A shift in math instruction

I'm sure we have all heard a lot about the "shifts in mathematical instruction," but sometimes I think that we get caught up in the shifts in the content of our instruction at the elementary level.  Who teaches time? Where does money get taught?  Third grade doesn't teach multi-digit multiplication anymore?  

The content that we teach has changed some, but in my experience, it is not the hardest shift in our instruction.  The hardest shift in our instruction is explained in the TED talk included below, The Five Principles of Extraordinary Math Teaching by Dan Finkel.  The video is about 15 minutes long, but in it, he highlights some of the importance in this shift for teachers and parents.

These are the principles he highlights:

1.  Start with a question.

2.  Students need time to struggle.

3.  You are not the answer key.

4.  Say yes to your students' ideas.

5.  Play!

Where do you see yourself in these practices?  Can you choose one that you think you can improve?  What supports can you find to help you move forward?

Same or Different?

Looking for a new routine to use in your daily workshop?  Same or Different could be your answer!

This blog has a great variety of images and videos for teachers to use to get this routine started in their classrooms.  There is also a link to a Teaching Channel kindergarten lesson using this routine.

It's just one more way for us to encourage student talk around math.

Estimate! Estimate! Estimate!

A key to building our students' number sense is to practice estimating.  Many times, students and parents look past the estimation part of a computation problem, valuing instead the final, more accurate answer.  However, John Van de Walle's research revealed that estimation is a higher-level skill.  It is important for our students to be able to mentally manipulate numbers through estimation.  It is a real-world skill that they will use daily as an adult.

We know that predictions are important in reading.  It helps readers to focus their comprehension to determine if their predictions are correct.  It also gives them a little more ownership of the story as they read to find connections between the predictions they made and the reality of the story.  As readers grow more proficient, their predictions tend to gain accuracy.  The same is true with mathematical estimates!  Our students will grow in their abilities to estimate the more that they practice.

Math is Fun has a good post that highlights for our students the value of estimation.  It also has a page of estimation games to help students practice in a fun way.

However, for whole class or small group practice, here a couple resources to help you practice regularly in your classroom. 

For K-2:  This Powerpoint has estimation activities for your students to practice.  There are 40 slides in the presentation, and maybe it will give you more ideas to implement this skill into your classroom.

Estimation 180 is a website that I have shared before.  It has images that build off of each other to help students use prior knowledge to make a best estimate.

All of these resources are good for building our students' understanding of number.  What resources have you found helpful in your classroom?  Share in the comments below.

A little STEAM to mark 100 days!

Look what I found in one of our buildings recently!

Outside of the music room, I found this AWESOME bulletin board!  Thanks to Michelle Hardwick for letting me share her awesomeness!

We know that the 100th day of school is becoming a biggeR and biggER celebration in elementary schools, and this bulletin board knocks it out of the park!

It's a relatively simple concept...students look at 100 in so many ways on this day, why not with sound, too?

Inside each of the little milk bottles is a different item--100 of each.  They have been hung on the board so that students can explore the sounds that are made by the different items.

Not only do I love this for its fabulous STEAM connection, I love it for all of the possibilities it offers us...

For example:

    What if you marked the 50th day of school with a container of items, would it be half as loud as a container with 100 of the same item on the 100th day? What changes?

    Looking down into the container of 100 thumbtacks, what is your estimate for how many thumbtacks the container will hold?

    How will changing the container change the sound of the item?

    If we dumped out the items in one of the containers, what are some different ways that we could count them that would help us in the event that we lost track of our count?

    If you had 100 paperclips on the 100th day, and you created another bottle with 100 paperclips but you added a clip for each day after the 100th, how many days would it take for the sound to be distinctly different?  Would it be different?

     Why do we mark 100 instead of 90?  90 is the halfway point of the year?  What fractional part of the year is the 100th day?  What do containers with 90 items sound like?

What uses can you think of for this idea?  Share in the comments below!

Algebraic Thinking Puzzles

I am often asked about ways to challenge our students during math workshop.  I believe it is important that we have a variety of problems that we use.  I also don't think we should spend much of our time accelerating content to teach our students things beyond our grade level.  There are many ways we can build their thinking and logic skills by having them look at numbers more flexibly. Building deeper thinking skills will enable them to persevere as they move into more challenging problems in the future. 

I recently came upon this site.  I think it could have many uses in classrooms as low at 1st grade.  Teachers could use some of the puzzles for a whole class think aloud.  They might also choose to have students work in partners to solve the puzzles.  They might print out a few of the puzzles and have students work on them on paper.  They might introduce some individual students to them.

These puzzles offer students opportunities to think algebraically about numbers and to better explore the meaning of equality and balance.  

Solveme puzzles has three levels of problems:  Explorer, Puzzler, and Master.  Problems become progressively more difficult as students move through the levels.  There are some that involve fractions and negative numbers.   I solved all of my problems as a guest, but you might find it beneficial to create accounts for students.

Let me know what you think of this site.  Feel free to share it with a colleague.  Try some of the puzzles yourself--you might find that you enjoy them, too!

Student Accountability for Fluency

A discussion we have all of the time--with each other, with parents, with students--is about learning multiplication facts. "Why don't they know them like we did?" 

It is important for them to understand multiplication and how it works.  It is important for them to have efficient strategies to help them determine the product of two numbers. It does make future, more complicated math less daunting. We do want them to learn those facts--it is a 3rd grade standard: 3.OA.7:  

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

However, many of our students do not know them. They do not remember them from year to year. They continue to struggle with recall of these facts throughout their schooling.

We need to remember that fluency is not just measured by automaticity.  Fluency also includes efficiency, accuracy, and probably most importantly, flexibility.  For the purpose of this post, I am mainly focusing on the element of automaticity.

As many of you have heard me say, I do think some of this is the changing of the times.  Students do not have a need to use their memory as we did when we were their age--they have so many tools that will remember things for them.  When I was a child, I knew all of my friends' phone numbers.  People today have no need to memorize their friends' phone numbers.  I can't tell you very many of my friends' cell phone numbers today, but I still remember Gena Corbin's phone number from 1978.  Our students don't memorize things very often anymore.  This is not a skill that is well-developed in them, as it was for us.  And--it makes sense. Why memorize things when you can access them in the click of a button?

I think this question also leads into the next reason I believe they don't learn them as we wish they should.  They know they don't need to--they'll be able to access them easily as they get older.  In their minds, learning these facts has little value.

While we can't change these factors, we can help our students to retain more of these facts.  The best way is through use.  Games and other activities that ask them to know their facts will help them to remember many of them.  Daily usage of facts and discussion/teaching of strategies/Number talks in the classroom will help many of them to make sense of the facts and the patterns found within them.

I had a middle-school teaching friend who shared this with me.  I think it puts the accountability of the facts onto the students.  First, give each student a multiplication chart.

As they practice facts and find that they know some from memory, they can begin to cross them out.

This will allow them to only see the ones they don't remember from memory, and they won't continue to look back at the ones for which they have demonstrated mastery. It would be a good thing for the class to discuss how the facts that you know can help you to learn facts you are still struggling with.  This could be the subject of multiple number talks.

They should be able to better self-assess their knowledge of these facts and will be able to see their growth as their chart becomes darker and darker.

3.OA.7 is a standard that will help our students in the long run.  We want them to be successful in them.  However, too many of us are putting too much pressure on ourselves to get our students to learn them.  Maybe, using this method will put the focus onto our students for mastery.  

We make it our goal for them to "master" these facts by the end of their year with us, but in recent trainings, 4th, 5th, and 6th grade teachers all said that students come to them not knowing these facts, so they had to work on teaching them all over again.  Each year, teachers send students on thinking that they have mastered these facts...

Only a handful of our students are mastering these facts. Because really--students can access this information in an instant. They don't understand why we think it is important.  It is our job to offer students many opportunities to use them, to practice them, to self-assess their knowledge and understanding of them, and to have strategies in place that they can use when they don't remember the product quickly.  The stress we are putting on ourselves now to help students gain mastery isn't working (for them or for us).  

We need to put the ball in their court.  We need to show them how valuable knowing these facts is as the math becomes more difficult.  We need to make them the owners of this learning.