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By Robert Kaplinsky

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KG- 6th

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Snapshot Assessments by FWPS

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Grade 2

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Collecting Data Learning Targets & Standards KG

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Collecting Data Learning Targets & Standards KG

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Comparing Tasks - Allowing for Problem Solving

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Comparing Tasks - Allowing for Problem Solving

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CGI

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Erma Anderson

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Multiplication & Division

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Addition & Subtraction

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At the start of this school year in our elementary school, we decided to focus on differentiation strategies all teachers can use in their classroom. To be more specific, we invited all teachers to explore strategies they can use during Tier 1 instruction (RTI), not necessarily differentiating for students with moderate or severe disabilities, but strategies that can make the learning accessible for all students in the classroom.

Students that require Tier 2 or Tier 3 instruction benefit rom support from the Math Learning Support Specialists AND benefit from these Tier 1 interventions and learning experiences in their classroom.

During our first team meetings, all teams from kindergarten to 5 th grade explored a variety of strategies we could learn about and put into practice, and were invited to develop a professional team or individualized goal as part of our annual professional growth and evaluation model.

"Parallel tasks" was a popular strategy the teachers identified. I'd like to share some simple strategies so you can give it a try.

1st grade team working and learning together at Shanghai American School

Mathematically Gifted

Let's not forget about our students who are able to show proficiency during the pre-assessment! We also need to intentionally plan for them. I am not referring to students who get answers quick or have memorized algorithms that give the impression of understanding mathematics; I'm talking about students who can problem solve by choosing the most efficient strategy to solve a problem, show their thinking with a pictorial or more abstract model, and can explain how they solved a problem and why they chose a particular strategy. Do you have some of those students? We do. There are not many, but there are some.

There are many strategies for them, however in this blog I will only explore parallel tasks. However, I do want to mention some strategies to AVOID with these students:

MOTS: More Of The Same work. This is the least appropriate way to respond. Students might start to hide their abilities.

FREE TIME: Students might find this rewarding, but it does not maximize their intellectual growth. Students will hurry to finish without giving it their best effort. Other students that require more thinking time, will feel they are "not good at math".

HELPERS: This does not stimulate their intellectual growth, and will put students in socially uncomfortable and undesirable situations.

PULL-OUT: This practice tends to be unrelated to the regular math classroom, and it does not allow students to go deeper in their understanding of the math content they are learning in class. Unfortunately, many of us did this for years!

COMPUTER TIME: Although there are great apps to practice math skills, it does not engage students in their conceptual understanding of math, increase their problem solving ability, nor increase their reasoning and communicating skills needed to justify their thinking.

Parallel Tasks

Parallel tasks are 2 or 3 tasks that focus on the same learning task/learning objective but offer different levels of difficulty. All students should be able to participate in the "Share-Out" at the end of the lesson which is the most important part of the lesson because this is where the teacher learns how students are tackling the problem, what strategies are they using, and what misconceptions they might have.

You can assign students to a particular task or you can give them options. I prefer to provide different options as this gives students more ownership of their learning pathway. If they choose a task that is too difficult, they can move to another one.
Example Learning target: Represent and solve problems involving addition and subtraction
Lesson objective: Use place value knowledge to subtract within 100

Standards: 2.OA.1, 2.NBT.5, 2.NBT.7

There are many great things to notice about these two slides.

First of all, the teacher will use the "slow release" function, to release each sentence one by one allowing students to notice and wonder about the context of the problem. Using Numberless Word problems is essential when creating parallel tasks. (To learn more about Numberless Word problems click here: https://bstockus.wordpress.com/numberless-word-problems/ by Brian Bushart)

For example, she/he might ask students, how many kinds of apples are there? Or how many apples could there be? (Estimation180 is a fantastic website that can support this type of thinking and dialogue in your class).

After the "release" of how many apples each child has, students might wonder about the question, and will then come up with the best questions. Give them a chance to discuss with a partner first before you ask a student. This gives them the chance to practice their question, and/or craft a question with their partner.

Next the teacher will show the 2 nd slide; this is when students have the choice of numbers they can choose to solve the problem.

Notice how ALL students will be showing the strategies they used to solve the problem, explaining how they solved it, and making sure that their argument supports their work (Claim-Evidence-Reasoning).

If students need to use manipulatives to solve, the first set of numbers allows them to use any type of manipulatives such as discs, unifix cubes, or single cubes. The second set of numbers will require ones and tens.

If you want students to move from using base ten blocks in order to try other strategies, encourage students to use the third set of numbers as they will have an incentive to think about another strategy.

For problems involving computation, you can add multiple sets of numbers to allow for ways to vary the difficulty level. You could also use parallel tasks to vary the level of problem solving and reasoning.

Open Middle

"Open Middle" is a great resource created by Robert Kaplinsky www.openmiddle.com that provides parallel tasks for the same standard, however the lesson objective might vary because students will show proficiency of it using deeper problem solving skills, than only computational skills. Take a look.

"Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards and provide students with opportunities for discussing their thinking." Robert Kaplinsky.

During the active engagement of your lesson, walk around to observe the strategies and different approaches that students are using to tackle the problem. This is where the teacher plans which students will be sharing their ideas making sure that a variety of strategies are shared. The teacher uses this time to look for opportunities to help students make connections between the different ideas shared.

Last week, I was in a 1 st grade classroom when the teacher asked a student to share how he persevered when solving a tangram puzzle. It was a fantastic share-out moment, and we all learned from this 6 year-old talking about not giving up!

Next steps...

When you are thinking about creating parallel tasks for your lesson, start by identifying the big idea you want to focus on and think about what your students might need. You could start by using different sets of numbers, the number of operations they can use, or making them open to allow for deeper problem solving, etc.

Start with a task from your original lesson then create parallel tasks in order to allow students to choose the task they will work on while making sure that sometimes the most difficult task is the first one. This will ensure that students consider all options before choosing their task.

If you are interested in reading more about parallel tasks, refer to "Teaching Student-Centered Mathematics" by John A. Van de Walle.

Other samples of parallel tasks:

1st grade sample. More resources at http://www.openmiddle.com

2nd grade sample

3rd grade sample. Based on #tapediagramtuesday by Duane Habecker

5th grade sample

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Differentiating: Using parallel tasks in your math lesson

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At the start of this school year in our elementary school, we decided to focus on differentiation strategies all teachers can use in their classroom. To be more specific, we invited all teachers to explore strategies they can use during Tier 1 instruction (RTI), not necessarily differentiating for students with moderate or severe disabilities, but...

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Article: Never Say Anything A Kid Can Say

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Article: Never Say Anything A Kid Can Say

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by Steven C. Reinhart

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Teacher & Student Behaviors

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Building Fluency

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With clarifications

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PLC

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K-5

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Article: Memorizers are the lowest achievers

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Article: Memorizers are the lowest achievers

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by Jo Boaler

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It's time to debunk the myths about who is good in math, and Common Core state standards move us toward this worthy goal. Mathematics and technology leaders support the standards because they are rooted in the new brain and learning sciences.

All children are different in their thinking, strength and interests. Mathematics classes of the past decade have valued one type of math learner, one who can memorize well and calculate fast.

Yet data from the 13 million students who took PISA tests showed that the lowest achieving students worldwide were those who used a memorization strategy - those who thought of math as a set of methods to remember and who approached math by trying to memorize steps. The highest achieving students were those who thought of math as a set of connected, big ideas.

The U.S. has more memorizers than most other countries in the world. Perhaps not surprisingly as math teachers, driven by narrow state standards and tests, have valued those students over all others, communicating to many other students along the way - often girls - that they do not belong in math class.

The fact that we have valued one type of learner and given others the idea they cannot do math is part of the reason for the widespread math failure and dislike in the U.S.
Related: Common Core math experts say teachers need to stop using shortcuts and math tricks
Brain science tells us that the students who are better memorizers do not have more math "ability" or potential but we continue to value the faster memorizers over those who think slowly, deeply and creatively - the students we need for our scientific and technological future. The past decade has produced a generation of students who are procedurally competent but cannot think their way out of a box. This is a problem.

We don't need students to calculate quickly in math. We need students who can ask good questions, map out pathways, reason about complex solutions, set up models and communicate in different forms. All of these ways of working are encouraged by the Common Core.

Mathematics is a broad and multidimensional subject. Real mathematics is about inquiry, communication, connections, and visual ideas. We don't need students to calculate quickly in math. We need students who can ask good questions, map out pathways, reason about complex solutions, set up models and communicate in different forms. All of these ways of working are encouraged by the Common Core.
Related: Should we stop making kids memorize times tables?
Technology leaders are publically arguing that calculation is not math, and that math is a much broader subject. Conrad Wolfram, one of the leaders of one of the world's most important mathematics companies, Wolfram-Alpha, urges schools to stop emphasizing calculating and focus instead on problem solving, modeling, thinking, and reasoning as these are the mathematical abilities that students need in the workplace and their high tech lives. This broad, multidimensional mathematics is the math that engages many more learners and puts them on a pathway to life long success.
Related: Testing gives third-graders upset stomachs, tears, even fevers
Part of the problem in the U.S. is the desperation of many parents to advance their children in math, pushing them to higher levels of math faster and sooner, somehow believing that a resume packed with advanced math courses will guarantee their future. Bill Jacob, a mathematics professor at the University of California, Santa Barbara, speaks openly about the dangers of students being pushed to higher levels of mathematics too soon. "I know it is hard to persuade parents that their students shouldn't race to get calculus, but I really wish they wouldn't. Too much content and depth is left out when they do." said Jacob, who is not alone in saying that he would rather have students in his university mathematics courses that have breadth in their mathematical experiences than any additional Advanced Placement courses. Experts in England are giving the same advice to parents of high achieving students. Geoff Smith, chairman of the British and International Math Olympiads warns that accelerating children through the system is a "disaster" and a "mistake". He, like me, recommends that high achieving students explore the mathematics they are learning in depth, instead of rushing forward.

Mathematics is not a subject that requires fast thinking. Award winning mathematicians talk about their slow, deep thinking in math. Fields Medal winning mathematician Laurent Schwartz wrote in his autobiography that he felt stupid in school because he was one of the slowest thinkers in math. Eventually he realized that speed was not important - "What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant."

Some school districts, such as San Francisco Unified, are trying to slow down the math experience, requiring that advanced students go deeper rather than faster. Students still reach calculus but the pathway to calculus consists of deep understanding rather than procedures and memorization. This is an important move. There is no harm in students being introduced to higher-level mathematics earlier, as long as the mathematics is enjoyable and ideas can be explored deeply. Third graders can be fascinated by the notion of infinity, or the fourth dimension, but they do not need a race through procedural presentations of mathematics.
Jo Boaler is a professor of mathematics education at Stanford University, co-founder of This story was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Read more about Common Core. www.youcubed.org, and author of What's Math Got To Do With It: How Teachers and Parents can Transform Mathematics Learning and Inspire Success. (Penguin, 2015)
New brain science tells us that no one is born with a math gift or a math brain and that all students can achieve in math with the right teaching and messages. The classrooms that produce high achieving students are those in which students work on deep, rich mathematics through tasks that they can take to any level they want. No one is told what level they can reach and no one is held back by narrow questions that limit students' mathematical development and creativity.

Many people across the U.S. have gross misconceptions about mathematics learning, thinking that mathematics is a narrow subject of memorization and speed and that people who do not calculate fast or memorize well are not 'math people'. We need to change the conversations about mathematics, communicating to all children that they can learn. We also need to change the way math is taught, valuing the different ways of thinking that are so important to the subject. Mathematics, itself, needs this and although change is hard, it should be embraced.

We need to broaden mathematics and open the doors of mathematics to all students. When we do this we will see many more creative, energized young people equipped to think quantitatively about our ever-changing world. We all need this.

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Memorizers are the lowest achievers and other Common Core math surprises

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It's time to debunk the myths about who is good in math, and Common Core state standards move us toward this worthy goal. Mathematics and technology leaders support the standards because they are rooted in the new brain and learning sciences. All children are different in their thinking, strength and interests.

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Modeling with manipulatives in Middle School

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Modeling with manipulatives in Middle School

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Progressions K-5th

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Progressions 5th-HS