Category Archives: Math Education

Student Performance Determines Teacher Success – Fair or Not?

The primary difficulty I have with student performance determining teacher performance is that natural ability seems to play a role in this phenomenon. My experience as a teacher for sixteen years has shown me a few things.

  • I taught 8th graders in an affluent district with kids who had always been successful on our state tests. Parents ran the school with an administration that let kids get away with almost anything for fear of parent interference, the principal was fired (actually promoted to the district offices), and the students did not seem to learn as well as I would have liked. I worked hard that year trying to get 8th grade math into their brains, but did not feel as successful as I had in the past or in the future with that endeavor. In the end, almost all of my students passed the state test that year.
  • I taught Pre-AP Algebra 2 students for four years. I had virtually 100% pass the state tests year after year.
  • I have taught in a dropout recovery program for the last six years. The state test has become easier, and I have become better at working with the students over the years. While there are years when there are great successes and times when things do not go as well, we are still able to get about 80% of the students to eventually pass the state tests. These are mostly kids who would have skipped the state tests at their home campus or failed, some with a record of failing the state math test every single year since they started taking the tests (usually third grade). My feeling is that every kid that passes should be a celebration, but if I happen to run into a semester with a 50% failing rate (which will eventually become 80% or so), that could be devastating to my performance review.

The second issue I have stems from the preceding information. Why would I want to work with the most challenging students to find some success when I could simply work with the best kids in the best districts and cruise through state testing results regardless of how much education was going on? Teachers will fight for the best kids in the best districts. Teachers will fight to get rid of kids on their rosters who have shown a lack of success over the years. Teachers will lie, cheat, and steal to give the appearance of student learning through a state test, especially in lower grades where science and social studies are not tested, for example. How does the fifth grade teacher who is responsible for kids passing a science test for the first time deal with the fact that the third and fourth grade teachers did not teach science to focus on math, which was being tested? Why would I share my teaching strategies that have shown success with my peers (competitors) because my successes will improve my chances of getting the better classes and not helping the other teachers will help weed them out? Why would I help a new teacher who is essentially trying to get my job when I have a track record of success with the GT kids?

Ultimately the only fair way to assess teachers’ effectiveness through student learning is to be able to determine exactly what each student has learned in the past, determine exactly what knowledge and skills have been added purely from that teacher’s efforts, and compare each students potential to the realization of that potential each year. I am pretty sure none of that is possible, let alone through a mostly multiple choice state test given on one day of the year.

Is technology the answer to educational woes?

Who does not love a new piece of technology in their hands? This is true especially when that technology is specifically designed to improve that persons life by simplifying a dreaded task: calculators, word processors, apps, GPS, etc. The question becomes for education, does or will technology improve education and most importantly the learning of students?

I recently read Larry Cuban’s post:

This really got me thinking about technology as a teacher in a 1-1 school, where all students have a laptop computer in their hands every day in every class. As a math teacher, also, I have experienced the calculator revolution:

Technology absolutely has the potential to improve learning. However, as Cuban pointed out, technology is often poorly implemented in classrooms. My experience has shown that teachers are less willing to integrate technology into new modes of learning than as tools to do the same “learning” a different way. Schools and districts prefer to use technology as ways around learning in the classroom, with less effective strategies as credit recovery or original coursework learned through self-taught information and video explorations similar to online classes in colleges. These opportunities often are misused, provide too-easy possibilities for cheating, or do not match the learning styles of the students.

My primary question about technology concerns purpose: Are we pushing technology into the classroom because of its effectiveness in improving learning or is it being pushed as a money making opportunity? Next, I wonder why educational technology infusion has not become more standardized nationwide. Are teachers the specific roadblock? Is there so little educational technology support and software that everyone is just standing around waiting for the next big thing? Do students dislike technology as a tool for learning? Should education recruit the Halo team to create a Algebra 2 based video game, for example, featuring conic sections and three-variable systems of equations?

Ultimately, why has technology not been fully integrated into learning like cell phones in society or television into households? What are the specific challenges to merging the worlds of education and technology?

Do calculators make us smart or dumb?

Calculators help adults, speeding up tiresome divisions of real world money problems, for example.Calculators help explore high level mathematics by utilizing repetitive graphing techniques, for example.

The question is: For basic arithmetic, simple graphing, fundamental equation solving, and other low-level skills, does the use, or the use prior to mastery, of calculators make children less capable of learning higher levels of mathematics?

  1.  What do students think?
  2.  What do parents think?
  3.  What do math teachers think?
  4.  How early is too early for each concept?
  5.  How does this compare to other technological advancements, such as spell checkers or search engines?
  6.  How much of the basics in math should be required without a calculator?
  7.  Which students are most affected by this phenomenon?
  8. How do we compare internationally with our use of calculators in schools?

Any thoughts?


Improving elementary math education

I posted this on an old blog post (, but wanted to think about it more, so I thought I might post it here:

I am a little late here – 3 years. However…

I have long thought a reorganization of current resources may solve many of the problems with math education in the early years. Most of us will probably agree that if children do not learn math early, they are most likely not going to excel at math later; in reality, these kids will often struggle just to meet basic levels for testing these days.

Here is a possible plan:
Instead of having 5 teachers on a grade-level be the “know-it-all” for all subjects, which it may be being suggested they are not, perhaps you could have three generalists, one math specialist, and one math/science specialist. In the beginning, these teachers would simply be chosen from those available. As time goes on, however, administrators could hire specifically to fill the math specialist position for each grade level. A massive reorganization would be required, but it makes more sense to me.

This is just the beginning of the idea, but I thought I would throw it out there. This requires no additional money, training, etc., simply a reallocation of the available resources.

Feel free to respond.
Brett Bothwell

[If you respond to a blog post three years late, would anybody read it?]

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.