Monday, July 21, 2014

Book Study Monday: Teaching Numeracy, Critical Habits 5 & 6

Welcome to this week's Book Study Monday! If you're just joining us, we're reading and discussing Teaching Numeracy, 9 Critical Habits to Ignite Mathematical Thinking, by Margie Pearse and K. M. Walton.  

Reading Schedule

June 30
July 7
July 14
July 21
Critical Habits 5 & 6
July 28
Critical Habit 7
Aug 4
Critical Habits 8 & 9
Aug 11
Essential Components 1, 2, & 3
Aug 18
Essential Components 4 & 5

Habit 5: Predict, Infer, Recognize Trends, Use Patterns

"Inferring allows students in your math class to make their own discoveries without spoon-feeding the information to them.  In this view, understanding cannot be delivered by instructors, no matter how skillful, but must be created by learners in their own minds."

What I liked most about this chapter (and actually the one that follows) is that it conjures up the image of a classroom of thinkers. The quote above (p 55) sums up a major issue with mathematics instruction in the United States--we don't allow students to struggle.

Some of the most powerful research I have read relates to the cultural differences in the way we teach math in the United States compared with Japan and Germany. In 1995, as part of the Third International Mathematics and Science Study (TIMSS), Dr. James Stigler studied the instructional techniques of teachers in Japan, Germany, and the United States and documented the findings in his book, The Teaching Gap.  He found that teachers in Japan expected their students to be confused and struggle, while teachers in the United States felt that if their students were confused then they hadn't been clear in their explanations.  In other words, struggle is not part of our teaching culture in the United States.  I recently heard Dr. Yeap Ban Har speak about math instruction in Singapore, and one piece of information he shared drew gasps from the room. In Singapore, 20% of their standardized assessments are problems of a type students have never experienced before. Now THAT'S problem solving!  If you've got a little time, you might want to read this transcript of a panel discussion featuring Dr. Stigler in 1997. Has much changed?

The authors make a great point on page 56 about how important it is that learning is relevant to students.  Something as simple as using students' names in story problems can help draw them into the learning.  It's not that difficult to rewrite word problems using the students' interests and names, but it can have a big impact.  I watched a masterful teacher in my school last year do a Problem of the Day written about one of her students at batting practice (she hit 90 balls, 27 went over the fence and the rest stayed in the field). The students were so engaged and the little girl felt like a star! Not only was it a great math problem, but this teacher also exposed her students to an activity (batting practice) that many were not familiar with.

I was reminded that the purpose of the book is to "ignite mathematical thinking" when I read the passage on page 62 about modeling metacognitive self-talk. It's so important that we model this type of behavior for students, because it is a learned behavior. Just as reading teachers "think aloud" when they are modeling what good readers do, we should be consistently doing the same in math.

Habit 6: Question for Understanding

"To maximize problem solving, application, and the development of a variety of thinking skills, it is vital that we pay more attention to improving our questioning in mathematics lessons."

The research could not be any more clear on the topic of questioning in mathematics, and the authors did a great job of listing and categorizing it (p 69-71).  I always appreciate it when a book connects and spirals ideas, so here we see how questioning supports the previously discussed skills of monitoring and repairing and metacognition.

The questioning ideas on pages 71-73 are gold!  I, for one, will definitely be copying this page and keeping it close by.  Dr. Yeap modeled a couple of very powerful questioning techniques that I would like to add to the list.  The first technique was asking, "Your friend says that 8 + 6 = 14, because it's like 10 + 4.  Do you agree?". The other was so simple, yet so effective.  After giving him a solution he asked, "Are you sure?".  Right or wrong, he asked the question over and over.  Even as an adult who was, I should say, pretty confident with my answers, I immediately looked back and checked over my work.  And isn't that what we want our students to do?  I'm anxious to see if it works for them as well as it did on me!

There are so many great ideas in these two chapters, and I can't wait to read the rich discussion that is certain to take place.  I'm boarding a plane later today for a math conference in Vegas, so I might not be able to respond to your comments right away. Remember, this is an interactive discussion!  Feel free to participate either by posting your own response to the reading or by replying to the comments of others.

Finally, I loved the I Learned/I Wonder two-column notes idea on page 77.  What a great way for students to summarize their thinking in their math journals!

So there's my recap of the two chapters.  What spoke to you?

BTW, I am once again out-of-town for a few days, this time at the Conference for the Advancement of Mathematics Teaching (CAMT) in Fort Worth.  I look forward to reading all of your great responses!

Sunday, July 20, 2014

What is Singapore Math?

I recently attended the SDE National Conference on Singapore Math Strategies, and it was four days of non-stop learning!  This is my second time to attend the conference, and it keeps getting better.  While there were many great sessions and presenters, the highlight for me was definitely getting to learn from Yeap Ban Har. Dr. Yeap is an internationally known educator, author, and speaker.  His presentation style made you feel like you were in his classroom--he was informative, engaging, and entertaining.

One of the first comments he made is that in Singapore they don't call it Singapore Math.  It's just math.  He went on to explain the history of how the math curriculum we know as Singapore Math came to be.  In the 1980's, Singapore was at the bottom of the educational heap.  Their scores on international assessments were among the lowest and their country's GNP was dismal.  The government decided that something needed to be done, and they turned to research for the answers.  They decided to focus on numeracy, rather than literacy, because research shows that mathematics skills are more directly correlated to the economic success of a country than literacy.

With the focus set on improving mathematics instruction, they studied the research about how students learn in general and, specifically, how they learn math.  From the research, they developed a national curriculum and philosophy of teaching math that was implemented in the early 90's.  Just over twenty years later, Singapore consistently ranks very high on international assessments and their GNP continues to rise.  Quite the success story.

While many people associate Singapore math with bar model drawing, Dr. Yeap said that was actually a small part of their curriculum.  Here's a graphic showing the framework.
One of the fundamental pieces of the Singapore philosophy is the concrete, pictorial, abstract (CPA) sequence of instruction based on the work of Jerome Bruner in the 1960's.  In the United States we more often refer to it as CRA, with the R standing for representational, but it's essentially the same thing.  Anchor tasks (think of these as their mini-lessons) feature concrete learning experiences and typically conclude with students documenting their mathematical thinking in their math journal--the representational and sometimes abstract piece.  So, for example, after doing an anchor task activity using ten-frames to explore different ways to add 8 + 6, the journal entry might look something like this:
It's also interesting how they use the student textbook.  He told us that although all the lessons he showed us came from the student textbook, the textbook stays closed during instruction.  This allows the students to construct their own learning, rather than being constrained by the textbook method.

Another piece of research that helped shaped math instruction in Singapore is Zoltan Dienes' Six-Stage Theory of Learning Mathematics.  Basically, Dienes states that Free Play, without formal vocabulary or rules, must be the first stage of all learning. He describes it as a "trial and error" activity.  Think, for example, about the ten-frames anchor task I mentioned previously. Students might be asked to build 8 and 6 on two different ten-frames and then be asked, "I wonder how we could add 8 and 6?"  This would be followed by a share-out of different solutions.  At the conclusion of the anchor task, students would be asked to record three solutions that make sense to them in their math journals.  I love how Yeap described an easy way to differentiate:  "Boys and girls, we have just discussed and shown many different ways to add 8 and 6.  Please record three ways that make the most sense to you in your math journal.  If you are really fast, record five ways.  If you are really, really fast, make up another way."

Yeap also referred to Vygostsky's theories on social learning and the zone of proximal development. Yeap summed up the social learning theory as students doing individual thinking, then small group work, and finally whole group sharing.  Vygostsky's zone of proximal development theory states that we learn best when asked to do tasks that are just beyond our comfort zone.

I hope you see that Singapore Math is really a philosophy for mathematics instruction--it's as much about how to teach as it is what  to teach.  After reading this, you may even realize that YOU are a Singapore Math teacher.

If you're interested in reading more about number bonds, which are a fundamental part of early numeracy in Singapore, check out this blog post.  For more information about model drawing, try this one.

Saturday, July 19, 2014


I ran across some great finds this week!  Enjoy!  Be sure to leave some comment love when you visit these talented educators!

From the Blogosphere...

Have you used QR codes in your classroom?  Tara at The Math Maniac has a nice little tutorial on how to create and use QR codes to make math practice more engaging.
Like many of you, Tanya at A+ Firsties is diving into a guided math approach next year!  She created these adorable labels and shared them for free this week. 
Learning is always more fun when students are up and moving!  This fraction twist on Musical Chairs posted by Erin at E is for Explore will be a big hit with your kiddos!

Found on Pinterest...
Fun Games to Teach Elementary Math Concepts by Eden Godsoe
Who doesn't love games?  This pin leads to a list of a number of popular board games and how they can be used to teach math.  What great information to share with parents!
All Things Upper Elementary: Dream House: An Additive Area Project (3rd Grade Common Core) - Blog post with freebie
This pin leads to a blog post on a very creative way to have students experience additive area, a 3rd Grade common core standard.  There's also a freebie!
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