturing is based on students who had the same peers in both classes, because that minimizes the chances that teaching styles — and their consequences — might differ depending on the composition of the class.

About the Authors
Guido Schwerdt is a postdoctoral fellow at the Program on Education Policy and Governance (PEPG) at Harvard University and a research at the Ifo Institute for Economic Research in Munich, Germany. Amelie C. Wuppermann is a postdoctoral researcher at the University of Mainz, Germany.

About Education Next
Education Next
is a scholarly journal published by the Hoover Institution that is committed to looking at hard facts about school reform. Other sponsoring institutions are the Harvard Program on Education Policy and Governance, part of the Taubman Center for State and Local Government at the Harvard Kennedy School, and the Thomas B. Fordham Foundation.

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Monday, April 18, 2011

TX Sovereignty ~ Common Core Standards

Core Standards only cover Algebra I, much but not all of the expected contents of Geometry, and about half of the expectations in Algebra II.


Texas House of Representatives - Committee on State Sovereignty

Meeting: 04/14/11



Written Testimony of R James Milgram, Professor Emeritus, Stanford University, member of the Common Core Standards Validation Committee


I would like to testify in support of the bill Rep. Huberty filed, HB 2923, to prevent the so called Core Standards, and the related curricula and tests from being adopted in Texas.


My Qualifications. I was one of the national reviewers of both the first and second drafts of the new TX math standards. I was also one of the 25 members of the CCSSO/NGA Validation Committee, and the only content expert in mathematics.


The Validation Committee oversaw the development of the new National Core Standards, and as a result, I had considerable influence on the mathematics standards in the document. However, as is often the case, there was input from many other sources – including State Departments of Education – that had to be incorporated into the standards.


A number of these sources were mainly focused on things like making the standards as non-challenging as possible. Others were focused on making sure their favorite topics were present, and handled in the way they liked.


As a result, there are a number of extremely serious failings in Core Standards that make it premature for any state with serious hopes for improving the quality of the mathematical education of their children to adopt them. This remains true in spite of the fact that more than 35 states have already adopted them.


For example, by the end of fifth grade the material being covered in arithmetic and algebra in Core Standards is more than a year behind the early grade expectations in most high achieving countries. By the end of seventh grade Core Standards are roughly two years behind.


Typically, in those countries, much of the material in Algebra I and the first semester of Geometry is covered in grades 6, 7, or 8, and by the end of ninth grade, students will have finished all of our Algebra I, almost all of our Algebra II content, and our Geometry expectations, including proofs, all at a more sophisticated level than we expect.  Consequently, in many of the high achieving countries, students are either expected to complete a standard Calculus course, or are required to finish such a course to graduate from High School (and over 90% of the populations typically are high school graduates).


Besides the issue mentioned above, Core Standards in Mathematics have very low expectations. When we compare the expectations in Core Standards with international expectations at the high school level we find, besides the slow pacing, that Core Standards only cover Algebra I, much but not all of the expected contents of Geometry, and about half of the expectations in Algebra II. Also, there is no discussion at all of topics more advanced than these.


Problems with the actual mathematics in Core Math Standards As a result of all the political pressure to make Core Standards acceptable to the special interest groups involved, there are a number of extremely problematic mathematical decisions that were made in writing them. Chief among them are:


1. The Core Mathematics Standards are written to reflect very low expectations. More exactly, the explicitly stated objective is to prepare students not to have to take remedial mathematics courses at a typical community college. They do not even cover all the topics that are required for admission to any of the state universities around the country, except possibly those in Arizona, since the minimal expectations at these schools are three years of mathematics including at least two years of algebra and one of geometry.  Currently, about 40% of entering college freshmen have to take remedial mathematics.  For such students there is less than a 2% chance they will ever successfully take a college calculus course.


Calculus is required to major in essentially all of the most critical areas: engineering, economics, medicine, computer science, the sciences, to name just a few.


2. An extremely unusual approach to geometry from grade 7 on, focusing on rigid transformations.  It was argued by members of the writing committee that this approach is rigorous (true), and is, in fact, the most complete and accurate development of the foundations of geometry that is possible at the high school level (also probably true).  But it focuses on sophisticated structures teachers have not studied or even seen before.  As a result, maybe one in several hundred teachers will be capable of teaching the new material as intended.


However, there is an easier thing that teachers can do – focus on student play with rigid transformations, and the typical curriculum that results would be a very superficial discussion of geometry, and one where there are no proofs at all.


Realistically, the most likely outcome of the Core Mathematics geometry standards is the complete suppression of the key topics in Euclidean geometry including proofs and deductive reasoning.


The new Texas Mathematics Standards


As I am sure you are aware, Texas has spent the past year constructing new draft mathematics standards, and I was one of the national reviewers of both the first and second drafts. The original draft did a better job of pacing than Core Standards, being about one year ahead of them by the end of eighth grade, so not nearly as far behind international expectations. Additionally, they contained a reasonable set of standards for a pre-calculus course, and overall a much more reasonable set of high school standards.


There were a large number of problems as well – normal for a first draft. However, the second draft had fixed almost all of these issues, and the majority of my comments on the second draft were to suggest fixes for imprecise language and some clarifications of what the differences are between the previous approaches to the lower grade material in this country and the approaches in the high achieving countries.


It is also worth noting that the new Texas lower grade standards are closer to international approaches to the subject than those of any other state.


I think it is safe to say that the new Texas Math Standards that are finally approved by the Texas Board of Education will be among the best, if not the best, in the country. (I cannot say this with complete certainty until I have seen the final draft. But since I am, again, one of the national reviewers, this should be very soon.)


So it seems to me that you have a clear choice between


Core Standards – in large measure a political document that, in spite of a number of real strengths, is written at a very low level and does not adequately reflect our current understanding of why the math programs in the high achieving countries give dramatically better results;


The new Texas Standards that show every indication of being among the best, if not the best, state standards in the country. They are written to prepare students to both enter the workforce after graduation, and to take calculus in college if not earlier. They also reflect very well, the approaches to mathematics education that underlie the results in the high achieving countries.


For me, at least, this would not be a difficult choice. So for these many reasons I strongly support HR 2923, and hope the distinguished members of this committee will support it as well.


Respectfully, R. James Milgram

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Sunday, April 17, 2011

The Price of "Innovation"

Some interesting reading...

Nationalized Education Nonsense

by Ze'ev Wurman over at Jay P. Greene's Blog

and then, a little something for any "pie in the skiers"

who might happen to visit here:

The Innovation Mismatch: "Smart Capital" and Education Innovation

over at the Harvard Business Review.

Hey, Jay P. Greene - They used "SMART" Hmmmm....

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Friday, April 15, 2011

Grades vs. Learning

Beware of "good grades" and investigate the math content taught in our schools! 

Teaching Math to the Talented

In short, the percentages of high-achieving students in the United States—and in most of its individual states—are shockingly below those of many of the world’s leading industrialized nations. Results for many states are at a level equal to those of third-world countries.

U. S. Math Performance in World Perspective

Overall results. The percentage of students in the U.S. Class of 2009 who were highly accomplished is well below that of most countries with which the United States generally compares itself. While just 6 percent of U.S. students earned at least 617.1 points on the PISA 2006 exam, 28 percent of Taiwanese students did.


Unfortunately, the United States trails other industrialized countries in bringing a large proportion of its students up to the highest levels of accomplishment. This is not a story of some states doing well but being dragged down by states that perform poorly. Nor is it a story of immigrant or disadvantaged or minority students hiding the strong performance of better-prepared students. Comparatively small percentages of white students are high achievers. Only a small proportion of the children of our college-educated population is equipped to compete with students in a majority of OECD countries.

Major policy initiatives within the United States have in recent years focused on the educational needs of low-performing students. Such efforts deserve commendation, but they can leave the impression that there is no similar need to enhance the education of those students the STEM coalition has called “the best and brightest.”

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Friday, April 8, 2011

Important Information!

I don't believe that Algebra II should be required for high school graduation, but it is extremely important that parents and students know the implications for future success. 

Let's be open and honest and inform the public!


 Requiring Algebra II in High School Gains Momentum Nationwide

Washington Post

One [study] conducted by U.S. Department of Education researcher Clifford Adelman found that students who took Algebra II and at least one more math course attained “momentum” toward receiving a bachelor’s degree.

Side Note:  This "one study" was an extremely detailed analysis of about 13,000 students from highschool through degree completion or work placement.  You can find it here:


Answers in the Tool Box: Academic Intensity, Attendance Patterns, and Bachelor's Degree Attainment 

by Clifford Adelman
Senior Research Analyst, U.S. Department of Education

Under Selected Findings:  Of ALL pre-college curricula, the highest level of mathematics one studies in secondary school has the strongest continuing influence on bachelor's degree completion. Finishing a course beyond the level of Algebra 2 (for example, trigonometry or pre-calculus) more than doubles the odds that a student who enters postsecondary education will complete a bachelor's degree. [pp. 16-18]


Here's a 2002 report from Carnevale and Desrochers, but it may not be the one referred to in the Washington Post article above.

Standards for What?  The Economic Roots of K-12 Reform

Anthony P. Carnevale and Donna M. Desrochers

[p. 55]  Workers in the Best-Paying Jobs Have Typically Completed Algebra II


[p. 56] In the current education curriculum, these higher-level courses are the means by which people learn higher-level reasoning skills. Throwing out the current curriculum without a superior alternative in place would be like throwing out the baby with the bath water.

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Sunday, April 3, 2011

Everyday Math and TERC Investigations = Bad Math Ed in US


Q & A with Jim Milgram 

Q:  Do you prefer Traditional Math over Reform Math?




Q & A with Ze'ev Wurman

Q:   If you had to rate EDM vs. Singapore Math in achieving real math proficiency, what would be your ranking on 1-10 scale (10 being best) for each program?

A:  Proficiency is hard to define. I would use the preparation for an authentic Algebra 1 course (Nat'l Advisory Math Panel definition) instead.

TERC = 2,
EDM = 4,
Saxon = 7 or 8,
Singapore (Primary Math) = 10.

Clearly, supplementation may change the results for the less effective programs. 


Must Read Website on TERC

A:  Anyone interested in majoring in a technical area should have a much more traditional program than the reform programs. Though there is nothing intrinsically wrong with some of the reform ideas, the implementations are worse than horrible at this time.

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