I have never experienced any maths problems because kids do CS. The programming languages I’ve taught include decimals. In many programming languages, the statement x = x + 2 is written as x := x + 2 which reads as “x is assigned the value of x + 2”, which is ok. In languages that just use x = x + 2, the ‘=’ sign means ‘is assigned the value of’, which kids understand.

Overall, the students that choose Computer Science really enjoy it, and it is a wonderful class to teach.

]]>Equality sign as assignment is definitely confusing, maybe not as confusing in Java itself since in Java, equality is not described by the equal sign but rather by a special symbol ==, but it is confusing since it can be (and often is) confused by students as an equal sign. To our students, we say that x = x + 2 simply means that the value at the next moment of time is equal to the value at the previous moment of time + 2, i.e., that x(t+1) = x(t) + 2, which is now an absolutely correct mathematical statement. This may be a way to clarify, since by the time students at school learn basics of programming, they already have some idea about functions or at least about the fact that some quantities change with time.

]]>Readers might enjoy my new free book, The 4th R. I define the 4th R to be Reasoning/computational thinking. I recommend that it be integrated into all curriculum areas,starting at the earliest grade levels, much in the same way that we focus on and integrate the first three Rs (reading, writing, arithmetic).

See my free 80 page book:

Moursund, D. (12/23/2016). The Fourth R. Eugene, OR: Information Age Education. Download the Microsoft Word file from http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/289-the-fourth-r/file.html. Download the PDF file from http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/290-the-fourth-r-1/file.html. Access the book online at http://iae-pedia.org/The_Fourth_R.

]]>Active Learning Mean for Mathematicians?” in the current issue of the

Notices of the AMS. Congratulations on a work well done.

While much of what the authors bring forward is “not new news,” the forum in

which you offered it truly is NEW, namely the Notices of the AMS. The

organization and presentation were very engaging, with rich

illustrations to which readers could relate. As a former Editor (I

founded the journal PRIMUS years ago) I appreciated the elegance in

your writing and your narrative approach.

As a long standing member of AMS – over 50 years and as well with MAA –

I am so pleased to see the Society turning more and more of its

publication pages to teaching (while still maintaining its strong and

supportive efforts on research) the very mathematics which is the core

of the research effort in mathematics. Indeed, a few weeks ago at the

Joint Mathematics Meeting in Atlanta we offered an AMS Special Session

on The Modeling First Approach to Teaching Differential Equations.

This was one of the first such sessions the AMS offered which was

solely devoted to teaching. We suffered the lack of attendance due to

the weather “panic” that caused folks to leave Atlanta early, but we had

reasonable attendance and some remarkable talks.

I particularly appreciated the article’s words, “. . . lecturing in order to

cover more material is not always effective for students. By exclusively

considering course content coverage and responding to content coverage

with telling, we risk forgetting the many other elements of student

learning that active learning addresses, such as the cognitive goals for

students outlined in the 2015 MAA CUPM Curriculum Guide.” The fear (in

some case excuse) that faculty have for not using active learning that

coverage will be lost is simply not supported.

I have been in the active learning camp for years, indeed, once engaged

in active learning there is a sort of guilt feeling that happens if one

has to “drop back and punt” by going to lecture. Nevertheless, there are

times when we need to just tell them so min-lectures are not plain bad.

Years ago Kurt Bryan, a colleague at Rose-Hulman Institute of Technology

in Terre Haute IN co-taught a differential equations course and we

taught in very active mode, with in class modeling projects. On course

end evaluations the students said essentially, “We really liked when you

were `on’ and produced quality activities for us, but we did not like

when you were not `on’ and lectured.” They can tell the difference and

they know when they are engaging and learning. Hopefully, colleagues who

read your piece and who try to engage in more active learning get good

student feedback. However, Karl Smith of Purdue University’s Engineering

Education program, told me years ago that it can take as much as 5 years

to be proficient in active learning techniques, but he also said once

there you will not go back to lecturing. So true!

Now while I have your attention I want to share something we are working

on now which is an ultimate active learning effort, namely, teaching

differential equations using a modeling-first approach. We call it

SIMIODE – Systemic Initiative for Modeling Investigations and

Opportunities with Differential Equations. SIMIODE is about teaching

differential equations using modeling and technology upfront and

throughout the learning process. You can learn more at our dynamic

website, www.simiode.org, where we offer a community in which colleagues

can communicate, collaborate, publish, teach, explore, contribute, etc.

Check us out.

Finally and again, we should all thank and applaud the AUTHORS and THE Editors of the Notices of the AMS for this terrific piece.

PS I was particularly impressed with the Middlebury images as my wife is

a Midd grad!!!

Since writing this post, I’ve started using our online LMS gradebook. It isn’t a great fix. For example, since students take quizzes a different number of times, this data can’t really be stored in the gradebook. We have a D2L product. I did figure out how to do a “Selectbox” grade, so I have my EMRN system there. I have one column per standard and I update the dropdown menu each time a student makes an attempt at a standard. I also save some data in Excel on my office computer where I feel like I have more control over how calculations are handled.

Hope this helps!

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