## MrHonner.com has Moved! (3 of 4)

Greetings readers!

This is a third reminder that this blog has moved! In order to keep receiving free updates on mathematics, teaching resources, and mathematical art, please visit the new website at www.MrHonner.com and subscribe via email or RSS.

I will repeat this message once more and then deactivate this wordpress.com blog.

For more information, you can read the original message below. I hope to see you on the new site!

=============================================================================================

Over the past month, I have successfully migrated this blog, and all of its content, to a new self-hosted website: **http://www.MrHonner.com**.

I hope you like the look-and-feel of the new site! I am excited about all the new possibilities self-hosting brings, but I will continue to produce new blog posts on a regular basis.

If you wish to continue receiving updates from MrHonner.com, you will have to subscribe to the new site. (Software limitations prevent me from automatically transferring your subscription.)

Simply navigate to www.MrHonner.com, and enter your email address at the top right, under **Subscribe via Email**. You may also subscribe via RSS Feed by pointing your reader here.

I will repeat this message over the next few weeks, and then I will deactivate this wordpress.com blog.

I greatly appreciate your readership, your participation, and your support! I invite you to join me on my new platform; I hope you will.

Thank you-

Patrick Honner

## MrHonner.com is Moving! (2 of 4)

Greetings readers!

This is a second reminder that this blog is moving! In order to keep receiving free updates on mathematics, teaching resources, and mathematical art, please visit the new website at www.MrHonner.com and subscribe via email or RSS.

I will repeat this message two more times over the next 3 weeks and then deactivate this wordpress.com blog.

For more information, you can read the original message below. I hope to see you on the new site!

=============================================================================================

Over the past month, I have successfully migrated this blog, and all of its content, to a new self-hosted website: **http://www.MrHonner.com**.

I hope you like the look-and-feel of the new site! I am excited about all the new possibilities self-hosting brings, but I will continue to produce new blog posts on a regular basis.

If you wish to continue receiving updates from MrHonner.com, you will have to subscribe to the new site. (Software limitations prevent me from automatically transferring your subscription.)

Simply navigate to www.MrHonner.com, and enter your email address at the top right, under **Subscribe via Email**. You may also subscribe via RSS Feed by pointing your reader here.

I will repeat this message over the next few weeks, and then I will deactivate this wordpress.com blog.

I greatly appreciate your readership, your participation, and your support! I invite you to join me on my new platform; I hope you will.

Thank you-

Patrick Honner

## MrHonner.com is Moving!

Greetings readers!

Over the past month, I have successfully migrated this blog, and all of its content, to a new self-hosted website: **http://www.MrHonner.com**.

I hope you like the look-and-feel of the new site! I am excited about all the new possibilities self-hosting brings, but I will continue to produce new blog posts on a regular basis.

If you wish to continue receiving updates from MrHonner.com, you will have to subscribe to the new site. (Software limitations prevent me from automatically transferring your subscription.)

Simply navigate to www.MrHonner.com, and enter your email address at the top right, under **Subscribe via Email**. You may also subscribe via RSS Feed by pointing your reader here.

I will repeat this message over the next few weeks, and then I will deactivate this wordpress.com blog.

I greatly appreciate your readership, your participation, and your support! I invite you to join me on my new platform; I hope you will.

Thank you-

Patrick Honner

## Math Quiz: NYT Learning Network

Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a **Test Yourself** quiz-question, can be found here:

This question relates to mutual funds and investment growth: how much would $1,000 be worth after 35 years?

## What Skills Should Children Learn?

I know very little about early childhood education, but have recently started to think more about it. I greatly enjoy interacting intellectually with my nieces and nephews and find it fascinating to explore ideas like fractals, infinity, and ordering with them. But I don’t really know anything about the theory of how children learn, what they should learn, or when they should learn, mathematically, or otherwise.

To begin exploring the idea, I thought about possible fundamental questions and eventually settled on this: *What are some important content-independent skills that children need to learn?*

I posted the question on Google+, and Don Pata, MrBombastic, Jim Wilder, and Christopher Danielson all offered some great ideas. Here’s the list we compiled through discussion, in no particular order.

**Problem-Solving P****erseverance **— the ability to sustain focus and work through a problem to the end

**Intellectual Discipline **— the willingness to focus and invest energy on learning and development

**Number Sense **— an intuitive understanding of quantity: magnitudes, relationships, and scales

**Reflection **— the ability to objectively self-assess, refine, and adapt

**Communication **— the ability to express information and emotion in a variety of ways, and appropriately interpret and process the expressions of others

**Courage **— the willingness to fail

**Curiosity** — the habit of inquisitiveness and the ability to ask good questions

A good list to start with! Thanks for all the help, and if there are other suggestions, please feel free to leave them in the comments.

You can see the original thread on Google+ here.

## Math Art: Cube Towers

This is “Prime Divisor Cube Towers on Ulam Spiral”, by Berhard Rietzl, on display at the 2012 Bridges Math and Art Conference at Towson University.

This is an artistic representation of the numbers 1 through 144: each color represents a different prime divisor, and so each stack represents the prime factorization of the given number.

You can read more about this piece here.

## Regents Recap — June 2012: Poorly Constructed Questions

Here is another installment from my review of the June 2012 New York State Math Regents exams.

Below are a few examples of what I consider “bad” questions. “Bad” here might mean poorly worded, poorly conceived, or irrelevant. In addition, there is an example of a question with a problematic rubric.

First, a type of problem that occurs regularly, one that is a pet peeve of mine. From the Algebra 2 / Trig exam:

The concept of “middle term” is artificial and depends entirely on how one chooses to evaluate the given expression. This question does not test an authentic mathematical skill; it tests how well a student executes one particular method of evaluating this particular expression.

Next, an example of a poorly-phrased question, one that confuses mathematical terminology. From the Integrated Algebra exam:

To “solve” a system of equations, one must find the ordered pairs that satisfy the given equations. Apparently this question wants only the *y-values *of those solutions, but the phrasing confuses what it means to “solve a system” and to “solve an equation”.

Students can probably figure out what the question-writer wants to hear in this case, but the lack of precision will only exacerbate confusion about the word “solve”.

Here’s a problem on the Algebra 2 / Trig exam that is simply irrelevant.

This question tests one thing, and one thing only: knowledge of an arcane and largely irrelevant notation, namely, degree-minute-second representation of angles. Would anyone outside the nautical or astronomical worlds consider this even remotely valuable?

Lastly, this question from the Integrated Algebra exam is formulated in a reasonable way, but the official scoring guide poses some unnecessary problems.

This question asks the student to graph an equation and then, using the graph, determine and state the roots of the equation. The correct answer is “2 and -4”, and with appropriate work, is worth three points.

However, if the student gives the answer “(2,0) and (-4,0)”, the student can only earn two out of the three points. So if the student gives the coordinates of the points where the graph crosses the x-axis, rather than names the “roots” of the equation, there is a one-third deduction.

While I believe that the distinction between roots and points is important, losing one-third credit seems seems unnecessarily punitive here. If we want to test student’s knowledge of vocabulary, there are better ways to do it than by sneaking it in at the end of an involved algebra problem.

Moreover, since the question requires that the student use the graph, the student is already being forced to interpret the problem in a geometric context. Penalizing them for thinking of the roots geometrically, then, doesn’t quite seem fair.