Take a Moment to Pause and Reflect

The last few weeks of school can be a challenging time. You might find yourself rushing to finish projects, complete curriculum and bring closure to the school year.  In the midst of all of this end-of-year frenzy, many will ask students to pause and think about all they have accomplished and what they still have to learn, as a means of self-reflection.

Shouldn’t we ask the same of ourselves? Wherever you may be in your Singapore Math journey, reflection can be a valuable tool for continuing to improve your practice.

As you wrap up the year, take a moment to reflect on the following.

Celebrate the successes.

Maybe a particular lesson or unit stands out to you as one in which your students made the most progress or you felt the most confident with your instruction. Maybe you were able to reach that struggling student by approaching the concept in a different way or for the first time in recent years, your students enjoyed math. At the close of one of my lessons, I recall a fourth-grade student asking me if all our math classes could be like this one. Her comment caused me to pause and think about what we had done that she found so engaging and fun and I made a point to model more lessons in that way.

Think about how what you did made a difference and plan to do more of that in the upcoming year.

Acknowledge the struggles.

Thinking Blocks Multiplication & DivisionRecognize the areas within your instruction that were a challenge for you. Maybe your students really struggled with a particular concept or maybe you left a lesson feeling like you needed a do-over. Now is the time to pinpoint those stumbling blocks and think about what support you might need to improve your instruction in those areas. It was my first year teaching a Singapore Math curriculum. With hesitation, I approached a lesson on problem-solving using the bar model. It was a complete flop. Reflecting on it, I realized I hadn’t allowed myself enough time to practice with the bar model and develop the confidence I needed to answer student’s questions on the fly. So, I made a plan to practice bar modeling with Thinking Blocks over the summer. (Thinking Blocks is one of our favorite tools for model drawing. Find an interactive desktop version at MathPlayground.com and four iPad apps on the iTunes store.)

Accepting your struggles and using them as a means to grow professionally, will strengthen your instruction and ultimately, improve your practice.

Set a goal for next year.

Did you try something new this year that you would like to incorporate in more of your lessons? Is there an area within the content that you would like to improve your understanding and confidence? Do you have an idea about how to approach a concept differently? Take a moment to imagine what you want the year ahead to look like and set a goal to make it happen.

As you pack up your room and head off into summer bliss, know that you will return to the new school year with an awareness of all that you gained by reflecting on your practice.

 

 

 

Looking for summer reflections for your students? Check out: Summer Math Suggestions to Boost Student Understanding

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!

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.

Journaling in the Singapore Math Classroom

Communicating mathematically is a critical skill and goal for all of our students to reach by the end of middle school. In fact, Common Core Standards for Mathematical Practices, MP3, states that students will, “Construct viable arguments and critique the reasoning of other.”

Singapore’s Ministry of Education would tell you that there’s nothing Singaporean about Singapore math.  When developing their highly successful math curriculum, they took theory and ideas from mathematicians and educational theorists around the world and put them into action.

What should a math journal look like?

I have attended many workshops and make-and-take sessions on planning and preparing for student math journals.  Many have focused on setting up the student journal with a contents page and tabs to divide the journal into “notes,” “vocabulary” and “practice problem” sections.  While this will create a journal that looks really nice, what I have found to be most effective (and one that I actually use in the classroom) is taking a simple composition or spiral bound notebook and beginning on the first page.  Students make their first journal entry of the school year on page one and continue with entries on subsequent pages. Less is more!

Here’s what a journal entry page might look like:

journal-photo

The journal entry number just grows as the year progresses.  We might come up with the title as a class, or students can create their own.  The problem in the problem box can be copied by students or printed out for students to paste in their journals.

What should students put into journals?

There are four basic types of journal entries; investigative, descriptive, evaluative and creative.

Investigative: Students explore a new concept, solve a problem and make connections to prior learning.

  • Example: Three friends share a sleeve of cookies.  Each sleeve holds 32 cookies.  If each friend eats ¼ of the sleeve, how many cookies do they eat altogether?

Descriptive: Students describe or explain a concept or mathematical vocabulary.

  • Example: Use pictures, numbers and/or words to explain a polygon.

Evaluative: Students argue for or against a strategy or solution to explain why they think an answer is right or wrong, explain their choice of strategies or justify the most efficient strategy.

  • Example: Which of the strategies discussed in class today would you use to solve 245 – 97?  Why?

Creative: Students write their own word problem or create their own number puzzle.

  • Example:  The answer is 465 lbs.  What’s the question?

Here’s a sample student  journal page (click on image to enlarge):

scan0018

When should I ask students to make journal entries?

Journaling can be a very effective tool to develop communication skills in your students.  Depending on the type of entry, you could incorporate journaling into many parts of your math day.  Open a class with an investigative entry to engage students.  Consolidate learning and reflect on thinking with a mid-lesson descriptive or evaluative entry.  Enrich students with a creative entry for early finishers of independent practice.

The benefit of journaling for the teacher is it provides a concrete formative assessment.  By evaluating student responses, you can determine their readiness to handle a new task and check for understanding of concepts.  Student journals also provide a great launching point for discussion at parent-teacher conferences.

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Check out a resource from a previous post: Singapore Math and Math Journal Writing