Tag Archives: tracking

Tear Down the Math Education Reform Wall

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Recent news about math education in the United States shows that the students in this nation are lagging behind other countries and this crisis is getting progressively worse. It is a story as old as I can remember. In fact, perhaps you can answer this question, class: When was the last time that U.S. math education was considered to be doing well? My research on this subject travels back to 1957 with the Sputnik launch. Of course, the launch indicated that we were not doing well since we were outdone by the Russians, which means math education was lagging even then. The “New Math” ushered in a new approach to fix this problem in education. New math was a flop because it was too rigorous for most students. Thus, the nation embarked on a decades long pursuit of a math education system that would make all students successful in math and get us back to the self-determined role of worldwide leaders in math and science education. Because we are apparently still failing to achieve that goal, I began to consider why this was the case. I have many educational opinions, and several of them are wrapped into my explanation for the continued and progressing poor performance followed by an alternative approach to deliver us from this dilemma.

How did we get here?

First of all, the most recent realm in which to determine our failure is international testing. We perform worse than expected time after time. However, there have been plenty of educated responses explaining how we are being unfairly compared to countries who are not playing the same testing game we are, such as countries that only test their elite students, countries who should not be compared because of homogeneity and economic diversity disparities, etc. The analysis is available to suggest that the results are not as abysmal as we are lead to believe.

Secondly, media and politicians thrive on the need to show failures and a need to repair. Without such news, there would be less flash to their reporting. Without such a political platform, there would be no need to change the political posts already filled by successful leaders. As such, those who have the power to influence public thinking thrust the concept of poor math education upon us every chance they get. I can admit that I have never heard a politician state how awesome math education is in this country. Likewise, any news I do read that is positive about the results of math education are usually localized or temporary, such as for this year’s test for 4th graders; this reporting is usually accompanied by other areas where the math results are poor, perhaps 8th grade results.

Thirdly, I believe the majority of the push in math education since I became a secondary math teacher in 1995 has been towards dumbing down math education, removing “drill and kill,” making math accessible for all students, changing the focus from math as a “right or wrong” proposition into a purely conceptual thinking process, and steering away from the fact-based, skill-driven instruction towards a cooperative, discussion-style, discovery learning process. One reason for this change, perhaps, is that the best mathematical thinkers usually do not pursue careers in education; that is not to say that no great mathematicians become educators. Instead, many prefer to pursue more lucrative careers or opportunities that  provide a greater sphere of influence than the often distasteful educational universe. Without a significant presence of math professionals, the greater power in education tends to be held by those who are more likely to have struggled with their own math education. With a majority of non-math professionals controlling the curricula and instruction for math education, the prevalent push is for more and more approaches to math education that skew away from pure math instruction. Instead of accepting math for its position in the wider educational picture, these reformers who shy from traditional math try to make it fluffy/fuzzy or disguise the necessary rigor of math.

Fourthly, the more prevalent these non-math approaches to instruction have become, the worse the nation’s performance has become. With a poor instructional approach over decades, the teachers of our students are developing and presenting these poorer offerings, especially since they are the product of this system. The more traditional math teachers who present more traditional math instruction are attacked consistently and pointed out as mazethe problem, though the more prevalent alternative math education has been present long enough to have significantly impacted math education. At this point, the myriad of alternative approaches to math education (attempts to fix a broken system) have pervaded our culture for more than half a century and have created a maze of confusion. It follows that the alternative approaches to math education have failed to produce the changes constantly pursued.

How do we progress from here?

I am better at math than you! I have always been better at math than you and will always be. Of course, this is not targeted for all other people, but for approximately 90% of the rest of this nation, these statements are true. I am a high school math teacher who excelled in math classes from elementary through college. Although I have a tendency towards conceit, the information I am reporting here is arguably factual. Although I did not know when I was five that I would be a math teacher one day, I did know that I was very good at math and enjoyed it. With all of this being said, I am going to present a theory that will not be politically correct.

The “right” thing to do these days seems to be to tell every young child that they can be great at math. Some students have high levels of math aptitude and interest and could excel in math following a rigorous education program advancing considerably faster than is available generally. However, some students do not have a natural affinity for math nor natural talent. In today’s society, it has been determined that we must design a system of education for these students promoting the ideas that they can do math, should want to do math, and should enjoy math. If everyone would simply love math, everyone would be great at math, and we would dominate the world in the fields of cognition, education, and economics. The main complication with this philosophy is that our society values freedom of choice above education. Thusly, the dual-edged sword not A Nation at Risk - Averageonly forces those students who would prefer to do less work with abstract, rigorous mathematics to actually invest in mathematics more deeply than desired, but it also asserts to those who would be inclined to excel in mathematics and pursue advanced mathematical studies that anyone can do mathematics, thereby minimizing their special relationship with mathematics; at the same time that the curricula are being watered down for the most likely to succeed in and pursue mathematical endeavors, there is little benefit for the reformers’ “liberal arts” approach to mathematics for those students who are more likely to avoid mathematical studies as they age when they are given more choice in their coursework. The result of these efforts is mediocrity! This matches a criticism levied back in 1983 with one of the most famous calls to action, A Nation at Risk: “We talk a good fight about wanting to have excellent schools when in fact we’re content to have average ones.”

Ultimately, I believe that much of the reform in math education is catering to the least common denominator while hoping that the best of the best can still rise to the top. In the long run, as evidenced by the reformers own chastisement, the alternative approaches to mathematics education are failing to produce the desired results. I propose a different approach. I suggest that we institute a much greater level of rigor in the lowest grades with the purpose of discovering the divergent populations of students distinguished by comparative natural talent and comparative natural interest. In order to accomplish this, two major changes need to occur. Primarily, we need to place teachers in the lowest grades who are math specialists with high math aptitude and possibly some mathematical emphasis in their college work or professional development. Secondarily, we need to raise the amount of time spent with mathematics in those early grades. I have considered the disparity in time spent with English/Language Arts versus math activities, especially in the lower grades and believe that the lesser importance for math is a key challenge to successful math education throughout the K-12 system.

With these changes, we would be able to identify students with mathematical strengths and weaknesses. For those students who show little interest and/or ability, we move them along with the gentler, reform movement approach, maintaining high levels of expectation. These students may be placed on a path wherein Algebra 1 is taken in 10th grade. But, for those students who show greater interest and/or ability, we move them along with a more international, challenging approach. For these students, seventh grade ought to be the target for taking Algebra 1. Young children who enjoy mathematics will enjoy being pushed to excel, while those who prefer the myriad of options other than mathematics will enjoy a more compatible avenue. Especially because one size clearly does not fit all, this approach to mathematics education has the feel of honoring individuals rather than expecting a robotic product at the end of our assembly line school system. I feel as though these divergent paths to successful math education also addresses the psychoemotional needs of our students, which can be a significant factor in improving learning.

In the end, mathematics education reformers are consistently building walls that try to separate traditional from alternative practices and quite possibly teachers and students from the goal of greater math achievement. At the same time, students from all achievement levels are building walls of apathy and disinterest towards math instruction around SuccessStairs-400x250themselves.  Teachers, caught in the middle, help build all of these walls, attempting to appease all participants in the system, but generally satisfying no one. It is time to break down these walls and reuse the building materials to erect stairs of success for all students. This can be accomplished, ought to be considered, and should be implemented immediately.

 

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What Happened to Fran?

tornadoFran’s voice rang out like a gunshot amidst a large, crowded room. With the turmoil surrounding Texas math education and the plethora of data I was collecting in this focus group interview with six Algebra 2 teachers, I was suffering from information overload. At this early stage in my data collection process for my doctoral dissertation, every new statement added to the tornado of statistics, facts, and emotions swirling in my neophyte brain.

I was fighting to maintain my professional demeanor; meanwhile, I was giddy as these teachers not only wanted to participate in my study, but they had a lot of great quotes and thoughts about my research concerns. But then, like the turning point in a great thriller, Fran responded, and I sensed the chills scaling my spine as I realized, “This just got real.”

In attempting to discover the professional opinions of Algebra 2 teachers concerning the changing math landscape, my interview questions encompassed the Algebra-for-All movement, college versus workplace preparation, tracking, the 4×4 Recommended High School Plan (RHSP), graduation rates, and the impact on individual teachers’ teaching environments. Concerning the impact on teachers of the policy positions of the state of Texas, I asked about the panel’s desire to continue teaching high school mathematics. Their answers were contemplative but measured with a determination to remain in the profession despite the enormous challenges and silent agreement in spite of the policymakers. Fran dissented, however, as she spoke honestly with piercing, young eyes stopping and starting, “Yes… The things that we’ve talked about have… me wavering on whether I do want to teach… high school math anymore.”

I had already shifted my young research mind from wanting to prove my point as the impetus for getting a doctorate to wanting to truly find out what teachers believed. Now, my purpose shifted again from wanting to discover teachers’ opinions to needing to tell their story. I realized at that point that the voices of the teachers I would come into contact with along the way were significantly unknown, and their yearning to be heard was often emotionally overpowering. Ultimately, at least I heard their voices; my belief is that their professional opinions should matter to policy makers.

 Interacting with ten teachers at two separate high schools in two focus group interviews; ninety-one respondents to a lengthy online questionnaire; and three individuals during in-depth interviews, I discovered that these Algebra 2 teachers were optimistic about the potential impact of Algebra 2 on all students but were pessimistic regarding the realities of Texas’s expectations for all students. The teachers revealed a number of interesting opinions: graduation rates would probably be negatively affected by graduation and math requirements; Algebra for all was unlikely to be successful because students were generally unprepared for Algebra 1, let alone Algebra 2, and this level of mathematics is overwhelming for many students; honest assessment reveals that all students will not be going to college; high schools ought to work harder at developing alternative paths to graduation for children; requirements involving Algebra 2 need to be reevaluated; a one-size-fits-all approach is doomed to fail; the RHSP is not having the expected positive impact on students or education; tracking is valuable and should be expanded for mathematics while being purposefully monitored to emphasize and maximize success; recent changes were not improving student learning or opportunities for postsecondary endeavors: and, lastly,  more than one-third of the participants had a lessened desire to teach math.

In the end, the doctoral study process was powerful and enlightening. I found that consensus on most issues is difficult to achieve, but the Algebra 2 teachers in my study were passionate and informed members of the educational community who felt that their input was seriously undervalued by decision makers. I am hopeful that I am able to get some of their sentiments into the ears of governmental leaders, which may lead to positive social changes. I have received a lot of great feedback so far from those I have communicated my results to, with one explosively loud exception; when I e-mailed the executive summary of my dissertation to Fran early the following school year, the e-mail was returned with a delivery failure indicating she no longer worked in her previous position. I wonder if Fran will be an example or a trend.question mark

Full dissertation (Teachers’ Perceptions of State Decision-Making Processes for Mathematics Curricula by Brett Bothwell, Ed. D.) can be found in online databases or at http://gradworks.umi.com/35/44/3544187.html.

High school tracking for math classes

This is my first post on this new blog. I have a number of ideas to get up on the page, but need to find the time to get it going. This post stems from my doctoral research. I would love to hear what you think about my thoughts.

The current situation for Texas high school math education, generally speaking:

  1. The most advanced students typically take Algebra 1 in 8th grade, Geometry in 9th, Algebra 2 in 10th, Pre-calculus in 11th, and Calculus in 12th.
  2. The least advanced students take Algebra 1 twice-9th grade and 10th, Geometry in 10th and/or 11th, and finish with Mathematical Models and Applications in12th, resulting in a minimum diploma.
  3. Obviously, there are a myriad of situations in between. At worst, though, the least productive high school math students are 3 years behind at graduation. Of course, the level of learning is probably well below as well.

I would like to propose a new system for my pretend high school:

  1. The highest level, in general, would be called a University STEM track, which has Calculus or AP Statistics  as the expected final course.
  2. The second level, in general, would be called a University non-STEM track, which  has Pre-calculus or AP Statistics as the expected final course.
  3. The third level, in general, would be called a Junior College track, which has Pre-calculus or Algebra 2 as the expected final course.
  4. The fourth level, in general, would be called a Vocational track, which has Algebra 2 or MMA as the expected final course.
  5. The fifth level, in general, would be called a Liberal Arts/Fine Arts track, which has MMA as the expected final course.
These five tracks can all lead to postsecondary educational opportunities, and each more closely relates to the ability, desire, and future plans for individual students.
Different tracks do not have to mean "bad."
An Algebra 2 example of how curricula would match the graduation tracks, while not being overly burdensome on teachers follows:
  1. The university tracks(1 and 2) are to be parallel Algebra 2 classes. They should have similar six weeks calendars. The STEM curriculum/course should be more rigorous and in all ways a more challenging math class. Teachers may need to modify pacing, depth, and style, but the curricula should be similar enough as to not be considered a whole different course.
  2. The junior college track would be the present on-level Algebra 2 course and is the stepping stone between the two major level differences. If a child wanted to take a step down from the university track or up from the vocational or fine/liberal arts tracks. It is unlikely that a student will be following a liberal arts track and choose to move to the university STEM track and be successful. However, track switches are possible, and this is a good compromise.
  3. The vocational and liberal arts tracks would, like the university tracks, be parallel course tracks. The  major difference, however, would be the theme of the courses pointing to non-mathematical or job cluster math. These math courses would be taught relatively close to the watered down versions that are acceptable today and are considered minimal. Depth of abstract math understanding is not the goal in this class, though learning Algebra 2 methods and thinking is still imperative.

Track choices:

  1. “Placement” tests before 6th grade and 8th grade would be implemented to determine appropriate tracking levels, along with teacher recommendation and input from parents, students, and counselors.
  2. Choice would be the norm, with input being expected from teachers and counselors to best match students with a track.
  3. Additionally, brief, non-comprehensive, parent/student reviews of placement would be conducted semi-annually. If no changes were expected, the process could be bypassed.
  4. Comprehensive reviews would be conducted annually, involving all parties. If no changes were expected, the process could be bypassed.

This is not the final development of the ideas, but a good start towards making high school math education more student friendly.