Singapore Tops TIMSS 2015!

The 2015 Trends in Math and Science Study (TIMSS) results were recently published. Students in fourth and eighth grades from more than 40 countries worldwide participated in the most recent test. This test marks a 20-year span of comparative mathematics and science achievement data collected and once again East Asian countries topped the charts.

What does the TIMSS test?

The TIMSS tests students’ math and science knowledge. For the sake of this post, we are going to focus on mathematics. Both content domains (Number, Geometry, and Data) and cognitive domains (Knowing, Applying and Reasoning) are tested every four years.  Student achievement is then compared to other participating countries.  Singapore’s students once again ranked number one in the world, marking the fifth time Singapore has scored highest on the TIMSS  since the country first participated in 1995.  Students in the United States trail students in Singapore by 79 points for fourth grade and 103 points for eighth grade.

TIMSS Results for Select Countries – Fourth Grade Mathematics

1995 2003 2007 2011 2015
         
Singapore 625 (1) 594 (1) 599 (2) 606 (1) 618 (1)
Hong Kong-SAR 587 (4) 575 (2) 607 (1) 602 (3) 615 (2)
Republic of Korea 611 (2) 605 (2) 608 (3)
Chinese Taipei 564 (4) 576 (3) 591 (4) 597 (4)
Japan 597 (3) 565 (3) 568 (4) 585 (5) 593 (5)
Russian Federation 532 (9) 544 (6) 542 (9) 564 (7)
England 513 (16) 531 (10) 541 (7) 542 (9) 546 (10)
United States 545 (11) 518 (12) 529 (11) 541 (11) 539 (14)
Average* 529 545 500 500 500

* International Average in 1995 and 2003, Scale Average since 2007

How challenging are the questions?

The questions on the TIMSS can be broken down into four levels, or benchmarks; Advanced, High, Intermediate and Low. The examples below are from fourth-grade problems.

A low-level question tests basic mathematical knowledge:

Percentage of students able to answer a low-level question: 99% Singapore, 98% U.S.

 

An intermediate level question tests the ability to apply basic mathematical knowledge in simple situations:

Percentage of students able to answer an intermediate level question: 93% Singapore, 79% U.S.

 

A high-level question tests the ability to apply mathematical knowledge and understanding to solve problems:

Percentage of students able to answer a high-level question: 80% Singapore, 47% U.S.

 

An advanced level question tests the ability to apply knowledge and understanding in a variety of relatively complex situation and to explain mathematical reasoning:

Percentage of students able to answer an advanced level question: 50% Singapore, 14% U.S.

To sum it up, students in the U.S. are really good at solving basic computation questions but struggle with applying their knowledge to solve problems in high and advanced level questions.

For more information about the TIMSS and a complete report, visit http://timssandpirls.bc.edu/timss2015/.

How does Singapore do it?

In a nutshell, a Singapore Math curriculum focuses on deep conceptual understanding and problem-solving with an emphasis on the “why” over the “how” of math.  Concepts are introduced, practiced to mastery and immediately applied to solve both familiar and novel problems. Students are given ample time to grapple with problems to find multiple solutions which develops flexibility with numbers and logical thinking.

In contrast, traditional curricula in the U.S. has tended to focus on memorization and procedures. “Ours is not to reason why; just invert and multiply.”  Math has been taught as a series of steps to follow to tackle what appear to be unrelated concepts. Many concepts are taught per grade level with little time to practice and master before moving on to the next concept; often referred to as a spiraling curriculum. This limits deep mathematical understanding.

What can we do?

There’s still hope. There are a few curricula in the U.S. that follow the Singapore math approach to deepening mathematical understanding and problem-solving.  You can read more about Primary Mathematics and Math in Focus here.

If you are not in a position to change your curriculum, you can integrate some of the best strategies from Singapore into your current curriculum.  Take time to teach basic concepts to mastery, focus on developing number sense with mental math activities and help students to visualize word problems with bar modeling.

Each year more and more schools, school districts and home-schooling parents are making the switch, but just buying new textbooks is not enough. Professional development and teacher training is an often overlooked piece of the puzzle. (That’s where Math Champions comes in. For information on how we can help you use Singapore Mathematics,  please complete the form or send us an email.)

[contact-form to=’cassy@mathchampions.com’ subject=’TIMSS Post Help’][contact-field label=’Name’ type=’name’ required=’1’/][contact-field label=’Email’ type=’email’ required=’1’/][/contact-form]

 

Source: TIMSS 2015 International Results in Mathematics. Copyright © 2016 TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, and
International Association for the Evaluation of Educational Achievement. All rights reserved.

 

 

Test Prep: Is it really necessary?

For many, Spring brings with it those two dreaded words: standardized tests.

Whether your school is required to take PARCC, Smarter Balanced, state mandated standards-based tests or ERBs, you inevitably will want to make sure your students are prepared.  Many teachers will plan to block out two to three weeks prior to the testing dates to review and teach content that may not have been covered, but is this interruption to instruction necessary?

It’s estimated that students and teachers lose an average of 24 hours of instructional time each year administering and taking standardized tests.  This doesn’t include time taken out of the instructional day for test prep so that number may even be quite higher.

Q: But, I need to review to make sure my students remember concepts taught at the beginning of the year.

 A: Not if you have been teaching to mastery.

Teaching math with a mastery-based program that is rich in problem-solving may all but eliminate the need for any test prep or review.  If your students have a solid foundation in the basics and have practiced applying that knowledge to solving problems throughout the school year, then nothing a standardized test can throw at them should be unachievable. With a cohesive curriculum, where concepts build on each other, your students have essentially been revisiting concepts throughout the year. So, trust in what your students have learned and skip the review.

Q: What about going over topics that I haven’t covered yet?

A: How much success have you had cramming for an exam?

If material is thrown at students for the sake of a test a few things can happen.

  • Students won’t retain information. If students have not been given enough time to progress through the concrete-representational-abstract phases of learning, they will likely not be able to recall concepts or apply those concepts to the unfamiliar situations they might encounter on the standardized test.
  • Students will be stressed out. They will feel the pressure (that unfortunately, you are likely feeling as well) to get a good score on the test. Learning becomes just something to do for a test.
  • You will get false positive results. Have you ever had the teacher in the next grade up comment that students couldn’t remember a concept that you know you taught? Or, better yet, had test scores reflect learning, but students couldn’t perform at the next grade level? That can be a result of concepts being taught too quickly.

So, rather than block out a few weeks to cram in topics that you haven’t covered, try integrating them into other areas of your day. Do some data analysis in morning meeting. Add some questions about telling time to your calendar activities. Play with measurement and geometry during recess (The weather is getting nice, right?).

If you follow the sequence in your well-thought-out curriculum and teach some of those missing concepts after testing, it’s ok. Your students will experience those concepts in an order that makes sense and will be able to make connections, apply their thinking and master those concepts. That mastery will stay with them into the next year and will be reflected on upcoming standardized tests.

After all, we don’t stop teaching after standardized tests.  Well… that’s probably a topic for another post.

photo courtesy of Alberto G.

Mantra for 2017: Make math make sense!

The return from winter break brings with it a refreshed outlook on teaching.  Teachers return with an eagerness and enthusiasm for the profession and students return seeming just a little more mature.

Return from winter break also brings with it a sense of urgency.  Maybe you’re not as far along in the curriculum as you had hoped. You realize that the frantic push to cover material before break has left students unable to recall content taught.  You are feeling the pressure of standardized tests looming.

The 2015 TIMSS results were recently published and once again, Eastern Asian countries top the charts.  In fact, the gap between the top 5 scoring countries and the United States was 54 points.  What sets them apart is their commitment to teaching mathematics at a deep conceptual level with a focus on thinking and problem-solving.

All of that can be very sobering.  Take a deep breath and set some goals.

Ask more, tell less

  • How do you know that’s correct?
  • Are you sure?
  • Why does it make sense?
  • I wonder why that works.
  • Can you solve it in another way?
  • Can you build or draw a representation?
  • What do you see in your head?
  • Can you prove your answer is correct?
  • You and your neighbor have different answers, who is correct?

Allow time for understanding

It’s easy this time of year to get caught up in the pressure to cover content, but remind yourself that memorization is not the end goal, understanding is.  Taking the time to focus on the concrete-representation-abstract approach will ultimately lead to deep conceptual understanding.  Your students (and their test scores) will reap the benefits.

Help students make connections

  • How is this like what we just learned?
  • Does this remind you of anything?
  • Can you make a connection between this and what we have already learned?

By setting a few simple goals, you will set yourself and students up for a successful remainder of the year!

Mental Math Breaks

rock paper scissorsTo make the most of the upcoming weeks, try taking some mental math breaks.

These few weeks between Thanksgiving and winter break can arguably be the most challenging weeks to keep on pace with curriculum and keep students engaged.  With the anticipation of the holidays and a much-needed winter break on students’ minds, they can quickly lose focus.  Now more than ever, you will find the need to give your students mental breaks in the day.  So, why not practice a little math?

The following games can be practiced just about any time and anywhere if you have a few simple materials on hand.

Make Ten

Skills Practiced: Sums to 10, 20 or 100

Materials: Number cards 0-10, 2 of each or enough for as many pairs as you will need for your class

Pass out 1 number card to each student face down.  When you give the signal to go, students cycle around the room to find another student with a card whose number when added to their own makes ten.  Once they have found their partner, both students sit down.  You can reshuffle the cards and play multiple rounds.  Set a timer for each round and challenge your students to beat the fastest time recorded.

Variations:  Program the cards to make 20 or 100

Rock-Paper-Scissors-MATH!

Skills Practiced: Addition and Multiplication facts

Materials: none

The game is played like Rock-Paper-Scissors except when students say, “MATH!” each student shows 0-5 fingers on one hand.  The first student to say the sum of their fingers and their partners fingers combined wins the round. Students can play best 2 out of 3 with one partner and then rotate around the room to find a new partner and continue to play until time is up.

Variations: Find the product of the two sets of fingers or use both hands to find the sum or product.

Ping! Beep! Ping-Beep!

Skills Practiced: skip counting, multiples and common multiples

Have the class stand.  Choose a target number. Let’s use 4 for our example.  Begin by having students count off, starting with one.  Instead of saying the number, the student that would say 4 says “Ping”.  As the count continues, for every multiple of 4, students say, “Ping”.  Every time a mistake is made, the count starts over.

For more of a challenge, choose 2 target numbers.  Let’s use 4 and 5 for our example.  Begin at one.  For every multiple of 4 or 5, students say “Ping” and for every common multiple of 4 and 5, like 20 students say “Ping-Beep”.  The count starts over with every mistake made.

Challenge your students to beat the count from previous rounds.

Keep your students focused with these movement games and practice some mental math at the same time!

Number Talks in the Classroom (Part 2)

elevateFrom our previous post on Number Talks, we explained how to establish a safe and respectful classroom environment and shared examples of appropriate topics of Number Talks in Kindergarten through 5th grade. Read Part 1.

Number Talks in Action

Environment plays a key role. Students should gather at a designated meeting area in the classroom away from writing materials or have writing materials tucked away if working at desks.  I’ve allowed students to sit on top of desks just for this purpose.

The following outlines the flow of a Number Talk.

 

Teacher: Students:
Teacher writes 27 + 18 on the board. “When you have found one way to solve it hold up your thumb.  If you can think of a second way to solve it, add a finger.” Holding up their thumbs if they have found a strategy to solve the problem.  Adding in fingers for each additional strategy they come up with.
Teacher: Students:
“Let’s share answers.” Teachers records all answers, right or wrong. “48, 47, 45”
Teacher: Students:
“Would anyone like to argue for or against one of the answers?”

Teacher records strategies on the board as students share, and labels them with numbers and/or student names.

“I agree with 45 because I know I need to add 2 to 18 to make it 20, and I can get the 2 from the 27 which leaves me with 25 to add to 20, which makes 45.”

“I disagree with 48 because you would need to add 30 to 18 to make 48 and you only have 27.”

“I disagree with 47 because you would need to add 20 to 27 to get 47 and we only have 18.”

“I also agree with 45 because I know that 20 and 10 makes 30 and 7 and 8 makes 15 and 30 and 15 is 45.”

“I also agree with 45 because I know I need to add 3 to 27 to make it 30.  I can get 3 from 18 which leaves me with 15 and 30 and 15 is 45.”

Teacher: Students:
“It looks like we have 3 strategies that work to get us the answer of 45 and are able to disprove the other two answers.  Can we all agree that 45 is the answers?”

“If you had a similar problem to solve, show with your fingers, would you choose strategy 1, 2 or 3?”

Teacher could use this time to discuss efficiency of strategies.

Students hold up 1, 2 or 3 fingers to choose their strategy of choice.
Teacher: Students:
Teacher writes 38 + 23 on the board.

“I want everyone to use strategy 3 (or other strategy of teacher’s or student’s choice) to solve this problem.

“When I count down from 3, say the answer.  3-2-1…”

Teacher clarifies any remaining confusion, if necessary.

Students holding up thumbs and fingers when they have solved the problem and say answer when prompted by the teacher.

Looking for a way to deepen number sense, build confidence and celebrate different ways of thinking?  Then, give Number Talks a try!  Please comment and share your experience.