Product Endorsement: TI Graphing Calculators

It occurred to me today that it's been over 18 years since I first got my own, brand new, TI-85 graphing calculator. At the time, it was the top of the line, and I was thrilled to have it. And since I have been a math teacher for most of those last 18 years, it has gotten a tremendous amount of use.

And it works just as well today as the day I bought it.

In the meantime, I have added a TI-83 to my calculator collection. I do not use it quite as often as my TI-85, but it, too, has served me well.

One thing I have done just a few times, but which my students have collectively done many times, is to drop my graphing calculator on the floor—often a tile floor, sometimes carpet. I always instinctively cringe whenever I see or hear one of them reach the floor under the influence of gravity—but today I cannot recall a student who had to do anything more than put the batteries back in to get it to work properly. If the product can also survive years in a teen's backpack, then surely it is durable!

I would happily encourage anyone needing a graphing calculator to purchase the appropriate level Texas Instruments machine. They are durable, relatively user-friendly (relative to your mathematical understanding, that is), and even have a pretty good resale value, should you decide to exchange yours for cash.

Will Michigan Change its Graduation Requirements in Math?

In April of 2006, the all-wise legislature of Michigan passed, and the ever-more-all-wise governor signed, legislation that instituted a statewide set of public high school graduation requirements. These requirements meant that in every school district in Michigan,

Students must complete at least Algebra I, Geometry, and Algebra II, or an integrated sequence of this course content that consists of 3 credits, and an additional mathematics credit, such as Trigonometry, Statistics, Pre-calculus, Calculus, Applied Math, Accounting, Business Math, or a retake of Algebra II. Each pupil must successfully complete at least 1 mathematics course during his or her final year of high school enrollment. (See page 26 of this document)

This means that if you want a diploma (beginning, in general, with the Class of 2011), you have to earn four credits of math. Three of them must be in Algebra I, Geometry, and Algebra II. I also blogged extensively on this topic last August, saying the following [this is the slightly-abridged version]:

But the Biggest Problems lie here: The inevitable outcome of the MMC policy will be a combination of the following things:

• The dropout rates will soar. Already, it has been reported that 20-30% of freshmen students failed Algebra I last year—statewide. These students, plus many more who came close to failing, are already discouraged from taking Algebra II (not to mention the other newly-required courses) and will be more likely to choose dropping out than frustration. Dropout rates that were released this week are already dismal enough.
  
• The course known as Algebra II will be watered down...a lot. In order for many to pass, teachers and administrators will feel the pressure to make the class easier so that more kids will pass. This pressure will come from nearly every corner...and it will be effective in most places. Note: The "curriculum standards" will not change, just their application in the classroom. The test scores, on the other hand, will change.
  
• Social promotion will return with a vengeance. Yes, students will be passed along by teachers who, quite frankly, don't want them (and perhaps their ill-mannered, complaining parents) in their classrooms next year. It's already going on in public schools without the newly added pressure. Some teachers will face administrators administering that pressure.
• The disgraceful irony of this will be that the teachers/education system will be blamed. Teachers and schools who hold the line on not watering down the math courses and who do not practice social promotion will take heat for no other reason than a larger number of failing students—when they ought to be commended for encouraging quality work. Admittedly, there are teachers who aren't doing the job as well as they should (but is this not true in every vocation?). Yet I think that ignorant legislators, ambivalent parents, and apathetic students will all be getting less of the blame that will inevitably come when this MMC is shown to be unsuccessful.

In sum, I think the MMC is a bad idea. As a math teacher, I want every student to take as many math courses as they can. I want students to enjoy them and be successful—this is my passion. But not every student is capable of being equally successful, and it may be that other coursework is more appropriate for some students or more conducive to their long-term success. The MMC does not allow much liberty in this regard.

This will eventually become another example of a well-intentioned, poorly-thought-out, dictated-from-the-capital government policy that has the unintended consequence of failure. Significant decisions like these belong in the hands of local school leadership.

It turns out I was wrong on just one point: Before the Algebra II course, in particular, could be fully watered down, the legislature is moving to remove this requirement! According to articles in the Detroit Free Press and the Detroit News, the following legislation is on the move:

• The Michigan House has introduced a bill that "would allow students to bypass the tougher math requirement by taking three years of math, with the only mandated courses being algebra I and geometry. The third math credit could be in a course like financial literacy, which teaches students money management skills." (From the Free Press; emphasis mine)
• The Michigan Senate unanimously passed a bill to grant that "math-related career and technical education courses could fulfill the Algebra II graduation requirement for high school students." (From the Detroit News, emphasis mine)

Interestingly, the Michigan Department of Education opposes the House legislation but supports the Senate legislation. Still trying to figure that out....

Blogprof brought this to my attention earlier in the week; he is strongly opposed to the watering down of the standards. Read his comments here and here. I am also opposed. As a math teacher who works with public school students, I recognize that the standards are unrealistic based upon the reality in the classrooms. They cannot be realistic until all math teaching, from kindergarten on up, is both thorough and rigorous, free of the fluff that infests so much of the curriculum now.

Math educators disagree among themselves what will improve math education most successfully; but all of us believe it can and must be improved. Here are a few of my suggestions:

• Focus both on drill/practice and concepts. Students who drill and practice all the time have difficulty handling real-life problems; students who know how to solve the problems but can't compute accurately are not going to be successful, either.
• Keep calculators out of students' hands before high school, except for certain occasional things where their use is helpful. If you think they should never be used, just tell me what the square root of 11 is to six decimal places, and I'll agree with you. I wrote an entire blog post on this topic.
• Return the setting of curriculum standards to individual school districts. It makes them more accountable for success and failure...as it should be.
• Institute full school choice for all taxpayers. Are you not satisfied with your kids' progress at Lawton? Move them to Paw Paw. Displeased with Detroit Public Schools? [Who isn't?] You get the idea....
  

Most importantly, parents need to be involved—both in encouraging their children and making sure they are provided with a quality education, in math and every other subject. The work of the parents in a child's education is much more important than the work of the state.

On the Use of Calculators by Students

As a math teacher for most of the past fourteen years, I get a lot of questions about when, whether, and which calculators should be used by students. This subject gets a lot of attention from time to time when someone or some company recommends that little kids (even kindergarten students!) should be given unfettered access to calculators...of course, the littlest students maybe should just have 4-function calculators with jumbo buttons.

Most people older than me have a predictable (and generally correct) response: Ludicrous! These children should have to learn their math facts and computation skills the old-fashioned, tried-and-true way: By doing it manually!

Let me share a few bits of wisdom on this topic:

1) The older generation is right about this: There is no good substitute for making students learn to do basic mathematics in their head, or on paper with pencil. They need to know addition facts, times tables, and, yes, even how to divide two fractions. Everyone should know these, for one cannot really have "mathematical functionality" in our society without such basic skills.

2) There is a place for calculators. In the elementary school, however, it is a small place. Calculators can be occasionally used by the discerning teacher to emphasize, review, or otherwise augment a lesson. I think most elementary students actually like the novelty factor of using a calculator from time to time, and this is healthy. [Aside: My children received a couple of $1 dollar-store calculators for Christmas gifts—one of the most fun-per-dollar-spent gifts ever given in our home. They love them, but Daddy still makes them learn their facts without it.] And given the fact that most standardized tests now (or likely soon will) allow for calculator use, there is a benefit to students being able to function with them. In the junior high, calculator use should still be occasional, but as students (by this point) should be fluent with computation, using valuable class time to slog through basic but time-consuming calculations is not usually efficient.

3) In the upper grades, calculators are a useful tool. In some cases, they are necessary (how many of us know what the square root of 67 is, or cos 34°, or ln 11 ?), unless you want to go back to using books of tables, as was common practice 45 years ago. But here is the danger: High school students' knowledge of basic computational facts seems to be inversely proportional to their calculator usage! I have told my junior and senior students that I wanted to see them in a mental math face-off with the 5th or 6th graders. I think they're scared! I think the 5th and 6th graders have a real chance of beating them!

In summary, all students need to be fluent with basic computations and estimations. Students ought to be able to calculate change mentally, estimate simple interest with or without a pencil, and know how to find 30% off the price of that sale item in the mall...as well as the sales tax they'll pay for it. Perhaps in another entry, I'll discuss the merits of graphing calculators vs. other kinds.