Category Archives: News

Help Wanted: Math on a Stick

The following is cross-posted from Talking Math with Your Kids.

I want to tell you about a vision of a beautiful thing, and I want to ask you to help make it happen.


math.on.a.stick.for.blog

 

Math on a Stick logo by Emily Bremner Forbes, who makes beautiful things. Many thanks, Emily!

Math on a Stick will be an annual event at the Minnesota State Fair (12 days of fun ending Labor Day!) that engages young children (4—10 years old) and their caregivers in informal mathematics activity and conversation using the Fair as a context.

  • Parents will push children on a protractor swing so that together they can notice the angles and fractions of a circle the children travel through.
  • Parents and children will use beautiful tiles to make shapes and intriguing patterns.
  • They will comb the fairgrounds looking for groups of many different sizes, asking questions such How many mini donuts are in a bag?, How many sides does the Agriculture-Horticulture building have? and Why is it so hard to find a group of 17?
  • They will notice the rotational and reflection symmetry in a wide variety of plants and flowers, then copy these symmetries by making a paper flower to take home.

Math on a Stick has four components:

  1. The Math-y Midway
  2. The Garden of Symmetry
  3. The Number Game
  4. Visiting mathematicians and mathematical artists.

Find out more about each of these below.

The major question now is whether Math on a Stick happens for the first time this year or next. The organizing body is the Minnesota Council of Teachers of MathematicsThe Math Forum is by our side. Max Ray and Annie Fetter from the Math Forum plan to come to Minnesota to help run the event. The Minnesota State Fair and Minnesota State Fair Foundation love the idea. We just need to convince all parties that it is possible to pull this off in the coming three months, and we need to locate the funding to make it happen.

Your Call to Action

We’ll need help with three things:

  1. Volunteer hours this summer, before the Fair
  2. Volunteer hours during the Fair
  3. Funding

Of course I expect that most who heed this call will hail from the great state of Minnesota, but I encourage others to consider scheduling a visit. This will be a wonderful event, and the Minnesota State Fair is truly a grand spectacle.

Volunteering

Before the Fair, we’ll need help finding and creating the things that will make the event go.

During the Fair, we’ll need help staffing the event. It runs 9 a.m. to 9 p.m. August 27—Sept. 7. We’ll have have about four shifts a day and we’ll require multiple people staffing each shift.

If we get Math on a Stick up and running this summer, one of our first orders of business will be to establish our volunteer website. Please check your summer calendars, pencil us in, and keep an eye on this blog for more information.

Funding

If you (or someone you know, or an organization you are involved with) are in a position to help fund Math on a Stick, get in touch with the Minnesota State Fair Foundation to let them know you’d like to help make this happen. Our overall budget is on the order of $20,000.

The specifics

Here are specifics on the four components of Math on a Stick.

The Number Game

The major activity at Math on a Stick is The Number Game. Adapted for math from the Alphabet Forest’s Word Game, children and parents are challenged to find groups of every size 1—20 at the fair. Examples: A corn dog has 1 stick, a cow has 4 legs, the Ferris Wheel has 20 carts.

Players receive a form they carry with them around the fair to record their findings, and can return with a completed form to claim a ribbon. Additionally, players can email, tweet, and post to Instagram, their Number Game fair photos. These are curated by Math on a Stick volunteers and posted to a public display that resets each day so that collectively State Fair attendees recreate daily a new visual answer guide to the Number Game.

The Math-y Midway

A protractor swingset, tables with fun tessellating tiles, and images from Which One Doesn’t Belong? and a (forthcoming) counting book to play with and discuss.

The Garden of Symmetry

Flowers are grown in planters along a path. As you walk from one end of the path to the other, you pass flowers with increasingly complex symmetry. Grasses (with one line of symmetry) are near one end. Irises are a bit further along (with three rotational symmetries), and sunflowers are near the far end (with MANY symmetries). Visitors to the Garden of Symmetry are invited to carry a tool consisting of two small mirrors taped together to investigate symmetries in the garden and the interpretive signage.

Visiting mathematicians and mathematical artists

An activity area is set aside for a daily visit from a mathematician or mathematical artist. Each provides engaging, hands-on math activities during a scheduled period each day. We will draw upon talent from Minnesota, as well as nationally (budget allowing).

For full details on the event, have a look at our Math on a Stick white paper.

Hit me in the comments with any questions you have.

Get in touch with me through the About/Contact page on this blog.

Please help us build this thing. It’s going to be great!

Building a better shapes book

Just a quick note here for the folks who are (a) not on Twitter and (b) not following Talking Math with Your Kids.

I created a shapes book for all ages. The digital version is free for now. Details are in this post over at TMWYK.

3

New Desmos lesson(s)

You should seriously go check out Polygraph. Four versions of a delightful and challenging game:

  1. Lines
  2. Parabolas
  3. Rational functions
  4. Hexagons

The hexagons will be familiar to long-time readers of this blog.

Screen shot of hexagons

I have run the parabolas version in College Algebra, and the hexagons version in my Ed Tech course. It was a huge hit both times—lots of conversation happened both electronically and out loud in the classroom. It’s a ton of fun.

I am especially pleased with the rational functions version. It makes for challenging work—even among the mathematically astute Team Desmos in recent trial runs.

Read the Desmos blog post on the matter if you like.

[News] A new project

Back in the spring when the Letter to Jack was a hot item, I took to Twitter to wonder why there was no Common Core Math for Dummies. One thing led to another, I proposed it to Wiley and now you can expect it in the spring.

Audience is parents, and this may appear in the title (Common Core Math for Parents For Dummies is the working title). It goes for the big picture in each of the grade levels, K—8.

The For Dummies format is pretty rigid but there will be no mistaking authorship. A few sample section headings (and the grades where they will appear) to whet your appetite:

1st grade. Saying bye-bye to key words

1st grade. Understanding the importance of ten

2nd grade. Why units matter

2nd grade. Place value

2nd grade. More about place value

2nd grade. Seriously. Place value.

4th grade. Multiplication: What is it and why not just memorize the facts?

5th grade. Standard algorithms: Doing things “the old-fashioned way”?

6th grade. Dividing fractions—More fun than you’d think!

6th grade. Area: It all goes back to rectangles

8th grade. Congruence and similarity: Two kinds of sameness

Catch you all later. I have some writing to do!

I’ll keep you posted.

5 reasons not to share that Common Core worksheet on Facebook

(NOTE: If you arrived here via Facebook, welcome. You may also be interested in the perspective of a middle school teacher, Mr. Aion. Click on through for more.)

You are browsing Facebook on a Sunday evening. Someone has shared a baffling piece of math homework that was sent home with their child. Accompanying commentary bemoans the current state and future trajectory of mathematics teaching and learning, and lays blame for this at the feet of the Common Core State Standards.

You are baffled by the worksheet too. You are about to click the Share button.

But here are five reasons that’s a bad idea.

1. Credentials are not a trump card.

Almost invariably, the parent who shares the worksheet cites a degree as a credential for the critique. “I have a Bachelor of Science in electronics engineering,” wrote the parent in the recent “Letter to Jack”.

frustrated.parent

The math you need to know to be an electronics engineer is different from the math you need to know to be a math teacher. I am quite certain that electronics engineers use math that I have not studied, and similarly I use mathematical ideas that they have not studied.

When my teacher friends watch the following video of my son Griffin, they tend to see that a number line would be the right thing to draw to capture his thinking, and they tend to know what is coming when he goes to solve the problem on paper. They tend to describe my son’s work as demonstrating competence or proficiency with subtraction, but suffering mechanical errors when solving with paper and pencil.

Non-teachers who view this video are less likely to see a connection to the number line, and they tend to consider Griffin’s knowledge of subtraction to be weak. 

The difference is that teachers have a different kind of mathematical knowledge from electrical engineers. Not necessarily more or less knowledge—different knowledge. This is because different mathematical knowledge is required to do their job.

Deborah Ball refers to this different knowledge as mathematical knowledge for teaching. It is what mathematics teachers know who are more successful in their work. This knowledge includes common errors with standard algorithms, as well as their sources [start at about 2:30 in this video]. It includes common correct, alternative ways of performing and showing computations.

Moral of the story: You may not want to look to an electrical engineer as your primary resource for the current state of math teaching.

2. It is probably misinterpreted.

Homework time can be stressful. This is not new to Common Core. 

Parents are trying simultaneously to be helpers and enforcers. When a child does not understand what appears to be something simple, tempers can flare

We parents are not at our most rational at these times, and this may prevent us from fully understanding the goal of the task. 

When Frustrated Parent wrote to Jack, he committed two important errors of misinterpretation: (1) He assumed that Jack’s method was being taught as a preferred algorithm for subtraction, and (2) He assumed that something unfamiliar to him must be complicated.

(NOTE: Frustrated Parent is in fact male. A quick Google search will turn up his interview on Fox News and his public Facebook post about this letter.)

These are totally understandable. I do not hold Frustrated Parent in contempt for his frustration.

I am simply asking the rest of us to resist sharing without asking critical questions.

The strategy shown on this particular worksheet is counting back

This is how many people count change: You gave me $20.00 for a $3.18 item, so you get $17 minus $0.18 in change…that’s $16.90 minus $0.08…$16.82. 

The number line Jack drew captures this thinking. 

The number line could have been improved by (1) arrows on the arches, and (2) smaller jumps to suggest that Jack is counting by a small number (as it is, the relative sizes of the pictured jumps on the number line suggest Jack is counting by 10s or 20s to the left of 127—as Frustrated Parent notes in a later Facebook post).

fp.better.num.line

This worksheet was not about getting students to use the number line as an algorithm. It was about having students try to understand the thinking of someone else.

This may have been a bad worksheet—but not for the reasons cited when people share it on Facebook.

[For the record, in this case Jack’s error was forgetting to subtract the 10 in 316. He counted back three hundred, then six ones. The result is that his answer (indicated on the left-hand end of the number line) is too big by 10. He gets 121. The correct answer is 111.]

3. It is probably not “Common Core”.

There is nothing in the Common Core State Standards that requires students to use number lines to perform multi-digit subtraction. In fact, standard 4.NBT.B.4  requires students to “Fluently add and subtract multi-digit whole numbers using the standard algorithm”.

The standard algorithm, of course, is what the frustrated parent suggests that Jack use.

4. Anecdotal evidence is not research data.

While parents who share these worksheets in frustration will make claims such as the old way worked for me, the research evidence is quite strong that the old ways did not work.

Changes being made to American mathematics teaching are (1) very slow to take root, and (2) based on years of American and international research on student learning. 

5. Teachers need our support, not our scorn.

The frustration and anger of a parent who is struggling to help their struggling child is completely understandable. Any parent who claims they have never been frustrated at homework time is living in (a) a fantasy world, (b) denial, or (c) both.

But when we widely share the product of others’ frustration online, we amplify the anger. Ultimately, classroom teachers are the targets of this anger, as they are the public face of the education system. As a group, teachers work very hard with limited resources. They are called upon to equalize the inequities our society creates, and to offer not just equal educational opportunities, but equal educational outcomes to all children.

Now—more than ever—teachers need our support, not our scorn.

What to do instead

If you are Frustrated Parent, you can write a level-headed note to the teacher. It might look something like this:

Dear Ms. Crabapple,

I worked with my child on this problem tonight. Neither of us could figure out what is going on with the number line. You can see the work we did together, but we did not know how to write an explanation to Jack. We are confused. Please help.

Sincerely,

Frustrated Parent

If you run across the work of another Frustrated Parent online, please consider asking someone about it before sharing it as evidence of the decline of American mathematics education.  Some possibilities:

Ask a teacher friend. You probably have at least one on Facebook. 

Ask on Twitter. There are many eager-to-help math teachers who follow the hashtags #mtbos and #mathchat—sincere questions asked on those hashtags will get sincere answers and offers of help.

Ask on a website. The Mathematics Educators stack exchange is a new resource for people to ask and answer questions related to teaching and learning mathematics. Anyone is welcome to ask a question, anyone can answer, and everyone votes on the quality of the answers so that you can easily find the best ones.

Read my book. Since writing the first version of this post, I wrote a book. Common Core Math For Parents For Dummies was published in April, 2015. Its tone is informative and supportive. It does not treat you as a dummy.

Related

The New York Times published a piece on “Common Core homework” in July. I wrote a response to it that clarifies a critique in the article about dots. I invite you to read there for more information.

Note: Things got far beyond my ability to curate in the comments, so I needed to turn comments off. I would be more than happy to take up the dialogue on Twitter or through a pingback to your blog. You can also contact me if you wish to discuss further—Hit the About/Contact link at the top of the page.

Second note: I will curate and organize the major threads of the comment discussion in the coming days. In the meantime, I have sequestered the existing comments as the discussion threatened to overwhelm the point of the initial post. I have not deleted them.

The latest “Common Core” worksheet

You have seen this on Facebook.

Original (Click to enlarge)

Ugh what a mess.

Please share the annotated version widely.

I’ll say what I have to say (comments closed) and move on. If you wish to discuss further, hit me up on Twitter or pingback to the blog. Want to talk in private? Click the About/Contact link up top.

Also, Justin Aion—middle school teacher extraordinaire—wrote up his views on the matter. You can read them over in his house.

Here goes…

The intended answer

Dear Jack,

You only subtracted 306 from 427, not 316. You need to subtract another 10 to get the correct answer of 111.

Sincerely,

Helpful student

The purpose of this task

I cannot say whether this was the right task for this child at this time because I do not know the child, the teacher or the classroom.

I can say the following:

  • Analyzing errors is a useful way to encourage metacognition, which means thinking about your thinking. This is an important part of training our minds.
  • The number line here is a representation of a certain kind of thinking—counting back. The number line is not the algorithm. The number line records Jack’s thinking. He counted back from 427 by hundreds. Then he counted back by ones. He skipped the tens. We can see this error because he recorded his thinking with a number line.
  • Coincidentally, the calculation in question requires no regrouping (borrowing) in the standard algorithm, so the problem appears deceptively simple in its simplified version.
  • This task is intended to help students connect the steps of the standard (simplified) algorithm with reasoning that is based on the values of the numbers involved. Why count back by three big jumps? Because you are subtracting 300-something. Why count back by six small jumps? Because you are subtracting something-something-6. Wait! What happened to the 1 in the tens place? Oops. Jack forgot it. That’s his mistake.

So what?

The Common Core State Standards do require students to use number lines more than is common practice in many present elementary curricula. When well executed, these number lines provide support for kids to express their mental math strategies.

No one is advocating that children need to draw a number line to compute multi-digit subtraction problems that they can quickly execute in other ways.

The Common Core State Standards dictate teaching the standard algorithms for all four arithmetic operations.

But the “Frustrated Parent” who signed that letter, and the many people with whom that letter resonated, seem not to understand that they themselves think the way Jack is trying to in this task.

Here is the test of that.

A task

What is 1001 minus 2?

You had better not be getting out paper and pencil for this. As an adult “with extensive study in differential equations,” you had better be able to do it as quickly as my 9-year old.

He knows with certainty that 1001 minus 2 is 999. But he does not know how to get the algorithm to make that happen.

If I have to choose one of those two—(1) Know the correct answer with certainty based on the values of the numbers involved, and (2) Get the correct answer using a particular algorithm, but needing paper and pencil to solve this and similar problems—I choose (1) every time.

But we don’t have to choose. We need to work on both.

That’s not Common Core.

That’s common sense.

[Comments closed]

Twitter Math Camp

I want to use this space to make a pitch for a conference session.

See, there is this thing called Twitter Math Camp. It is professional development by teachers, for teachers—nearly all of us connected through Twitter. It takes place this summer near Tulsa, OK.

I am presenting with Malke Rosenfeld. Our official description is copied below.

Malke and I have developed a really productive collaboration this year. You can browse both of our blogs to see the kinds of questions and learning this collaboration has developed for each of us.

Here is my pitch for our session…

We are planning a session that will force our groups (including ourselves) to wonder about the origins of mathematical knowledge. We will question our assumptions about terms such as concrete, hands-on and kinesthetic.

We will participate in mathematical activity both familiar and strange—all in the service of better understanding the relationship between the physical world and our mathematical minds.

We will dance.

We will make math.

We will laugh and possibly cry.

Below is an example of Malke’s work. When I participated in a workshop last summer, my head was spinning with math questions as a result. It’s great stuff and we will use it as a launching point for inquiry into our own classroom teaching.

So if you’re coming to Tulsa, please consider joining us for our three 2-hour morning sessions.

Of course you’ll miss out on other great people doing other great sessions. But you won’t regret it. I promise.

And if you choose a different session (perhaps because you’re leading one of them!), I have a hunch there will be after hours percussive dancing in public spaces. Come join in!

Our session description

This workshop is for anyone who uses, or is considering using, physical objects in math instruction at any grade level.  This three-part session asks participants to actively engage with the following questions:

  1. What role(s) do manipulatives play in learning mathematics?

  2. What role does the body play in learning mathematics?

  3. What does it mean to use manipulatives in a meaningful way? and

  4. “How can we tell whether we are doing so?”

In the first session, we will pose these questions and brainstorm some initial answers as a way to frame the work ahead. Participants will then experience a ‘disruption of scale’ moving away from the more familiar activity of small hand-based tasks and toward the use of the whole body in math learning.  At the base of this inquiry are the core lessons of the Math in Your Feet program.

In the second and third sessions, participants will engage with more familiar tasks using traditional math manipulatives. Each task will be chosen to highlight useful similarities and contrasts with the Math in Your Feet work, and to raise important questions about the assumptions we hold when we do “hands on” work in math classes.

The products of these sessions will be a more mindful approach to selecting manipulatives, a new appreciation for the body’s role in math learning, clearer shared language regarding “hands-on” inquiry for use in our professional relationships and activities, and public displays to engage other TMC attendees in the conversation.