The case for changing the teaching of math
In today's paper, I write about the debate over how to teach math. College professors are arguing that high schools aren't teaching what students need to know for college. Too many students now have to take remedial classes when they arrive. About half of the high school graduates in Maryland who go to state community or four year colleges need a remedial class in math.
Interestingly, students who are put into a high math track early have an enormous advantage because they can take Advanced Placement Calculus classes and place out of the introductory classes at schools like College Park. But if they are left out of that high level math education, students may be far less prepared. I wonder what math teachers have witnessed? What do you think of the current math standards?
Specifically, the Abell Foundation argues in a report that the Algebra I/Data Analysis test now required for graduation isn't really Algebra I. Students are spending time learning other material that wastes their time and keeps them from getting a solid grounding in Algebra I, the report argues. The state says the HSA was never intended to be anything but a minimum standard and that school systems could still teach standard Algebra I.
Should the standards be changed?






Comments
Great story Liz! This shows you exactly what happens when the politicians get overinvolved in education: they end up dumbing down the curriculum so they can crow about their ever-increasing pass rates.
MSDE's comments would be laughable if the effects of the policy weren't so sad. NCLB puts intense pressure on schools to increase "proficiency" pass rates, so of course that's where the focus is going to be. If you don't keep those pass rates moving up, your school gets restructured or shut down. This pressure is especially intense in schools serving struggling students. So for MSDE to say that schools are free to teach higher level skills is totally disingenuous. You're also "free" to drive 30 miles over the speed limit, but you do so at your own risk.
Posted by: Baltimore educator | July 12, 2009 1:03 PM
I just read the story of changing the teaching of math and I agree wholeheartedly that the teaching of math needs to change. But it doesn't start at high school but it begins in elementary school.
I had the opportunity to observe some math work for 1st grade last year and I noticed, it had angles and shapes. It was geometry. I asked a 1st grade teacher and was told that that was a part of the curriculum. I was horrified.
I said, that a lot of these students don't even know their basic math facts. The response was, that was what was in their curriculum.
Second point, I agree with is that there are way too many objectives in the curriculum for a student to be able to master all of them. I saw a documentary that compared our math books to the size of the math books in countries like Japan and it was a huge difference. The Japanese book was significantly smaller. Guess what--the Japanese are far ahead of us because they don't try to cover everything all at once.
Last point to make is in Maryland and in this country we seem to want to help students feel good rather than help them succeed. I have observed that in a particular county in Maryland, you have to have permission to retain a student even if their work is significantly below grade level in one or more subjects.
I know nobody ever asked parents in the classes I attended if they would allow their students to be held back.
Maybe that is also why we have so many students in remedial classes. Maybe they never made the grade when they were in elementary, middle and/or high school. Check it out--to see what is going on.
Of course education officials won't let you know that this is going on but it is.
Posted by: Anonymous | July 12, 2009 1:24 PM
I'm glad the issue of math achievement made the front page of the paper today. Preparing students in mathematics for college level study is indeed an important issue.
One thing I'd like to see in such an article would be information about how many more students are now attempting college work than before and therefore are taking "college prep" coursework in high school. It is difficult to judge the trends without such information.
I teach in a Maryland elementary school and I agree there is an issue with students mastering basic facts fluently. The curriculum emphasizes problem solving and concept attainment which is important for 21st century learning. Practicing math facts then becomes homework. I'd like to see more parents support this by quizzing their children in their basic facts when it is assigned by the teacher.
MSA and HSA high-stakes testing is causing negative instructional impacts such as the issue of Algebra I courses being diluted as described in the article. Finland who tops the list of educational performance does not use high-stakes testing (http://www.schoollibraryjournal.com/blog/1340000334/post/20022802.html). Instead they focus on providing a highly qualified, respected, and supported teaching force; project-based learning; and broadband access to the web. I'd like to see the US move in that direction.
Finally, there are great advances in educational technology (interactive whiteboards, learner response systems, individualized learning management systems) these days. I’d like to see more funds available to apply these technologies to mathematics instruction at all levels.
Posted by: Kathy Benson | July 12, 2009 1:53 PM
For those of you who missed it, the Baltimore Curriculum Project held a very informative conference on this awhile back, with leading experts from Hopkins, Stanford, and Michigan State University.
Larry Schugam there can provide you with DVD's of it if they are still available.
http://www.baltimorecp.org/leadingminds/
Posted by: Steve Kaiser | July 13, 2009 8:31 AM
For those of you who missed it, the Baltimore Curriculum Project held a very informative conference on this awhile back, with leading experts from Hopkins, Stanford, and Michigan State University.
Larry Schugam there can provide you with DVD's of it if they are still available.
http://www.baltimorecp.org/leadingminds/
Posted by: Steve Kaiser | July 13, 2009 8:32 AM
For those of you who missed it, the Baltimore Curriculum Project held a very informative conference on this awhile back, with leading experts from Hopkins, Stanford, and Michigan State University.
Larry Schugam there can provide you with DVD's of it if they are still available.
http://www.baltimorecp.org/leadingminds/
Posted by: Steve Kaiser | July 13, 2009 8:32 AM
Good article, Liz; however, the math problem doesn't begin in high school. I haven't read the Abell report but I hope they looked at the elementary math program. Teaching math "concepts" before children understand and, yes, MEMORIZE basic arithmetic facts, is ludicrous. When students arrive at the 9th grade without knowing multiplication, division, etc., how does anyone expect them to master algebra?! MSDE has created this monster of an elementary math curriculum that downplays the mastery of basic, foundational math facts in favor of "problem-solving" and now they are too proud to admit it. Hard to make much progress unless the direction changes from Grasmick's office.
Posted by: Sandra | July 13, 2009 9:49 AM
What a great article, thank you. Our education system is failing on so many levels. Addressing the math curriculum is one of them. We have recently adopted the atrocious math curriculum, Investigations/TERC. Talk about failing our children, this program is so aligned with doing just that, it is scary. If there are problems now with 50% of students entering college needing remedial math, I think that number is only going to grow if our educators don't get on the right track. And no, the answer is NOT to add more standards or objectives to the curriculum. Let's get back to building a solid foundation for these kids by getting back to the basics and leaving this fuzzy, conceptual learning style behind. If you had a body builder who wasn't able to (but required to) lift 300 lbs., you wouldn't help him by adding more weight. You'd reduce the weight and get him/her solid before moving on to more. Why do parents see, know and understand this concept but our Dept. of Education does not?! Mayday, mayday!
Posted by: Michele | July 13, 2009 11:19 AM
Elementary Basic Education ..
This is where young students MUST learn the simply basic math tables, when they have an unlimited capacity for absortion. Addtion, substraction, multiplication and division must be instilled at an elementary level. NOT High School. What happen to times table memorization? These young minds can (and do) absorb much more than we adults give credit to. Early is the Key.
Every parent of an elementary school child should insist these math skills are in place before moving on to Middle and High School. Even our parents and Grand Parents with an eight grade education have better math skills than our own college age children. What a digrace! Let's get back to the basics where the basics are needed.
Posted by: Dawn Orth | July 13, 2009 2:10 PM
Interesting article. It finally confirms what I and many other social studies teachers have suspected. Being unable to understand math carries over into so many other areas - I've always thought that the economics unit I have to teach in government would go a lot smoother if my students had a basic understanding of what an interest rate was.....So instead going into more depth in my actual content area I have to spend 40 minutes in each class teaching percents. Is MSDE trying to support or undermine me? I wonder sometimes.
Posted by: Nadine Von Canstricus | July 13, 2009 10:09 PM
Why is it always the curriculum and mandated tests (and students and parents) that are at fault when there are bad outcomes? It seems to me that there's enough blame to go around. How many kids that have had enthusiastic and engaged math teachers through their K-12 years have to take remedial math courses? I'd guess very few.
There are way too many teachers that don't like math that are teaching it. There are excellent math teachers, but if they are not in the majority how are students who come from an environment that's told them math is hard and boring and where math and careers requiring math are seen as unobtainable going to learn how cool it is to be able to encrypt data or calculate instantaneous velocity?
The whole idea behind the "touchy-feely" math was to make it accessible and exciting. Things like manipulatives are about touching math. IMO that's not the problem. The problem is dreary, boring, painful math classes and a culture where loving math is socially unacceptable. Turning that around is hard and will take work from the schools, through the teachers and to the parents. It also means we need to convince math geeks that teaching school is something they should do and getting them to keep their enthusiasm going in a classroom setting. Give the kids a reason to care about multiplication and memorizing the times table will go much quicker.
Posted by: a parent | July 14, 2009 12:21 PM
THANK YOU, a parent!
Almost every problem mentioned in Liz's article could be solved by replacing the many mediocre mathematics teachers in this country (ESPECIALLY at the middle scohol level) with top notch thinkers and practioners of the craft of math teaching. If you think I'm wrong, cast your mind back to the best math teacher you ever had. (If you were even lucky enough to have one of that rare breed, that is.)
That person was probably smart as a whip, deeply mathematically literate, and passionate about the subject enough to make you work hard and actually learn something.
Of all the prescriptions needed to solve the ills mentioned in the article the other day, it's the standard of teaching excellence for math teachers that must increase - by a lot.
Posted by: It's the teaching | July 14, 2009 12:50 PM
I am a seven year high school math teacher in Baltimore City Schools. In my experience there are two major reasons for the math gap. First, the gap doesn't begin in high school. I give my students the same numeracy diagnostic math test every year. Every year the median results for my 9th to 12 grade students is fifth grade. More precisely, over the last seven years the median score has decreased from the middle of fifth grade to the beginning of fifth grade. That is, our high school students cannot do long division, do not understand fractions, cannot complete unit conversions, calculate percentages or read a ruler. It is silly talk to expect that a semester of remedial math is going to bring a student up from fifth grade to be adequately prepared for 9th grade algebra.
The second reason is that there are few consequences for failing Maryland's required courses. Students are allowed to 'do' classwork over, complete substitute work, carry administrative 'messages' to teachers, and, if all else fails (pun intended) administrators simply change course grades so that students graduate. The pressure to raise graduate rates is enormous and documenting altered grades has been useless.
Posted by: Brad Fields | July 14, 2009 3:48 PM
I am not a math person but my father was an engineer and I taught math well enough to have high scoring third graders for many years. I knew I had to do it and I had to make the kids love it! I agree with a parent and It's the teaching...except that too often the projects, manipulatives, warm and fuzzy math was not boring, was fun, and engaged the kids but had little or no meat. Excellent math teachers are hard to find and hard to keep. Currently there are under ten on the list of possible hires. We need great math teachers who teach in an engaging way but teach meaningful math at the same time. Recently I observed a group of students spend a long time on a math project they loved but in the end, really had no idea what they were supposed to have learned. I know there must be a way for this lesson to have worked but the teacher was not skilled enough(yet) to go the final mile. Perhaps it comes down to better teacher training and follow up meaningful PD! Also, there are very few things kids have to memorize anymore but facts is one ting and this is on the kids and parents! Yesterday in Giant, I saw a grown woman counting on her fingers.She finally got out paper and tried to add up the numbers and then asked another shopper. Simple addition.If students have a decent foundation, classroom time is ever so much more effective.
Posted by: wise educator | July 14, 2009 4:12 PM
Where are the MSA scores? This blogsite announced they would be out last Tuesday and I still haven't seen them. Is there an issue? Too inflated, perhaps?
Posted by: Mike | July 14, 2009 4:26 PM
Per an interview with Dr. A on WYPR @ noon today - an announcement will be made on 7/21. It sounded like it would be good news, but no data was leaked. I think the WYPR website has recordings of the show.
Posted by: a parent | July 14, 2009 5:02 PM
@ its the...I am concerned that everything is always blamed on teachers. Yes, there are math teachers who are not qualified (because most people qualified have jobs people treat them as professionals, work in a better setting, and do not have to worry about being cussed out by children whose parents always say its the teachers fault!) There are teachers who are not up to par in other areas as well. I agree, though, that the biggest need for math teachers is middle school. But most teachers do not want to teach in an environment such as many middle schools in BCPSS. My question is, when do parents take responsibility for their children? If a student can not add, subtract, multiply or divide, why isnt that student's parent helping them? Until we hold this kids accountable for learning basic skills, we can not expect them to perform math at a high level! Thats like expecting a child who does not know the alphabet to write a paper on the functions of the brain as it relates to education. Its just not possible.
Posted by: concerned teacher | July 14, 2009 10:00 PM
@ its the...I am concerned that everything is always blamed on teachers. Yes, there are math teachers who are not qualified (because most people qualified have jobs people treat them as professionals, work in a better setting, and do not have to worry about being cussed out by children whose parents always say its the teachers fault!) There are teachers who are not up to par in other areas as well. I agree, though, that the biggest need for math teachers is middle school. But most teachers do not want to teach in an environment such as many middle schools in BCPSS. My question is, when do parents take responsibility for their children? If a student can not add, subtract, multiply or divide, why isnt that student's parent helping them? Until we hold this kids accountable for learning basic skills, we can not expect them to perform math at a high level! Thats like expecting a child who does not know the alphabet to write a paper on the functions of the brain as it relates to education. Its just not possible.
Posted by: concerned teacher | July 14, 2009 10:01 PM
I have been teaching mathematics for eight years with enthusiasm and dedication. In response to ‘a parent’ I ask what about the parents. I can’t tell you how many parent conferences I have been in where the parent admits in front of the child that they never liked math either. A child’s perception of mathematics is formed long before he comes to my class! How about if we as parents turn off the TV and play a round of flashcards with our elementary aged children if we want to go back to the basics!
Posted by: a teacher and a parent | July 14, 2009 10:50 PM
Could you please cover Baltimore County schools? I would love to know what is up with all the changes. Who is really running things? Certainly not the board...they simply say "yes" and our system takes a turn backwards.
Posted by: Mike | July 15, 2009 5:09 PM
Could you please cover Baltimore County schools? I would love to know what is up with all the changes. Who is really running things? Certainly not the board...they simply say "yes" and our system takes a turn backwards.
Posted by: Mike | July 15, 2009 5:09 PM
Could you please cover Baltimore County schools? I would love to know what is up with all the changes. Who is really running things? Certainly not the board...they simply say "yes" and our system takes a turn backwards.
Posted by: Mike | July 15, 2009 5:09 PM
As a math educator, I cannot take exception with the data - it is what it is. I know that there are many reasons that students enter 2 or 4 year colleges unprepared and needing remedial assistance in mathematics. One important one is that many students never intended to attend and did not prepare themselves for college entrance by taking appropriate mathematics courses along the way.
The Maryland mathematics curriculum for Algebra II is well-aligned with the Accuplacer assessment, used by many higher education institutions in our state for placement purposes. That alignment has been reviewed, studied and validated numerous times. The challenge we face is to insure that all students in every classroom across the state have access to highly effective learning experiences for all of the content that is in the written curriculum.
It is possible for a student to learn both the concepts, processes and the skills of mathematics. It requires a teacher with a deep understanding - not just a fluency with sets of mathematical procedures. It requires that a highly skilled teaching force - with not just a highly qualified, but a highly effective teacher in every classroom.
The difference between the written curriculum and the taught curriculum varies from classroom to classroom, school to school, county to county, and beyond. The variability of the implementation of any curriculum is extensive.
Regarding the use of calculators, I believe that we should expect today's learners to use the tools that are currently available - appropriately and accurately. To do this actually requires students to be more knowledgeable about the mathematics being used, as the calculator is only as accurate as the button pusher. A knowledgeable student knows when to use the calculator and when the computation is more easily done by hand or in the head, and more importantly, has an expectation of a reasonable answer prior to the pushing of any buttons.
The high school assessments were always designed to establish a floor. Just a few years ago, Maryland's floor was the functional math test - intermediate grade content.
The discussion surrounding the mathematics curriculum and its implementation and outcomes are important to the future of our citizenry. We must find ways to align what is written on paper with the learning opportunities afforded to each student in our state. I could not agree more with a prior post about the need for all students to have access to a college preparatory curriculum. It is hard to imagine a job or career that will not require some level of higher education. Right now, it is just not the case.
Posted by: Joy Donlin | July 15, 2009 5:28 PM
A parent asks: "Why is it always the curriculum and mandated tests ... that are at fault when there are bad outcomes?"
My approach is to start at the top of the food chain. When things are going bad, it’s almost always the generals, not the soldiers.
Clearly, we need to recruit and retain lots of bright young energetic people into teaching math. But that is never going to happen unless conditions improve. Again, I would start at the top. Nothing demoralizes a soldier faster than being led by a buffoon.
If this country is serious about improving science, technology, engineering and math (STEM) education, we need to put people in charge who have actually accomplished something in these fields. Right now the show is run by clowns with Ed.D.s who barely passed their required Stats for Morons class in grad school.
Look at Arne Duncan, the US Secretary of Education. A BA sociology major basketball player. Nothing against sociology or basketball, but what qualifies this dude to lead us to 21st century excellence in math, science, and technology? The mealy-mouthed hack couldn’t solve a differential equation if his life depended on it.
Posted by: michael | July 15, 2009 11:48 PM
The subtitle of this article is based on a misconception. The only state evaluation high schools give in mathematics is the Algebra/Data Analysis High School Assessment. The curriculum for this test is intended to be the minimum level of Algebra that all students must master. It is not a complete Algebra I course, but it has raised the bar for many students. It is not intended to prepare students for college. It is intended to validate that all students who graduate from a Maryland High School have a minimum proficiency in Algebra and Data Analysis before they enter the work force. Many courses are offered that prepare students for college including Advanced Placement Mathematics in both Calculus and Statistics. Students must pass at least an Algebra II course to be successful in college.
Another situation that leads to low placement scores is that many students complete their four credits of mathematics before their senior year. When they arrive at college to take the placement test they have not studied mathematics in over a year. The adage “use it or loose it” also applies to mathematics. The students forget what they have learned and their scores reflect this gap in instruction.
If the need for remedial courses is to decrease, parents and schools need to encourage students to take higher level math courses and to take them during all four years of high school
Posted by: Kathleen House | July 16, 2009 7:07 AM
Recent articles in the Baltimore Sun have quoted an Abell Foundation report as the evidence that students require remediation at an alarming rate. No responsible K-12 educator would suggest that there is not a remediation problem that we must deal with across the state, but on the other hand, it is critical that data not be misrepresented in the conversation. Some of these articles also quote various college-level professors who provide anecdotal evidence about the remedial problem with Maryland graduates. I wonder if these professors are able to distinguish between Maryland students and out-of-state students just by looking at them. Or is it possible that some of the “remediation” problem is with out-of-state students as well.
The foundation document that is used to show the extent of the ‘remediation problem” is the Student Outcome and Achievement Report (SOAR). A close reading of the SOAR Report, however, indicates that 37% of students in Maryland who attend institutions of higher education go out of state to do so. Additionally the SOAR Report only captures students who take either the SAT or the ACT. It turns out that the SOAR sample represents only about 29% of a typical graduating class, and it does not include some of our “best and brightest” who go to out-of-state institutions.
Even more fundamental is the fact that the entire SOAR Report is based on student self-reported data resulting from a questionnaire that students complete when they take the SAT or ACT. Based on this questionnaire, students are classified as “core” or non-core.” The core students are ones who are deemed ready for college because of the courses they supposedly took while in high school (at least according to their self-reported data). However, that definition falls apart when one looks more closely at the data. For example, the SOAR Report shows that in 15 of 24 jurisdictions, non-core students outperform core students in their first mathematics course in college. That defies logic, not to mention that it flies in the face of everything that experts around the country say about the need to take rigorous courses in high school. It also suggests quite clearly that there is a problem with the definition of core and non-core, which calls into question the conclusions that are drawn from such a report.
There are at least three other issues that would allow for a more balanced presentation of the “remediation” problem.
1. Community colleges have open enrollment, meaning that nearly anyone can be admitted. Currently in Maryland, students do not have to complete a college preparatory curriculum in order to graduate from high school. However, those same students can be admitted to community colleges. Of course they will require additional assistance, but it would be inappropriate to call it remediation when they have never had the appropriate courses in the first place that would prepare them for college. In the big picture, we have many more students in college than ever before. One could argue that providing such opportunity for a broader cross-section of society than ever before is a good thing even if it means that some of those students require extra assistance. Hopefully, we can one day make certain that all students will graduate from high school “college-ready.” But that will require a much broader consensus on a variety of issues, not the least of which is a change in graduation requirements.
2. It is reported that the average age of community college students is approximately 26 years old. If that is the case, then students who are returning to school after a fairly lengthy absence will indeed require additional assistance, even remediation if they had the courses while in high school. Any reader of this article should reflect on what kind of assistance he/she would need if he/ she were to return to school at this time. We should be glad that these students want to return to school because it is good for the economic development of this state. But we should also recognize that they will require remediation if they have been out of school any length of time.
3. Finally, we have a serious teacher preparation problem in Maryland. Those very same institutions of higher education that complain about the need for remediation prepare less than a third of the teachers that Maryland needs each year to meet its hiring demands. If students do not have excellent teachers throughout their educational experience, they will undoubtedly face challenges as they exit high school. Whose fault is that?
The “remediation problem” is not just a K-12 problem as some of the recent articles and quotes suggest. It is a serious problem for the entire P-20 community, and it will take a collaborative effort to eliminate the problem. Finger pointing will not solve the problem regardless of its origin. Committed educators and others who will thoughtfully look at good, reliable data will be a major step forward. Hopefully, the long-awaited longitudinal database, once fully funded, will help resolve this part of the issue. Beyond that it will take responsible people of good will who have the best interests of students at heart to come together in a collaborative manner to address this serious issue.
Jim Foran
Executive Director
High School and Postsecondary Intiatives
Maryland State Department of Education
Posted by: Jim Foran | July 16, 2009 11:39 AM
I think the analysis of the article must actually be separated into its two components: the curriculum and the implementation (teaching) of that curriculum.
For the curriculum, Maryland adopted the Voluntary State Curriculum (VSC) for grades K-8 and the Core Learning Goals (CLGs) for HSA subjects such as Algebra I. In that light, I strongly disagree with many of the readers' comments. As a mathematics consultant for districts across the US, I can assure you that Maryland has a model mathematics curriculum. The VSC puts all students on a strong vertical trajectory toward rigorous high school courses. Students must individually choose to enter Algebra I by the 8th grade so that they may take AP Calculus by the 12th grade. The controversial Algebra I curriculum mentioned in the article and subsequent defined Maryland mathematics courses actually align quite nicely to the College Board Standards for College Success. In fact, Maryland is one of the few states to recognize the importance of an early foundation for statistics content- a concept so often reported missing by our business partners. Additionally, the depth and breadth argument against many state’s mathematics curriculum is also answered in Maryland’s Assessment Limits. These Limits further define for teachers the extent to which the curriculum is tested at each grade to eliminate the need to go the feared “mile wide and inch deep.” These efforts by MSDE have yielded not only the qualitative acclaim by curriculum reviewers but also the quantitative gains posted in increased state scores and national AP scores.
For the implementation (teaching) component, however, the reader must look for responsiblity past the state and into the local classroom. For example, many references were made to the lack of mastery of the basic skills. I encourage those readers with such concerns to look at the program chosen by their district or school to implement the state’s curriculum. Finally, as several other responses indicated, the most powerful variable affecting any child’s success continues to be the individual classroom teacher.
In summary, a job well done to the Maryland State Department of Education for its continued leadership in curriculum/assessment and a continued plea to local districts to continue to seek and retain those best qualified to deliver that curriculum.
Posted by: Kathryn Kubic | July 20, 2009 8:25 PM