How much does the understanding of your students of coordinate systems improve by teaching them with the Pomegraphit method rather than teaching the regular way?

I haven’t run any specific study comparing this approach to introducing the coordinate plane with any other. I tend to a) draw inspiration from the Freudenthalian work on “progressive formalisation,” and also from the fact that I can always add the numeric coordinate plane. But I can’t subtract it once it’s added.

How do you arrange the transition from this method to using numbers?

I give them a single fruit on the coordinate plane. I ask them to “send a text message to a friend that precisely describes the location of that fruit.” They find it challenging. They rely on imprecise language. Then I add a grid to the plane and ask them to repeat the exercise. They feel something like relief. The grid is a tool to enhance their communication. They still tend to say things like “four left and three down,” which I need to help them formalize to (-4,-3).

]]>I am an educational studies student from Munich and I am currently participating in a seminar about teaching Math in English. I just found your blog and I really like your method of teaching the coordinate systems. But I’ve got a few questions.

How much does the understanding of your students of coordinate systems improve by teaching them with the Pomegraphit method rather than teaching the regular way?

Do you use this method only to introduce the topic?

How do you arrange the transition from this method to using numbers?

I look forward to your reactions

Katrin ]]>

A college diploma, originally, meant graduates have a certain level of advanced knowledge.

Agreed. More for some majors than others. A general level of advanced knowledge for all a/k/a general education.

But throughout your comment, you assume the definition of “advanced knowledge” should be “the punishing and pointless symbolic manipulation of Algebra 2.” That currently *is* the definition, but it should be revised as soon as possible.

A BS / HS diploma should require a foreign language. It shouldn’t be Latin.

A BS / HS diploma should require some literature. It shouldn’t be the installation manual for a rotary telephone.

A BS / HS diploma should require some history. It shouldn’t be a semester-long course analyzing the Tariff of 1824.

Etc.

]]>Our entire high school math program is premised on the fact that kids should get as far as they can in math in order to get success in college. Now some colleges are allowing students to get college credit for middle school math, while others are getting castigated for making a college diploma mean something.

If you’re going to argue that college needs no high school math, then why not start pushing for high schools to be able to teach low level math? Right now, most high school students aren’t allowed to take anything lower than pre-algebra, If colleges are allowed to say “oh, who needs this? She’s just going to be a nurse. Let’s give her a college diploma and hope no one notices she couldn’t pass a high school algebra class”, then why aren’t high schools allowed to say “look, half our kids don’t know middle school math. Can we stop pretending to teach them advanced math and give them a better grounding in fractions and ratios?”

Moreover, isn’t your point that good teachers can engage and get any students to learn? And haven’t you, in the past, pushed back on teachers who argue that no, some of this math is too hard for the students, that they need either interest or ability? Why isn’t it the job of college professors and the older students, responsible for their own decisions, to learn enough math to justify a college diploma?

Most students take algebra 2 in high school. Most college students can’t demonstrate algebra 2 ability in college. Generally, it has been agreed up to this point that ability to do advanced math is a key requirement for a college degree.

So it seems to me that people who get angry at the very idea that advanced math is reasonable for college ought to be pushing for much lower high school math requirements. Because far more kids are being shoved into math classes they don’t want, then shoved into summer school to offer seat time for a passing grade, and I don’t see people getting upset about that.

]]>I guess the question is this: if college doesn’t need math beyond algebra, then why does the job need college?

Is this a trick question? Lots of jobs needs tertiary education but don’t need intermediate algebra. e.g. Here’s a nurse who’s required to find the roots of some goofy-ass transformed quadratic.

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