Math Advice for Second Grade

My husband, Roger, runs the technology lab at Rancho School in Novato. Early in the school year we did a blogging workshop for the teachers at the school to give them more tools to communicate with parents or create audiences for student voices. One second grade teacher, Ms. Rich, uses her blog to keep parents up to speed on class activities, and homework. I noticed one posting offered great advice for parents on ways to make math interesting at home. Check it out!

Math Assessment in the movies

I heard of someone who gave a speech once showing math errors in commercial movies. I've never found out who gave that speech, but I was intrigued by the idea and after seeing this humorous mathematical bit from a Ma & Pa Kettle movie, I've been on a search for more. This one I love to show teachers as an example of a great assessment item. Just show it to a fourth grader and ask what's going on to get a clear idea of their understanding of multiplication, division and....well I don't want to give it away.
Two days later: At the Asilomar CMC Math Conference and Gary Tsuruda showed this clip in his keynote. This clip is from and Abbott and Costello movie, but the math part of the script in both movies is almost identical.

More Spirals

I've been playing with Zack's spiral design which I mentioned in the previous post. It's fun to have it in a tool like Geometer's Sketchpad where it's a real mathematical object and you can play with it and change it and color it in different ways. I was surprised to think somehow this design was not like Zack's because this had four spirals and it seemed Zack's had only two. However, re-visiting Zack's design I see he used each color twice: a simple difference but it seemed quite different to my brain. I keep thinking about this in terms of an assessment I saw at a conference where they gave students a square and asked them to shade it to show four equal parts, and to do this in several different ways. The four color version would be a good solution. Zack's two color version would be a good solution to shading the square to show two equal areas. Of course in each case there's a little empty square in the middle that would have to be divided as well.

Squares or Spirals

One thing I love about math is that there are so many ways to see things. My 11 year old friend Zack came over and was very excited to show me something he learned at school. He got a ruler and paper and sat down and meticulously created a square, then found the midpoints of the sides to create another square and then found the midpoints of those sides to create another square and on and on. I, of course, completely jumped to the conclusion that I knew what he was doing even though he said, "It's not what you think."
Naturally I imagined a traditional symmetrical design that highlights the squares and midpoints. - like the one to the left. But then Zack began coloring his design starting with a tiny triangle in the center and working outward. I couldn't figure out what he was doing and when I came back about a half hour later his work completely surprised me and others who had been visiting at the time.

I realized then that Zack and I could spend days exploring his drawing along with a myriad of other drawings that share the exact same lines. This is when I longed for a technology tool that would enable us to draw a perfect square and could easily find the midpoints of the sides and could connect those midpoints to create a subsequent square; then we could make copies, stretch it, turn it, color it in a variety of ways and really see what we could find out about it. It's these times when technology can take your mind off the measuring and drawing, and can give you a chance to explore the pure mathematics of the design. At times like these I'm glad to have a tool like Geometer's Sketchpad, which I went ahead and played with to make the designs above.

But to begin, Zack and I don't need anything. I'll probably just ask Zack if there's more pink or more orange in his drawing and how he could prove it one way or the other. Then I imagine we'd start thinking about ways to color the original square such that there's the same amount of pink as orange. And that would just be the start of the conversation. At the point when he wants to start drawing another copy I'll probably show him Geometer's Sketchpad and see where it leads. Stay tuned! Zack will be back and we'll see what we come up with.

Expanding Your Horizons - Math & Science for Girls

If you haven't heard of the Expanding your Horizons (aka - EYH) conferences you're missing out. These are one day conferences for girls in which women role models, from math and science related fields, do hands-on workshops with girls to inspire them to consider working toward careers in science, technology engineering, and math. I've been involved in the Mills College conference and the San Franciso State Univ. conference, but there are conferences all over the Bay Area and in most states in the country. The San Francisco EYH is coming up Saturday November 3rd, so if you know any middle school girls who would benefit from some fun inspiration in these areas, check it out here. And to find other sites around the country check with the national organization here.

Magnetic Blocks

Here's another favorite magnetic puzzle, or play thing. It has that great "pop into place" feel as the pieces go together. There are 24 identical pieces that make a cube and plenty of other interesting shapes. Fooling around with it gives people mathematical insights, and under a teacher's guidance with a little questioning it can be turned into a great lesson in area, perimeter, and volume, angles and more. But for the most part it's just fun. It's called Mag-Blocks.

PhysLink the Science eStore carry's the 24 piece set ($14.99). This looks like a great place to get interesting learning things for home or classroom.

Discount School Supply offers a double 48 piece set $21.95 - that's two cubes. What a deal! Check it out! Whoa! As of 10/2/07 the 48 piece set was on sale for $17.95 - that's a really good deal. However the colors changed and it's hard to tell if the pieces are the same size. But I'm gettin' one now.

Math Book Helps Girls Embrace Their Inner Mathematician

Here's a good one from Wired Magazine, back in August of this year.

"The actress who played Winnie Cooper on The Wonder Years, Danica McKellar, is a self-proclaimed math advocate for girls who might otherwise shy away from a subject that Barbie once famously described as 'hard.'

McKellar's math book for junior high girls, called Math Doesn't Suck: How to Survive Middle-School Math and not Break a Nail, will be out Thursday. It has the look and feel of a teen magazine, but puts heavy emphasis on fractions and pre-algebra."

It's great to see celebs encouraging girls in math. The Expanding Your Horizon's conferences have been doing it for 30 years, but this will surely help the message go mainstream in a bigger way.

A Whole School Turns Math into Magic

Here's a very inspiring video from the George Lucas Education Foundation, www.glef.org showing how Fullerton IV Elementary School in Oregon made math the highlight of their program. It takes significant professional development to create this kind of math culture, but just imagine the payoff for the students, the teachers, and the school. Their test scores soared, but more importantly, math became the favored subject of nearly all the students.

Bagels, Pico, Fermi - Mastermind with Digits

There's a great logic game that's like Mastermind with numbers. You guess a three digit number and you get clues as to whether you got any of the digits correct and whether you got them in the correct place. When you make guesses, you get a clue. The clues are:

• Bagels means a digit you guessed is not in the number,
  
• Pico means a digit is correct but in the wrong position
  
• Fermi means a digit is correct in the correct position

For instance suppose you guess is 457 and get the clue Fermi Bagels Bagels. It means one digit is in the correct place and two are not in the number at all. But you don't know which digit the clues apply to.

You can play it on paper or a blackboard with kids. Here are the instructions.

Or you can play it online. There are no instructions on this page and you enter your guesses via pull downs, but it works fine. (When it gives you the clues it just lists the Fermis first, then the Picos, then the Bagels - it doesn't give a clue as to which digit each refers to.)

And a tidbit on the name from the instruction page. I always find these connections interesting.

"We don't know the official origin of the name of this game. Bagels are shaped like zeros and indicate that there are no correct digits. Pico (peek-oh), from the Spanish meaning 'beak' or 'peak,' is used in science as a prefix meaning one-trillionth. For example, 1 picometer = 10-12 meter. who later moved to the United States. Enrico Fermi (fair-mee), 1901-1954, was an Italian-born atomic physicist. He won the Nobel Prize in 1938."

Concrete or Abstract Manipulatives

I was talking about "virtual manipulatives" with teachers from Willow Creek Academy and some of them brought up the fact that younger students really need the concrete experience with real objects. I certainly agree since there's nothing like "hands on" experiences. But the digital versions of traditional manipulatives, like these online pattern blocks, are still great for those who are moving from concrete to abstract, and for children who might like to play online at home with parents when the real thing isn't available. It's also the case that online you can change the color of the blocks, you can have as many blocks as you like - no shortage, and you don't have to worry about bumping your pattern and messing it up. Plus students can grab a screen, put the design in a word processor and write about it, which is a wonderful way to get students to articulate ideas about patterns and other mathematical relationships.

For those who want the real thing you can find nice wooden pattern blocks online, or even Giant foam pattern blocks for the floor from Learning Resources

Math Wonders with Seven Pieces

Now that I've posted about Tangrams I find myself pondering why they're so amazing. Just think, seven simple pieces that hold a myriad of geometric relationships such that they can be combined to create all the shapes above. And they're not easy. Just give it a try. Tangrams

Or better yet, sit with a young person and work on it together. Talk about what your brain is thinking as you try to use the seven pieces to make the different shapes. You could ask questions like: Which of the shapes has the greatest perimeter? Which shape has the greatest area? How could you design a shape with the pieces that has the maximum perimeter, or the maximum area?

Tangrams - Geometric Brain Sharpener

I just love Tangrams. I'm not that great at doing them but I love to watch my mind think as I work out a solution. The shape of "the sitting man" for instance seems easy because you know right off where two of the pieces go just by looking at the shape. So there are only 5 other pieces to place. But as you do it you discover that getting those large triangles in place can be tricky, and if you listen to your mind thinking about the options you'll find it's fascinating to see your strategies of looking at the areas of pieces, and lengths of sides, and ways that pieces could fit together to fill a certain space. And for kids - if we can get them to be aware of their thinking I believe there will be a great deal of transfer to all kinds of problems related to area, distance, angles, triangles and more. Play with it and see what you think. Try Interactive Tangrams

Fun Math Stuff Meets Standards

It's not that standards necessarily kill the fun stuff in math, it's just that when the learning is broken down into so many little objectives that have to be descreetly assessed, it feels like there's just no time to step back and play around with general concepts. However CTAP region 4 has spent a few years finding the great online interactive resources (the fun stuff) and aligning them to the California standards and the CA adopted math textbooks. This makes them much easier to integrate, which provides students with real opportunities to experiment with concepts in a ways that can't be done with paper and pencil. The project is called the Middle School Math Project and there's a matrix for 6th grade, 7th grade, and Algebra 1 with all the standards, resource links, and pages of the textbooks to which they align. Look for the little hearts to see CTAP's favorites, and look for the little earth icons to see ones that are online interactive tools - like this collection of Geometry applets in the National Library of Virtual Manipulatives.

Inspiration for Math Education

In light of NCLB and the standards movement, teachers are so pressed to raise test scores that it's easy to forget some of the intriguing, fun, math things we used to have time for in the "good old days". So this blog will help remind us of some of the conversations, resources, and really "cool things" that inspire math learning.

Like for instance. I just came across a very elegant simple puzzle, called Ball of Whacks - a 30-sided polyhedra made up of 30 identical magnetic pieces that just pop into place. You've got to feel it to believe it.
Check it out. Here's a little movie of it - Ball of Whacks