Thursday, October 11, 2018

Does it look right? Does it sound right? Does it make sense?




These words were always such a big part of my instruction of reading workshop.  Students used hand signals to help them remember the three questions as they reviewed what they had just read.  Many times, they realized the word they had just read did not sound right or make sense in the context they had just read.  So---they worked to figure out what the new word was that they were struggling to read.

Do we teach our students to do this same kind of thinking when solving a math problem?  In my experience, it is a less common practice.  Sometimes, a teacher will ask the students if the answer makes sense, but really, shouldn't we be teaching our students to ask themselves that question?

Tying our math instruction to real world situations allows for the students to better make sense of their answer.  We need to be intentional in our plans to teach students to make sense of situations and solutions. One of our biggest goals during math instruction is for our students to EXPECT that their answer will make sense.



Friday, September 7, 2018

Rethinking Grouping in Math Workshop


As we continue to work to grow in our role as leaders of mathematicians, we need to begin to rethink our use of grouping in the elementary classroom. Ms. Boaler gives a strong argument for us to consider why we should not use ability grouping in our classroom.

For a long time, we thought that grouping our students by ability during math workshop was a great way to meet everyone's needs.  I know. I did it for a long time, too-- many different groups, many different activities.

But, as we learn more about best practices of mathematical instruction, we discover that providing ALL of our students the opportunity to be engaged in rich, challenging, mathematical activities and tasks. 

This does not mean that reteaching skills to some of your students is not the right thing to do.  Of course, there are times that reteaching and scaffolding are necessary for our students.  Having flexibility in our grouping is important and should not be so difficult as we learn more about our students

In the past few years, I have read articles and books about this.  I have participated in professional development that discusses this.  I have listened intently to members of my PLN discuss the importance of eliminating tracking and the impact it can have on our students.  Here are some of the best resources I have used to gain this mindset:




Another great article to read is this one by Nick Tutolo.  Although it is focused on middle school/high school math, its points are still important for us, as elementary teachers, to consider.

This change in our instruction is not without some challenges.  However, I believe that we will be able to see more growth in ALL of our students if we begin to use some of these best practices:


  • Low floor-high ceiling activities
  • Use of CRA instruction in order for all students to build their conceptual understanding
  • Number talks that encourage and embolden students to use methods/strategies that help them understand better
  • Use of visuals for all math concepts allowing all students to gain an understanding
  • Building time into your schedule for your students to participate in explorations and other tasks to grow their critical thinking
  • Continued modeling of growth mindset in our words and actions
  • Eliminate referring to our students by ability 
What changes can you make in your classroom to allow all of your students to grow as mathematicians?





Friday, August 31, 2018

Continuing to Find Ways to Build Math Talk


I have participated in a number of professional discussions in the last week around the concept of Number Talks.  You may remember that I blogged about Sherry Parish's book before. It is an excellent resource to help you get started with Number Talks.

Many classrooms use Number Talks every day.  It is a great tool for building mathematical discourse, exposure to new strategies, and strengthening students' flexibility and fluency.

However--some people are a little intimidated by Number Talks.  It has some elements of the unknown, and this makes teachers a little leary to try it with their own students.  This is totally understandable.  One way to make this work is for the teacher to work on the anticipation part of the number talk fully.  By anticipating all of the possible ways a student may respond, it will give you the preparation to feel confident as you step into the Number Talk.  It will also allow you time to prepare visual images to represent ways that the students might explain.  It is important that we show the students' ideas using visual representations as this will allow us to reach more students.



Here is a great example of ways that students might see 18 x 5.




I do believe that the term Number Talk is broader than just the use of functions with numbers as is found in the Number Talks book.  Of course, traditional number talks often involve quick-look cards and other visuals to help students visualize the math, but they are still considered to be from the basic concepts presented by Sherry Parrish in her book.

If you click on the tab labeled Routines located at the top of this page, you will find links to resources and videos of a large variety of mathematical routines that will encourage students' math talk.  There are many low-floor/high-ceiling activities which are good to put the students (and sometimes the teacher) at ease when doing a number talk.  In these types of tasks, nearly everyone can find an answer right away, but because these routines lend themselves to multiple answers, we find students recognizing all kinds of things besides the obvious.  Using these type of routines in addition to Number Talks will help your students to grow in ways you won't believe!

Challenge yourself to something new.  Try to add routines to your math class each day--you will be glad you did!

Saturday, August 18, 2018

Genius Hour Podcast

Whether you are a beginner to the Genius Hour or are just playing around with the idea of using it in your classroom, I recommend that you listen to this VrainWaves podcast where they interview AJ Juliani.  It has so many great ideas for getting started (big or small), organization, and accountability!

And... you can listen to it as you work in your classroom.

https://itunes.apple.com/us/podcast/vrain-waves-teaching-conversations-minds-shaping-education/id1365316994?mt=2&i=1000413447686

Monday, August 13, 2018

Virtual Concrete Manipulatives

We know how important concrete manipulatives are for our students as they build a deeper understanding of mathematical concepts. Being able to see and manipulate objects enables students to visually represent problems, see patterns, and make connections.

Hopefully, you have a variety of manipulatives in your room that students can easily access at all times.  Virtual manipulatives are important to have easily accessible, too!  Now is a good time to download some of these apps onto your iPad, bookmark on your computer, links in your SMART Notebooks or PowerPoints and/or add to your Symbaloo!

There are a lot of great FREE virtual manipulatives out there, but today I want to focus on the apps by Math Learning Center.  I have good success with many of them. The site has a lot of other good resources, so when you have some time, check them out as well!


Fractions: This app not only allows you to create bar or circle models of fractions, but it also to layer fraction models to see if they how they compare to one when you add them.
3/5 + 1/3 < 1
The app allows you to place number models or write directly on the screen as well. Take some time to explore the capabilities of this app!


Vocabulary Cards: Another great app that you can probably find multiple uses for! There is a large database of words in this app divided into grade bands K-2 and 3-5.  You can choose to see them all or only certain words.  Each card has 3 parts: the word, examples, and a definition.  You can choose which part you want hidden.  You can also choose the language for the card. I can see these being used as individual review for students, but I can also envision one of these on the board as an intro activity or even a quick exit task.

Money pieces:   The money pieces app allows you to display money with or without the accompanying base ten blocks depending on student needs.  It also has a variety of tools similar to the games Bears in the Cave or Pennies in the Hand where you can put your coins up and then hide some.  For example.  I have a pocket in the above screen.  If I told you that I have 35 cents altogether, can you tell what I have in my pocket?


With the click of a button, I can remove the pocket to show that there is a quarter in it.  You can do this similarly with a hand or a bank.  

Money seems to be difficult for children anymore because they have less interaction with it than we did. Our students don't get the same opportunities we did to spend cash, but it is still important to understand, and this app will give them some basic experiences with it.


Number Frames:  This app not only allows the important 5 frame, 10 frame, and Double 10 frame, it allows you to customize the frame you want up to 120. As with many of the apps, it allows you to enter number sentences and to write on the screen.  This app is not just for Littles!  Teachers in 3-5 can use it to explore place value as well as patterns in multiplication.


Number Lines:  I love this app!  It has so many options for you to customize the number line including fractions, decimals, hidden numbers, hidden tick marks... I think it really helps students to represent their work, and it marries nicely with the beaded number line for moving from concrete to representational.


Number Pieces:  There are two versions of this app.  The one I am showing above is more advanced than the version called Number Pieces Basic. It is base-ten blocks, but you can break the large pieces apart to show number relationships. You have choices in color and orientation of the pieces.  Again, you can enter number sentences or write on the screen.


Number Rack:  You know how much I love this one!  It comes in handy as a teacher model on the SMARTBoard as students manipulate their own Rekenreks.  It is customizable by sets of 10 up to 100. It allows for teacher annotations like the others, but it also allows for teachers to hide beads as below.  Well worth your time to explore this one--not just for Littles!

Do you know how many beads I have hidden?



Pattern Shapes: It is so important that we give students time to play with pattern blocks!  This offers a blank mat for students to create their own patterns.  It also has templates (as above) for students to fill in with shapes.  (Very good for sharpening visual skills)  For older students, it has two different grid backgrounds to allow exploration of area and perimeter.


Geoboard:  The geoboard app has different sizes of geoboards and allows for customization in many ways.  Another great one to have up on the SMARTBoard as students manipulate their own geoboards.



Partial Product Finder: While still in Beta form, this is an awesome app to help your students better understand partial products as well as the distributive property.  You can customize the rectangle up to 30 x 30 and then decompose one or both sides.  The matching equation shows up at the bottom of the screen. I have blogged about this one before--it is awesome!

I highly recommend that you take some time to explore these!  Hopefully you will find some that you make available for student use just as you do other manipulatives.  Maybe you'll find ways to use them within your instruction.  Whatever works best for you and your students!  

Let me know if you have other virtual manipulative apps that you would recommend!



Saturday, August 4, 2018

Culture-Building for the New School Year

How do you plan to transform the culture of math (teaching and learning) in your classroom or building this year?  Have you had a chance to think about this?  It can be easy to get caught-up in the content that will be covered and forget the importance of building strong mathematical communities in our classroom.  However, the time spent building your students into teammates in math will be worth it.  Go slow to go fast.



Let's think about Ron Ritchhart's Cultural Forces that Define a Classroom and how they can impact our building of a math community.

1.  Physical Environment:  Is your classroom arranged in a way to promote collaboration?  Are the spaces clear where students can gather? Have you thought about the places where students will be able to visually share thinking?

2.  Interactions & Relationships: What steps can you take to build a feeling of respect which will allow students to be confident enough to share their ideas and strategies?  What will you do to be sure all students and their ideas are valued in your classroom? How will you encourage collaborative inquiry for your students?  What methods will you employ to build  a growth mindset in students? How will emphasize growth and celebrate success?

  • This sample chapter from Thinking Together: 9 Beliefs for Building a Mathematical Community by Rozlynn Dance and Tessa Kaplan supports these concepts.
  • More ideas can be found in this sample chapter of Count Me In!: Including Learners with Special Needs in the Inclusive Classroom by Judy Storeygard.

3.  Expectations: What are the cornerstones for your mathematics community?  As your class determines the classroom norms, which ones do you feel MUST be part of the list? How will these be enforced?


4. Time:  How will time be structured during your workshop?  What will you put in place so that students don't feel pressure to work through concepts quickly? On the other hand, how will  you build efficient use of time for your students?  What will you do to be sure you offer enough thinking time for students?  In what ways will you support your students to show perseverance?

5. Language: What do you think is the key mathematical language for your students to learn during the year?  What will you do to build their mathematical discourse?  What language will be modeled for them to use when working with partners or small groups?  Will your classroom contain a word wall or other location where students can easily refer? What growth mindset language will you be sure to include?


6.  Routines & Structure: What daily mathematical routines will you put into place, and how will they help build mathematical discourse in your classroom? How will your math block be structured?  What management routines will you have in place to help your classroom run smoothly?

7.  Opportunities:  How will you regularly opportunities for all students to interact with rich math tasks? In what ways will students grow in the math practice standards as well as the mathematical content standards?  What types of explorations and problem-solving will you use in your classroom?  Will they promote perseverance in your students?  How will students be encouraged to find and explore their own mathematical questions? 


8.  Modeling:  How will you model creativity and risk-taking?  In what ways will you provide examples of collaborative talk and respectful debate? How will students know that this is a safe classroom to take risks? What will you do to share your own wonderings and questions with your students? How can you be intentional about modeling perseverance?

How can you take risks this year in order to grow as a math teacher?  What resources can you use to help you to learn more about best practices in mathematical instruction? Using these 8 ideas as a starting point should help you on your way!






Monday, July 23, 2018

Looking for Explorations/Investigations to do with your class?



Explorations and investigations help your students to take ownership of their own learning and are a great way to get students excited about math!  They encourage critical and creative thinking skills.  They build a sense of math community, and make us all better mathematicians.

If we get started with predetermined explorations, and our students become comfortable with the format, they may begin to come up with their own explorations that you can embed into your instruction!  

I have posted about a number of explorations either that I have done with students or have seen others do. However, I wanted to remind you of some good places that you can go to find an exploration that works for you and your students!

WIM:  The weeks of inspirational math from Youcubed are all set up and ready to go for you.  I have blogged about them before, and I can't say enough about how they not only encourage a growth mindset, but also that they are a lot of fun!

Math Solutions:  This location is full of exploration options for you.  Many have a great connection to literature.

Math for Love:  The free lessons on this site typically involve investigations.

100 Numbers to get students talking: This task has step by step directions and examples of how to use it to build your students' group work abilities this year.  

Finally, I have blogged about some different explorations that you could try in your room.  You might find one that will be a great review or introduction for your students this year.  To find the blog posts, look over at the right side of my blog at the labels.  Click on the explorations label, and it will show you all of my posts about explorations.


If you have other great explorations to share, please post in the comments below.

What a great way to start your year of math learning!  Beginning with some explorations will give you plenty of time to get to know your students, build your classroom culture, and develop your routines.  Let me know if I can help in any way!