I had a new experience at Johns Hopkins University yesterday. I had a young woman in my office explaining why she had dropped my elementary Calculus I course.

She found that she was completely unprepared for college level mathematics. She had been made completely calculator dependent. She said that at the beginning of the course she was shocked to see that certain things could be done without a calculator (sorry no details).

Furthermore, she is in contact with her classmates around the country and they are all having the same experience. I encouraged her to organized them to give what I will politely call "feedback" to her high school and her community.

We are, of course, seeing just the tip of the iceberg. Few students have hit college who have gone through reform math all the way K-12. The real crisis for students is still in the future.

We have, in general, been protected at JHU from unprepared students but obviously there is something wrong here too. For one thing, I discovered yesterday that our placement test was voluntary! Duh.

I worry that the College Board and its tests may well be headed in a direction that will hurt colleges. They have recently written math standards that are, well, not so good. They are trying to fix that up but you get comments like"we are getting conflicting advice". Of course they are. When they asked one of the authors of Core-Plus and a mathematician, they are bound to get conflicting advice. They want to reconcile that advice. That very desire is problematic.

He followed that email up with another:

Today I have something else to add. Had lunch with my usual Wednesday crowd and I was told by a physicist that he ran into a student in his physics class who couldn't divide .3 by .5 because they didn't have their calculator.

I do believe this kind of thing is new to JHU and to hear two cases in two

days suggests we need to do something about it here.

W. Stephen Wilson

Professor of Mathematics

Department of Mathematics

Johns Hopkins University

And people wonder why I don't focus on calculator use in my math classes!

Dr. Wilson gave permission to use his name/title to add whatever gravitas would be lacking from an anonymous complaint.

## 19 comments:

Unbelievable. Well, not really. I've been having this horrible sneaking suspicion that the state colleges will be/are just passing students through as "educated" just as high schools have been doing, kicking the problem down the road to us employers. And maybe the elite universities are doing it as well.

Gads.

The fact that this is new to JHU is a little surprising. I've been getting this sort of thing from my students for nearly a decade. They are heavily tech-dependent on the one hand, but on the other hand lack the basic fluency with technology that would allow them to use it in appropriate and novel ways to solve problems (all that talk about "digital natives" not amounting to anything).

You have to have calculators to do some tasks -- I wouldn't expect a calculus student to give me a two-decimal approximation for 1/(1+exp(-2)) right off the top of her/his head -- but when comes down to leaving 0.3/0.5 unsimplified then things are really getting out of hand.

Students have to be good at BOTH technology AND raw mathematics.

I am a calculator pusher in my lower level hs classes. I don't want to hold kids back because they can't do arithmetic. In my calculus classes, that is another discussion. We are forced to use the graphing calculator, as it is required for AP exam. A good teacher integrates both into the classroom. My students take both calculator and non calculator exams. Technology has enriched their understanding of calculus. They now can concentrate more on concepts and less on tedious calculations.

After we grade and score a test, you ought to see the pandemonium as my 8th grade students try to convert their score into a percentage.

Once I have taught them how to do that (again), I then get pelted with letter grade questions: "What would an 85% be?"

Sigh.

Part of that is because the state tests REQUIRE teaching of calculator use as part of their curriculum. They also teach such maddening things as estimating an answer rather than simply answering the problem. Now the state is trying to reword math by calling addition "composition" and subtraction "decomposition". No wonder kids are totally confused. I can still multiply faster than my own kids because my third grade teacher made us write the times tables every morning while she took up lunch money. Instead such skills as multiplication are taught as a six week unit and then teacher wring their hands that kids don't get it. Some things, like the alphabet and times tables, need to be rote memorization. I still have kids that can't file their names alphabetically and I teach high school. I used to think my ADHD kid would struggle in college, but instead he's probably going to end up in the top half of his class, because although he didn't do things by the book, he did learn how to figure things out. Maybe the rarified schools shouls start recruiting kids who can actually do work rather than relying on SAT's.

In Mr. Baker's AB class we are taught how to use our advanced graphing calculators to solve most calculus problems. Come test time we are required to do the problems without use of our calculators. This provides the knowledge to do the problems quickly for the SAT II and AP exams with the calculator, and also the knowledge to do the problems without creating calculator dependency. This teaching is, in my opinion equipping us for all possible scenarios.

PO'd - If you weren't preparing for the AP, would you use graphing calculators?

Don't get me started ...

Why is it so hard to make the case for doing math with a pencil and paper in the lower grades? THat's when they need to be learning how to do it WITHOUT a calculator.

And I've heard about enough of AP calculus. In my school there is not a single student capable of doing college-level math yet, AP is all the rage. I don't get it. Regular-track calculus IS AP as far as I'm concerned.

And the last I heard, calculators were recommended but not required on these exams (SAT, ACT, AP). (I'm not a math teacher so I don't know for sure about the requirement on AP). But as long as they are allowed that's all the justification a student needs to think he needs one in order to take the test.

Do we want to raise math competency in the United States? Then getting calculators out of the schools is a good first step.

Sign me ... still fighting the battle ...

Bob from Georgia

Bob are you teaching calculus in a high school? I sure hope not. Here is the AP Calculus calculator policy directly from collegeboard.com. It took a simple google search to find it. IMHO no one should be teaching upper level high school or college math and be unfamiliar with the AP and SAT testing policies. Why do you think students are taking these upper level math classes? I can assure you it is not for high school credits. If their own teachers can't prepare them for these tests then who will?

Calculator Policy

The use of a graphing calculator is considered an integral part of the AP Calculus course, and is permissible on parts of the AP Calculus Exams. Students should use this technology on a regular basis so that they become adept at using their graphing calculators. Students should also have experience with the basic paper-and-pencil techniques of calculus and be able to apply them when technological tools are unavailable or inappropriate.

Graphing Calculator Capabilities for the Exams

The committee develops exams based on the assumption that all students have access to four basic calculator capabilities used extensively in calculus. A graphing calculator appropriate for use on the exams is expected to have the built-in capability to:

* Plot the graph of a function within an arbitrary viewing window

* Find the zeros of functions (solve equations numerically)

* Numerically calculate the derivative of a function

* Numerically calculate the value of a definite integral

One or more of these capabilities should provide the sufficient computational tools for successful development of a solution to any exam question that requires the use of a calculator. Care is taken to ensure that the exam questions do not favor students who use graphing calculators with more extensive built-in features.

Proctors are required to check calculators before the exam. Therefore, it is important for each student to have an approved calculator. Students should be thoroughly familiar with the operation of the calculators they plan to use on the exam.

For results obtained using one of the four required calculator capabilities listed above, students are required to write the setup (e.g., the equation being solved, or the derivative or definite integral being evaluated) that leads to the solution, along with the result produced by the calculator. For example, if the student is asked to find the area of a region, the student is expected to show a definite integral (i.e., the setup) and the answer. The student need not compute the antiderivative; the calculator may be used to calculate the value of the definite integral without further explanation. For solutions obtained using a calculator capability other than one of the four required ones, students must also show the mathematical steps that lead to the answer; a calculator result is not sufficient. For example, if the student is asked to find a relative minimum value of a function, the student is expected to use calculus and show the mathematical steps that lead to the answer. It is not sufficient to graph the function or use a built-in minimum folder.

When a student is asked to justify an answer, the justification must include mathematical reasons, not merely calculator results. Functions, graphs, tables, or other objects that are used in a justification should be clearly identified.

There is more but I put the most relevant information in this post to see the whole policy go to:

http://www.collegeboard.com/student/testing/ap/calculus_ab/calc.html?calcab

"After we grade and score a test, you ought to see the pandemonium as my 8th grade students try to convert their score into a percentage."

Once when I handed back exams, a student raised his hand and said, "I thought you said the mean was 78," and I said, "Yes, that's correct." He then said, "So how can I have a 54?" I said, "I'm sorry, I don't understand your question," and he said, "Isn't the mean what everybody gets?"

Sigh indeed.

I am not a math teacher at all ... I'm a history teacher with another degree in computer science. AP calculus is pointless as the number of students I have met who are capable of doing college-level calculus is so low that it is not practical to have these classes. (Right now at my school there are zero students capable of doing college-level work in calculus.) A regular Calculus class prepares students for college much better than the AP overload.

That doesn't mean there aren't above-average and even gifted students in my high school; it just means that we are fooling them into thinking that they are taking a college-level Calculus course. Last year in my high school one person got a 4 on the AP exam; I don't expect anyone to get higher than a 1 this year.

And now, the main point of the post: Calculators, whether graphing, four-function, business/financial, or whatever will not help these students on an AP Calculus exam. I know that because the AP students from last year couldn't remember how to even use their calculators when they entered remedial math in their first semester of college.

If I give in an inch on the calculator issue, it's that the only time a student might want a calculator in K-12 math is if they get into Calculus in the 12th grade and, as I stated before, the number of students is pretty small. Otherwise we are fooling ourselves that students need a calculator to learn math.

But ... I'm a history teacher. I've got to worry about students who think that the best lessons are learned through watching a Disney cartoon. Then I run into 'em working at McDonalds where they have to wait for the cash register to tell them how much change to give me for my value meal.

Bob from Georgia

I show students how to manually calculate a square root (just so they can tell their grandchildren that they once saw it done), then I show them how to look them up in the tables. After that, I don't have a problem with calculators for square roots.

After I require students to memorize all sorts of common data on the unit circle, and we analyze the graphs of the trig functions, I don't have a problem with calculators for trig functions.

But being unable to do calculus without a graphing calculator? Unpardonable. Mr. Baker, mentioned above, appears to be doing it correctly.

The AP Program, which began as an experiment for elite students seeking college courses and credit, has now become a fixture in more than 14,000 US public schools. Beyond gaining experience, a student gains an edge; college admission officers say they place more importance on grades in college-prep courses such as AP than they do on any other factor.

Every state sees gains in students passing AP

By Ben Feller, Associated Press | January 26, 2005

WASHINGTON -- More students are passing Advanced Placement exams in every part of the country, as college-level work in high school becomes increasingly common -- and competitive.

In every state and the District of Columbia, the percentage of public school students who passed at least one AP test was up in 2004, compared with the graduating class of 2000. The Bush administration, which has been pushing to increase high school rigor, embraced the news, which followed other reports that have underscored how unprepared many graduates are for college or work.

Across the country, 20.9 percent of the public school class of 2004 -- one in five students -- took at least one AP exam, compared with 15.9 percent four years earlier. More significantly, 13.2 percent mastered an AP exam last year, up from 10.2 percent in 2000.

Research shows that success on AP exams is a strong predictor of success in college.

Bob please go read this article:

http://www.washingtonpost.com/wp-dyn/articles/A6900-2004Nov23.html

"The use of a graphing calculator is considered an integral part of the AP Calculus course, and is permissible on parts of the AP Calculus Exams."

As someone who has administered hundreds of exams -- many of them for ETS -- I do not understand how you can allow something on PART of the test and not others, and enforce it. What this policy translates to is that calculators are allowed on ALL of the exam, just not officially.

Anonymous at 11:21 pm: what does that article have to say about the use of calculators in k-12 math? Or about whether the students at Bob's high school are prepared for the AP Calculus exam?

The article cites research on the supposed effect of AP courses on the college performance of Texas high school students. Not the AP Calculus test, "an" AP exam. Matthews cites Jaime Escalante's success in preparing his students for the AP calculus exam, but that is a separate theme which Matthews links to the chart taken from "Do What Works."

I am coming to believe that US education could benefit from enacting a more rigorous, demanding curriculum for all students. This has no chance of happening, as parents are more interested in debating high school sports than high school curricula. Again, though, I find it hard to find the article's connection to the long term effect of calculator usage in the k-12 classroom, unless it is something like the illogical supposition, "the AP exam allows graphing calculator use, even failing an AP exam increases a kid's chance of succeeding in college, therefore calculator use increases college performance."

In response to this:

Again, though, I find it hard to find the article's connection to the long term effect of calculator usage in the k-12 classroom, unless it is something like the illogical supposition, "the AP exam allows graphing calculator use, even failing an AP exam increases a kid's chance of succeeding in college, therefore calculator use increases college performance."

I was in no way responding to the topic at hand, the use of calculators in high school AP calculus. I already posted the facts about the test and why I therefore agree that learning to use a calculator is necessary and important.

I was responding to Bobs comments here:

AP calculus is pointless as the number of students I have met who are capable of doing college-level calculus is so low that it is not practical to have these classes. (Right now at my school there are zero students capable of doing college-level work in calculus.) A regular Calculus class prepares students for college much better than the AP overload.

I do believe there is very relevant information in this article to dispute Bob's negative attitude towards AP tests for high school students.

Why should the College Board, an unregulated and supposedly "not-for-profit" organization, be allowed to guide curriculum in America? According to this, their standards are so low that the entire idea of the company- connecting students with colleges- seems to be just another money-making guise. What do you think about creating some sort of government-run standardized college entrance exam which could hopefully erase many of the failures of the SAT, AP, PSAT, etc?

Perhaps they shouldn't, but do you really think a politically-created test would be any better?

The "math wars" of the 90s would be child's play compared to what we'd see if the government got involved.

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