Hat Tricks: Logical Thinking with Shadowchild May 21, 2013

Anno’s Hat Tricks (by Akihiro Nozaki and Mitsumasa Anno) is a wonderful way to introduce children to the realm of logic and the powerful word “if”. The book goes through a series of “tricks”, all of which can be solved by applying that “mathemagical” word “if”– a word that opens doors to new ideas. Children are introduced to the concept of using “if” statements to test the truth of an idea or supposition in a logical way. The reasoning pattern of “if…then” can be very useful, and, indeed, branches of modern mathematics have been developed by applying the word “if”.

This delightful book is mainly about three children: Hannah, Tom (both of whom are clearly seen) and Shadowchild (who exists on the page only as a shadow). The writer gives a series of scenarios in which the reader is shown a certain number of hats (all either red or white) which are available, and then which ones of those hats are being worn by Tom and Hannah. We are to use logic to deduce what colour hat Shadowchild is wearing. Although the first number of scenarios in the story are quite easy, the difficulty level increases throughout the book, with the final trick being the most difficult. (If you are not sure of your own level of logical thinking, there are several pages at the end of the book devoted to parents and other older readers that will offer some assistance in the logic being applied in the different tricks.)

Sadly, I think the book is no longer in print, but it is well-worth your while to track down a copy. I know and your children will enjoy the challenges presented.
Mathematically yours,
Carollee

History of Math to Archemedes (Video) May 3, 2013

This interesting video was posted yesterday on the BC Association of Mathematics Teachers’ (BCAMT) list serve (thanks Kelvin Dueck) and I thought I would post it here on the blog. It begins with the earliest discovery of “math” and moves quickly through some of the major developments in mathematics through the time of Archimedes. It touches on base 60 (Babylonians & Sumarians), early approximations of pi, simple fractions (from the Egyptians), square roots, magic squares, the Pythagorean theorem, prime numbers , the Fundamental Theorem of Arithmetic or prime factorization, using the the sieve of Eratosthenes to find smaller prime numbers. Maybe some of the ideas will be “Greek” to you, but then again, maybe it will spark a bit of curiosity, too!

Mathematically yours,
Carollee

Math Thinking with SD#60 Learning Assistants May 2, 2013

I just finished a session with the teachers who work as learning assistants in SD#60. We had a great morning talking about how to help make math meaningful to students who are struggling. And it really all comes down to meaning. Caine & Caine (1994) report “The brain “resists having meaninglessness imposed on it. By meaninglessness we mean isolated pieces of information unrelated to what makes sense to a particular learner.”

Oh, how sad that so many students go through days, weeks, months, and even years of mathematics in school without making meaning! There are so many great tools and ideas for building meaning and making the connections that develop understanding! If a child is not “getting it” in some area of math, we need to go back in the conceptual development of the topic to the point where there IS meaning and then build from there.

What are you doing today to build meaning in mathematics with your students (or your own children?)
Mathematically yours,
Carollee

Twain Sullivan Elementary, Houston, BC April 27, 2013

What a grand day we had at Twain Sullivan Elementary yesterday, in spite of a number of “complications” (including losing power in half the school and, oddly enough, half the room we were in). I did not even remember to tell the participants that when I first pulled into the school parking lot in the morning, there was a beautiful rainbow settled just off to the side of the school. It seemed a good omen for the day – there is something lovely about a rainbow!

We were able to persevere through the strange complications and ended up having great session. The main topic of the day was number sense, and we particularly focused on helping students build particular relationships between numbers, thus creating connections that would lead to greater overall math understanding.

There were a number of handouts that we used, and I promised “clean copies” of those. Some of those handouts are also posted elsewhere on the blog, but for the sake of simplicity, I shall repost them here in one spot for easy access for the Twain Sullivan folks (and anyone else who is interested):

Powerpoint handout of the day
Student ten frames
Mini blank ten frames
Teacher ten frames
Large dot cards – set 1
Large dot cards – set 2
Large dot cards – set 3
100 dot arrays (6 & 12)
100 dot array (large)
mini blocks of 100 black dots
How far to 20?
How far to 30?
How far to 100?

The really large 10-frame that we used does not download properly – at least I have not figured out how to make it work.

If I have left anything off the list, let me know and I will add it on.

I hope I get to work with you all again in the future. I was impressed with your willingness to adapt what you are doing in math to make it better for your students. Thanks again for a great day in Houston, BC!

Mathematically yours,
Carollee

An addition poster “pour mes amis francophone”. April 22, 2013

Merci, Maria L. for letting me share this poster you have made for your French immersion classroom. It is always good to have a visual reminder of strategies students can use for math thinking.

Mathematically yours,
Carollee

NCTM 2013 Denver Presentation April 18, 2013

I am looking forward to a great hands-on session tomorrow as we are “Packing a Powerful Punch with Patterns” (presentation #500, located in the Hyatt Regency, Centennial Ballroom E beginning at 1:00). We will be focusing on how to help students make the transition from basic patterning skills to algebraic thinking, uncovering the deeper math that is embedded in patterning. Our vehicle will be growth patterns that we make out of pattern blocks. If you are here in Denver this week, I hope you are able to join us for the session.

The handouts given out in the session were a truncated version of the PowerPoint presentation, and as promised I am making the full version of the handout available here. If you use these in your classroom, I would love to hear from you about the lessons and even see some samples of student work, too.

Mathematically yours,
Carollee

Problem Solving in a Grade 1 Class April 16, 2013

I was in Mrs. Powers’ grade 1 class last week doing a problem-solving lesson during their math time. After reading the class the story How Many Feet in the Bed, we did a version of the question about the number of two-legged and four-legged animals possible for a given number of legs. The actual question read this: “In a pen on a farm were some chickens and some sheep. Devon was looking under the pen’s fence and counted 12 legs. How many animals could there be in the pen?” However, I realized when I got to Mrs. Powers’ class with the question ready to paste into student books that what I had wanted was for the question to indicate that the pen could hold chickens and/or sheep, thus allowing for four possible combinations and not just two. So Mrs. Powers and I talked to the children about the question and had them answer the intended question not the written one.

I should mention that we had a conversation before the class started to work on answering the questions about REPRESENTING our thinking. I often talk to children about their drawings when solving an answer – that we are doing MATH and not ART. The picture only needs to represent the things in the question in some way mot be a detailed drawing.

The students went to work with a will. Although ten frames and counters were also available, drawing was by far the method of choice used by almost all the children for solving the problem. Clearly the two students whose work you see here took me at my word about “representing” their thinking, and each drew “sketchy” chickens with two legs and “sketchy” sheep with four legs.

One student’s work shows all four solutions recorded correctly. The second sample also has four solutions, but two are the same. Looking closely, however, it looks to me like the solution in the upper left corner of that sample had the fourth correct answer of three sheep, but was erased.

Mrs. Powers was delighted with the children’s thinking. I predict the students will be doing more problem-solving in the weeks to come! Good job, class!

Mathematically yours,
Carollee