Math Conference Mania: Part 1

Last week, two mathematics conferences were held in San Diego: The NCSM (National Council of Supervisors of Mathematics) and the NCTM (National Council of Teachers of Mathematics. The first focuses on mathematics teacher-leaders and includes supervisors, coaches, and just about anyone who works at a department head level or is involved in a Professional Learning Community. The NCTM national conference is a whopper! Over 10,000 people attended this year and while those numbers are down from prior years, there were plenty of interesting sessions to attend and informative people to meet.

Singapore Math was well represented at both conferences, which prompted this tongue-in-cheek tweet from a @ddmeyer, a high school math teacher:

“Hey you guys! Has anybody heard anything about this “Singapore Math”?! #nctm10”

From the session descriptions alone, I counted:

NCSM: Six Singapore Math sessions for 1500 attendees

  • Singapore Math for the U.S. Classroom *
  • Lessons from Singapore: The Professional Development Required to Implement a World-Class Curriculum *
  • Intriguing Lessons About How Math is Taught and Assessed in High Performing Asian Countries
  • Developing a Singapore Math Curriculum: From Theory to Practice *
  • Using Singapore Math Model Drawing to Help Special Education Students and Struggling Learners Become More Capable and Willing Problem Solvers
  • Integrating Curriculum, Assessment, and Teacher Professional Development: Singapore and the United States *

NCTM: Twelve Singapore Math sessions for about 10,000 attendees

  • Linking Concepts, Context, and Problem Solving through Singapore Math Model Drawing
  • A Glimpse of Singapore Math in the Primary Grades
  • The Cutting Edge of Singapore Math: Problem Solving, Creative Thinking and Inquiry Thinking
  • The Singapore Math for Helping Children Solve Challenging Mathematical Problems
  • Singapore Math: Contextual Word Problem Solving Leads to Concept Mastery
  • Math with Meaning – Success the Singapore Way: Foundations of Number Sense
  • Does Singapore Mathematics Enhance Students’ Learning in the United States *
  • Making Connections: Problems from Singapore Classrooms
  • Lessons from Singapore: Using Visual Models to Teach Algebra and Number Sense
  • Using “Strip Diagrams” to Solve Algebra Word Problems
  • Intervention Strategies: The Singapore Way
  • Let’s Make Triangles With Sticks! Geometry in Asian Textbooks

Sessions with an asterisk (*) are ones that I attended and reviews of those are forthcoming. With over 750 total sessions, scheduling at NCTM was a challenge. There were three different venues and many of the Singapore Math-related sessions at NCTM ran concurrently or overlapped. Anyone truly interested in learning about Singapore Math could have attended six entire sessions or parts of all of them.

Of the six sessions at the NCSM, half were by Houghton Mifflin Harcourt’s Math in Focus series authors Patsy Kanter, Andy Clark and Dr. Fong Ho Kheong. They were the only sponsors at the NCSM conference sponsor area that displayed materials related to the Singapore Math Curriculum. (Also published by Houghton Mifflin Harcourt divisions and on display in the booth: Saxon Math, Think Math, McDougal Littell, Destination Math, Go Math)

This was my second NCTM conference (takeways from 2009 here) and my first visit to the NCSM. I can see that I will need to reserve the full week in the future to attend both. In addition to the Singapore Math-related sessions, I attended sessions on formative assessment, writing effective homework, coaching, asking good questions and fractions. My mind was expanded by renowned professors such as Deborah Loewenberg-Ball and Hung-Hsi Wu (session reviewed at Kitchen Table Math II).

Start saving now for next year’s annual conferences in Indianapolis, April 11 – 16, 2011!

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April is Math Awareness Month

Sponsored by the American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics, the theme for April’s Math Awareness Month (MAM) is Mathematics and Sports.  From the press release:

Sports offers a cornucopia of instances involving data, strategies and chance, each of which is perfectly suited to mathematical analysis. Beyond the obvious uses of mathematics for things such as rating baseball players and football quarterbacks, mathematics is used to design the dimple patterns on golf balls and the composition of racing tires; it is used for scheduling tournaments and for ranking teams; and it is used to determine tactics and to predict the ultimate limits in sports records.

Organizations and teachers from around the country have posted some ideas for the classroom and events at their schools on the MAM site. Even better, head to Subadra’s Math Awareness Month post on her blog: Library of Books, Links & More. Be sure to have a snack first, you might be there a while. There are over 50 great links to articles, activities, and books on mathematics and sport!

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Pi Day 2010

Are you ready?

Ice cube tray available at Amazon.

Pi Clock  at piday.org:

Clock in Terms of Pi

The San Francisco Exploratorium

is celebrating their 22nd annual Pi Day:

Come create Pi puns, participate in Pi-related antics—and have a slice of pie

Activities, music, and stories at Teachpi.org.

The site owners have sorted through hundreds of ideas and chosen their 50 ideas best  for celebrating Pi Day. (Be sure to check out the Pi Day Carols, too!)

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Upcoming Singapore Math Workshops

(Image courtesy of Indexed.)

I’ll be presenting “How to Use Strategies from Singapore Math to Strengthen your Math Instruction” at four workshops this winter. You can read more about these 1 day seminars and register by clicking on the city.

February 10 – Harrisburg, PA – Rescheduled for March 9th

February 11 – Atlanta, GA – Rescheduled for March 10th

March 29 – Rochester, NY

March 30 – Buffalo, NY

Whether you’re new to Singapore Math or just interested in learning more about some of the strategies, you’re sure to leave with a new understanding of the curriculum. (And a handy-dandy handbook!)

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i-Excel: Heuristic and Model Approach

From a discussion on the Well-Trained Mind Forums is a question about some the supplemental material available for the Primary Mathematics curriculum:

On the (SingaporeMath.com) site there are some supplemental books I don’t recognize, but I can’t tell what they’re for–if they’re new-new or replacing-CWP-new

Math Works?
i-Excel?
Math Express?
Brain Maths?

I wrote here about the MathExpress: Speed Maths Strategies.

i-Excel Heuristic and Model Approach (Update 2/2013 – Series going out of print and will be replaced with: Process Skills in Problem Solving)
Author: Li Fanglan
Published by Fan-Learning
Levels 1-6 available in the U.S. from Singaporemath.com

The i-Excel: Heuristic and Model Approach is a completely different type of workbook than the MathExpress series.  i-Excel books focus on problem solving. Can you deduce the meaning of “heuristics” based on the following description from the introduction?

At primary levels, Model Approach has been proven to be the most versatile and effective method to help pupils solve many difficult problems.Heuristic Approach, on the other hand, helps them handle the higher level problem solving by unconventional means.

Heuristic Approach

The first part of each book includes eight different Heuristic Approaches and then focuses on different Model Approaches based on topics taught at each level. Heuristic Approaches in Level 2 include the following:

  1. Guess and Check
  2. Act it Out
  3. Draw a Diagram I
  4. Make a List
  5. Look for a Pattern I
  6. Draw a Diagram II
  7. Draw a Diagram III
  8. Look for a Pattern II

Upper level Heuristic Approaches include: Simplify the Problem, Work Backwards, Make a Supposition, Solve Part of the Problem, Use Before-After Concept and Restate the Problem in Another Way. Each Heuristic Approach has a worked example, four or five practice problems and one more challenging problem to solve. (Some levels put these challenging problems into a separate unit.)
Here’s the challenge problem from Level 2 – Draw a Diagram II:

A pizza was cut into halves.
Jolene took one half and ate 2/3 of it.
a) What fraction of the pizza did she eat?
b) What fraction of the pizza was left?

Completed guided examples are included in the Answer Key at the end of this section. Make a note, however,  not all questions have worked solutions.

Model Approach

The second portion of the books works with the Model Approach as it applies to mathematical topics.

    • Levels 1-3 focus on applying the Model Approach with the four operations. They also have yellow, pink and blue rectangular stickers in the back of the book for students to use with the model drawing problems. These are important for students who are learning or struggling with drawing proportional bar models.
    • Level 4 has two parts consisting of 28 units on the Model Approach: Whole Numbers and Fractions. There is also a Part IV: Non-Routine Problems – Challenge Yourself 4.
    • Level 5 has sections on Whole Numbers, Fractions, Ratio, Decimals, and Percentage. Part VII includes 3 assessments.
    • Level 6 parts include ratio and Proportion, Percentage and Speed. The final section is entitled “Examination Practice”. Some of these problems are double starred for extra challenge.

Here’s an example of a ** problem from that unit:

Grace had a total of 120 red and blue pens in the ratio of 3:5. After she gave away an equal number of each type of pens, the number of red and blue pens left was in the ratio 3:8. How many pens did she give away altogether?

Good news if you’re scratching your head right now. All problems in Level 6 have detailed solutions worked in the answer key.

In the classroom

Most who have used Primary Mathematics would agree; the focus is on the bar model as the main problem solving strategy. The i-Excel series brings explicit instruction in additional problem solving strategies into the classroom. This is one of my favorite supplemental books to use with students. The challenge and variation makes it a favorite of students as well. I have incorporated the heuristics into a self-directed activity and have used the challenge problems for a “Problem of the Week”.

The Level 3 book includes a unit entitled “Act it Out” that became a great independent activity/group center. The example given is to use 10 coins to form the figure below. Moving only one coin at a time, what is the least number of moves to turn the shape upside down?

After working this example as a whole group activity, I could now have chips (coins) and new problems available in the classroom: as part of centers, as a substitute lesson plan, or for students to use as a quiet desk activity.

Have you used the i-Excel or Brain Maths series? Share your experiences in the comments below. I’d love to know how the books have worked in a classroom or in your home.

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MathExpress: Speed Maths Strategies

From a discussion on the Well-Trained Mind Forums comes a question about some the supplemental material available for the Primary Mathematics curriculum:

On the (SingaporeMath.com) site there are some supplemental books I don’t recognize, but I can’t tell what they’re for–if they’re new-new or replacing-CWP-new

Math Works?
i-Excel?
Math Express?
Brain Maths?

First, these aren’t replacing CWP (Challenging Word Problems series), but they are fun books that are great supplements for homeschooling families or classrooms.

MathExpress: Speed Maths Strategies
Author: Li Fanglan
Published by Fan-Learning
Levels 1-6 available in the U.S. from Singaporemath.com

I recommend MathExpress if you are interested in becoming faster and more fluent with mental mathematics. Book levels 1 – 3 focus on basic mental math strategies with the four operations. Beyond that level, if you’re using them with students, some of these approaches can start making math look like a series of algorithms to memorize or tricks. It’s important that students understand the reason why these “short-cuts” (as they are referred to in the books), make mathematical sense.

An example from Level 1- Express Strategy 13:

Can you get the answer in 10 seconds?
26 + 49 = ?
58 + 37  = ?

There is a visual & written solution for each problem on the next two pages. Here’s the first written solution:

1 and 49 make 50.
Rewrite 26 as 25 + 1.
Add 1 to 49 to get 50 before adding 25.

An example from Level 2 – Express Strategy 9:

Can you get the answer in 10 seconds?
342 – 190 = ?
237 – 172 = ?

Again,  there is a visual and written solution page for each problem. Here’s the first:

190 is 10 less than 200. Subtract 200 from 342 before adding 10.

After an explanation of the strategy, there is a page of practice, a page with two word problems and a Speed & Accuracy Test.

There are six volumes in the series:

Levels 1 and 2 include addition and subtraction.
Level 3 adds in multiplication and division.
Level 4 includes all four operations and decimals.
Level 5 has fractions and decimals.
Level 6 has strategies to check answers, percentages & advanced problem solving. Here are two 10-second problems from Level 6 and the first solution:

125 x 25 x 32
1/2 x 50 x 28 x 11

4 and 8 are factors of 32.
24 x 4 = 100 and 125 x 8 = 1000.
Multiply 25 by 4 and 125 x 8 before multiplying the two products.

Before working the solution to the second problem, the book provides this word problem:

A rectangular tank measuring 50 cm by 28 cm by 11 cm is half filled with water. Find the volume of water in the tank.

I highly recommend the upper level books for adults looking to improve their mental math abilities. I should also mention that the books have two diagnostic assessments at the back of the book, along with an Answer Key and Detailed Solutions. (You’ll find the solution to the 6th grade level problem above on 69.)

In the classroom

My students have so much fun working on these strategies. In a classroom, I’ve used these books with students AFTER concepts have been mastered to help students become faster with their mental computation. As an example, in a 3rd grade classroom, I would focus on the strategies in the Level 2 book for the first half of the year, then, depending on the students’ understanding of multiplication and division, I’d introduce some of the strategies from Level 3. These can conclude in wonderful mathematical conversations. Here’s an Express Strategy from Level 3 that should lead to an interesting discussion:

Can you get the answer in 10 seconds?
26 x 5 = ?
148 x 5 = ?

And the strategy:

2 fives = 10
Multiply 26 by 10 instead, then half the product.
26 x 5 = 26 x 10 ÷ 2

= 260 ÷ 2
= 130

I’ve used the i-Excel and Brain Maths series. I’ll post reviews on those also. If you’ve used these materials, please share how in the comments below. I’d love to know how they worked in a classroom or in your home.

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Problem Solving and Literature

Bar_diagram

Denise at Let’s Play Math has written up a some fourth grade level multi-step word problems (and provided bar model solutions) based on C. S. Lewis’  The Lion, the Witch and the Wardrobe. She concludes:

…as word problems become more complex, the bar diagrams offer significant help for students who struggle with the question, “What do I do?” Diagrams make visible the abstract relationships between numbers, enabling the student to decide which arithmetical operation makes sense in the context of the problem.

This is the fourth installment of her series on Pre-Algebra Problem Solving. Other posts  use Mr. Popper’s Penguins and Poor Richard to illustrate problem solving using bar models in earlier grades.

Enjoy!

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Word Problem Progression

These word problems come from  Practice A in the 5B Standards Edition Textbook (p. 68). This particular practice follows six lessons on “Percentage” and “Writing Fractions as Percentages”.  Notice how the challenge  progresses through the seven problems.

 

Let’s look at the underlying concepts of each problem:

5.  No computation is needed. “15 out of 100”

6. Variation in 2 levels

  1. Find complement: 37 marbles are green, how many aren’t?
  2. Convert to percentage.

7. Connects percentage to a fraction.

8. Find complement of percentage.

9. Convert fraction to percentage.

10. Corresponds to problem #5. Can you visualize: “if 14/50 how many out of 100?”

11. Multi-step. “Can you imagine how many of 100?” Demonstrates thinking proportionally.

12. First application to measures. Measurement is a continuous quantity, making this problem more abstract.

How does this progression lead to a deep understanding of the concepts?

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Creative Thinking Problems

From Accelerated Learning Primary Mathematics 3 by Ching Kheng Huat published in 1999 in Singapore. Have fun!

1. For both piles to have the same weight, which item belonging to the pile on the left should be exchanged with another item belonging to the pile on the right?

Balance_scale_problem

2. Replace the letters with numbers.

TEAR
+EAR
TALE

3. Fill in the boxes with appropriate numbers.

Fill_in_the_boxes

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NCTQ report recommends Colorado adopt Singapore Math

The National Center on Teacher Quality released a report entitled: Race to the top: Colorado may be used to high altitudes but can it compete in Race to the Top?

Commissioned by the Piton Foundation, the Donnell-Kay Foundation, the Colorado Children’s Campaign and the Public Education & Business Coalition, the report suggests 7 strategies the state might take while applying for the Race To the Top (RTT) funds.

  • Strategy 1: Performance management (Teacher Evaluation, Tenure & Dismissal) – Given the tremendous impact teachers have on learning, no strategy a state will take on is likely to have a greater impact on student achievement than one that seeks to maximize teacher and principal performance.
  • Strategy 2: Equitable Distribution of Teachers and Principals – Schools serving children living in poverty are more apt to employ teachers with lower qualifications than schools serving more affluent children.
  • Strategy 3: Induction – CO should develop a statewide system of induction support for new teachers, particularly in its high needs and remote rural schools.
  • Strategy 4: Compensation Reform – CO needs to move away from lockstep salary schedules towards a system that differentiates salary on a number of factors, including teacher effectiveness, the relative difficulty of a school setting and the demand for teachers with particular skills or knowledge.
  • Strategy 5: Teaching in STEM fields: CO should develop a coherent state strategy to address the difficulty school districts face in attracting and retaining sufficient numbers of qualified STEM teachers.
  • Strategy6: Statewide Adoption of an Effective Curriculum: Students achieve when 4 elements are in place: Standards, Curriculum, Teachers & Assessment.
  • Strategy 7: Educator Preparation (Including Alternate Certification) – In spite of countless studies looking at the value of teacher education, we have only been able to learn (apparently) that no single method of teacher preparation yields more effective teachers than another.

I’ll be honest, I haven’t read through the entire report as yet, however I managed to get through Strategy 6, in which the authors recommend statewide adoption of Singapore Math at the elementary level. The report notes that:

…curriculum has been troublingly absent in conversations about education reform as well as ignored in the indifferent approach some educators take to curricula adoptions.

… the current emphasis on human capital and effective teachers has been at the expense of an equally urgent emphasis on the importance of good curricula.

And when discussing common standards, the report flat-out states:

We would go so far as to say that if the standards were in conflict with the Singapore curriculum, a state ought to consider opting out of the new standards.

Well, you don’t hear that everyday!
Read and enjoy
.

(Cross-posted at KTM-2)

http://kitchentablemath.blogspot.com/2009/10/nctq-report-recommends-co-adopt.html
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