Best Practices: Where can you grow?

 It has been a crazy, stressful year.  The good news is that the end is in sight for this school year.  And, while we may still live with some restrictions when our new year arrives next fall, we anticipate that many things will return to a more typical format for instruction.

So--let's look with next year in sight.  I know your summer is looking promising.  You can't wait to just relax and enjoy all that the world has to offer without the weight of instruction on your mind.  However--I imagine, like me, you find it difficult to totally turn off school.  Here are some things you might consider looking into to grow as a math teacher for next year.  Think about these best practices.  Which ones seem reasonable for you as you continue on your math journey?  You might choose two; you might choose seven.  Do what works for you.

Daily Routines:  Using the beginning moments of your workshop to get everyone thinking around an interesting problem is a great way to get the juices flowing!  I would definitely include traditional number talks in these routines, but there are so many others to consider.  Look for low floor/high ceiling routines that allow all students to enter into the problem and encourage creativity and fun for all.

More Manipulatives:  CRA Instruction "puts math in students' hands so they can understand it with their heads."  All students benefit from this type of instruction, but sadly, we tend to move away from it too quickly. It is one of the best ways for students to gain conceptual understanding of concepts.

Numberless Word Problems:  Key words are cancelled.  They are not a good instructional practice because they do not encourage good thinking from our students.  Taking some time to think around word problems that do not have numbers is a fabulous strategy for our students.  It not only shows the link between reading skills and math context, but it puts another tool in our students' toolboxes that they can use when they are confused by a word problem.  Remove the numbers!

Counting Collections:  The counting collections activity is way more complex than just counting, but it is also as simple as just counting.  The CGI approach is really working hard in this activity that I love to use from K to 5th!  (It could be used with older students, too!) It is an in-action practice of concrete, representational, and abstract.  This can be done by individuals or in pairs, but as always, the sharing at the end is where the real learning occurs!  You do not need anything fancy to count, so don't feel like this is something you have to go out and buy materials for.

More Visuals:  Math is visual.  Find ways to help students SEE the math in everything you do.  From representations during Number Talks to counting aloud visuals to the Same/Different routine to Prime Climb or Tiny Polka Dot, put the math out there in a way that students can engage with and understand.  Visuals help all students to engage and step-in to the lesson.

Three Act Tasks:  These offer such a good opportunity for our students to  make sense of math, and they do not follow the "I do, we do, you do" instructional format.  There are so many available to choose from.  The tab at the top of this blog is a rabbit hole that will take you to quite a few.  How can you be more intentional about using them next year?

Heterogeneous Grouping:  Tracking students is not an equitable practice.  All students need the opportunity to see and do high level tasks.  Let's not limit our students.  Be more intentional about grouping your students with students of varying strengths.  Don't underestimate what your students can do.

More Incorporation of Data:  Jo Boaler has added resources to her Youcubed website around data.  SlowRevealgraphs.com  has a number of prepared slide decks for many different levels.  These can be used in math class or incorporated into content areas.  Teaching our students how to read, question, interpret, and create various data representations is an important 21st century skill.

Desmos:  This platform offers so much for students, but also for teachers!  The platform is manageable and you can find a large number of ready-made activities that go beyond DOK 1 on this site.  I have many listed and aligned by standard in the Resources to support CCSS tab at the top of the page.

Weeks of Inspirational Math:  I have blogged about this more than a few times.  1st time   2nd time  3rd time  I love these!  I believe strongly you will, too, and so will your students.

Puzzles:  Our students do not have enough experience with persevering through challenging problems, and puzzles (both paper and tangible) give them experience with this skill.  Maybe you just add a jigsaw puzzle table next year, or maybe you take on KenKens--either way, your students will grow! (and probably have a little fun along the way)

Each year, we step into our classrooms with a fresh start and with plans of doing better than the year before.  By challenging yourself to grow in your math instruction, you will not only grow, but so will your students!  Good luck.

Here we go!

Tomorrow is August, and that typically means the beginning to a school year.  And Oh! what a school year it is to be.  Like one we have never experienced before.

As we think about our students, safety is our priority, of course.  However, we also must keep in mind learning--as that is the reason the new year begins.

Instead of getting caught up in the things that our students missed without in-school learning last spring, let's think about what we as teachers always have done; let's meet our students where they are and move them forward.  We don't have to worry about teaching a third of the content from the grade before us. Let's pick them up where they are and move them into new thinking, into new content.

2020 is one that will always be remembered, we know that.  Let's not burden our students by making them feel behind or like they aren't ready for their new grade.  Let's build them up, and build them into students with knowledge and understanding.  It is what is best, and it will relieve the pressure on them--and you. 

Good luck in 2020 whether it be in-person, online, or a little bit of both!

  

Looking for Virtual Manipulatives?

While we are still unsure how our instruction will be delivered in the fall, there is one thing we are sure of....student's involvement in the concrete phase of learning math is important!

Sending home concrete manipulatives for all of our students may be too costly for most schools.  Purchasing enough to send home is not the only problem: we know it is doubtful that many of these tools will return to our buildings.  With that in mind, here I am going to highlight some of the best virtual manipulatives I have been able to find and use.

I highly recommend using these with students this fall even if we are face to face.  Allowing for guided use now will make it easier should they need to use them again at some point in the year.

I have always been a fan of Math Learning Center Apps, and I have shared these apps with many teachers before! These apps have always been free and easy to access and use.  Because of the pandemic's rise in at-home schooling, they have added an extra feature!  Sharing!  Four of the apps can be set and shared with students and/or students can share with you.  There is a video explaining how this works, and I have had success with it myself.  There are many great apps here.  Some of my favorites include the Number Rack, the Number Line, and the Partial Product Finder.  However, I can think of many great uses of the other apps.  I just have not used them myself in a classroom.

These are the apps that allow sharing at this time.

Toy Theater also has a great selection of virtual manipulatives. I do not have as much experience with these, but it has some great ones such as interactive hundreds and mulitiplication charts, a variety of counters, dice, and some graphing apps.  I think it could meet a lot of needs!

A great variety

Didax also has free online manipulatives. I have only found these while I've been sheltering at home, so I do not have experience in the classroom with them.  You'll find many that are available above, but here you will also find linking cubes and a math balance!  It also has algebra tiles and prime factor tiles that can be used in middle grades. (because manipulatives are just as important there!)

A few other places that you can find specialty links:

MathToybox has a Cuisenaire rods app.

ABCYa has some fraction tiles that are nice.

I hope you can take some time to explore these apps and find the ones that will work best for you and your students' needs!  It might be a good way to start the school year, whether we are virtual or in-person, to spend some time walking students through these tools, how to get to them, and how to use them.  That way, when the time arises, they will be able to use them more independently!  Remind them that they can use them and explore with them whenever they want.  Exploring these tools independently helps students to see relationships and make sense of it all on their own.

The other thing that is great about these virtual tools is that you can use them to create your visuals for your SMART docs, Google slides, or student tasks.  Math is visual, and these provide us with good ways to show the math to our students.

I hope we have the chance to use concrete manipulatives in August with our students, but now is the time to prepare in case we don't.  I hope you can find tools at some of these sites that match the ones your students typically use in the classroom.

THIS is the Message to Begin a New Year

What a great thing for us to do for our students: Help them understand the value of mistakes!  And now, at the beginning of the year, it sends a great message to all stakeholders:  This classroom celebrates mistakes!

"I have not failed.  I've just found 10,000 ways that won't work."  

Thomas A. Edison

Using Twitter to grow

If you are looking for a way to grow as an educator this year, I would recommend becoming more active on Twitter.

I'm sure you have other social media accounts, but this one will give you so much professionally!  Remember that there was a time when you didn't know how to upload a photo to Facebook or how to use a filter in Instagram or Snapchat?  You took them on and figured them out!  You can do the same with Twitter.  It doesn't take very long to become more comfortable with the platform.

I use Twitter now mainly as a math educator, but when I first became familiar with it, I used it to gain access to technology and classroom ideas.  It is all about following others.  You'll be amazed at the number of ideas and free resources you can find!

I would also recommend trying one of the many weekly chats that are on Twitter.  The first time or two, you may want to just read others' Tweets, but after a few times, you'll be ready to give it a try.  People on Twitter are very helpful and understanding.  Here are some weekly chats that happen throughout the school year that I would recommend.

#elemmathchat   :  Thursdays at 8:00 pm CST Math leaders from around the country lead discussions of different math concepts
#mathstratchat   :  This chat is not a live chat like the others.  Pam Harris posts a problem on Thursdays, and people tweet the way that they solved it.  It is amazing to see so many flexible thinkers!
#mathconceptions   : Mondays at 8:30 pm CST  half-hour long chat with great people around fun topics
#kinderchat, #1stchat, #2ndchat...:  Search these hashtags to learn more about each grade levels chats.  They are usually weekly.

At the time of the chat, just search the hashtag and then go to Latest.  It will help you see the conversation unfold...

If you are looking for some people to follow, here are some people (mainly math people) that will get you started.  Also, most of your schools have a Twitter account.  You can follow them, too.
@pearse_margie
@joboaler
@mraspinall
@educatormomof3
@gcouros
@Trianglemancsd
@JoyKirr
@Mathgarden
@eriksonmath
@dbc_inc

Give it a try!  I am happy to help you however I can. Before you know it, you'll be tweeting, retweeting, and using hashtags! #goals

As another year comes to a close...

The excitement of a summer of fun is palpable at this time of the year--in both students AND teachers.  It is important that everyone have a little time away to "sharpen the saw" and give some much needed time to themselves.

However, it is also a good time to set some goals for next year.  Next year--a new beginning.  Here are some ideas for change that you might ponder this summer, and maybe you will think of some ways to make them work for you.  

Start small!  You don't need to change everything at once!  Choose one change that you want to try to start the year.  Here are my ideas and some resources to help you:

More Number talks/Math discourse:  Consider starting each day with a number talk or other math routine that encourages student discussion, reasoning, and critiquing.  Many teachers find that these help build fact fluency.  Be sure to build visuals into your routines.  Be intentional with your planning.  You shouldn't plan a year's worth of routines/number talks this summer.  The routines will vary with what your students need.  A necessary piece to this change is that you must really build a classroom culture that encourages and celebrates risk-taking, making mistakes, and curiosity.  You can find a number of resources to help you with building routines here, or you can use the word cloud on the right and click on Number Talks or Routines to read previous posts about the subject.

Heterogeneous grouping:  Many teachers group students by their perceived abilities for instruction.  Not only is this inequitable, it also leads students towards a negative perception of themselves as mathematicians.  Consider trying Visibly Random Grouping or other heterogeneous groups during your workshop.  There may still be times where you focus your reteaching with a small group on a particular skill, but in general, we want to offer the opportunity for all students to work together as much as we can.

More time for Exploration: Be less helpful.  Let students make sense of it all on their own before you begin telling them what to do.  Let them struggle with it a little, and let them use manipulatives to represent their thinking and look for patterns. When they are done with exploring, then you can work your magic by bringing it all together at the end of the class.  You'll be amazed of what they can do when they are not being told what to do.  (This may take a while unless you have already built a great culture in your classroom for risk-taking.)  These explorations could be small ones in a daily lesson, or they can be larger ones like some that are available in the word cloud by clicking on explorations.  Using Jo Boaler's WIM are also great ways to build exploration into your classroom and inspire your students.

Make tech time meaningful:  Sometimes teachers get caught up in offering tech time every day during math.  I am not a huge believer in this, as there are so many good rich problems out there for students to solve and too many rote drill and kill sites for students to work on.  Move away from these rote sites.  Instead, place students in small groups and have them work to solve meaningful problems or puzzles like those from Nrich or KenKen.  When students do go online to do work, consider trying some of the activities found on Desmos that align with your targets.  These activities require student thinking rather than just computing.

Reach out to me if you would like my support as you start to make some changes in your math instruction.  I am happy to help!

Finally, if you like to read professional books over the summer, here are some to consider:  

    

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?

• Youcubed article on setting up positive norms in your math classroom

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?

• Scholastic blog post about math talk
• Sample Accountable Talk anchor chart
• Blog post focused on Number Talks

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?

• Dr. Nicki Newton's First 20 Days outline might help with some of these questions
• My blog page with links to best-practice routines

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? 

• My blog post on exploration resources

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!

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!