Tuesday, December 8, 2020

How have you changed?

2020 has, in many ways, contained both stagnation and growth. The stagnation is what seems to resonate with us.  So much time at home, a limited circle of people to interact, and a school year that makes it challenging to see the desired growth in our students tend to overpower our thinking.  It is easy to focus on these things, as they are such a part of our daily lives right now.

However, there are also so many ways that we have grown in the last year. We have gained more time for self-reflection, had time to actually pursue our interests, become quite adept at Zoom meetings, and for many of us, learned how to celebrate holidays with a small circle rather than our large family gatherings.  While all of these opportunities have not been our choice, they have allowed us to look at our lives in a new light, and hopefully, there have been things we have done that we hope to continue well after this pandemic is in our rearview.

But as a math teacher, what changes have you made that you want to stick around?  Have you eliminated pages of repeated problems?  Have you put more time into the hows and whys of student work rather than the final results?  Has making math visual been a priority in your instruction? Have you been more intentional with your practices and built in routines that fit your students' needs?  Do your students see math as more than just computation? Have you offered more opportunities for creativity and critical thinking?  Does your classroom culture celebrate mistakes as steps toward growth?  

I am hopeful that some of these changes have occurred for you, and that you see the value in keeping these practices into the return of our post-pandemic world. While that world still may be many months away, these best practices are good now. Remote, hybird or in-person instruction.  Polish them up so that you have them in good shape for our return to "normal" instruction. Whenever (and whatever) that may be.  





Saturday, October 17, 2020

So much good in one place!




Many of you are familiar with the beauty of Splat! and all that it can offer our students.  It also has the great quality of being a routine that can be used throughout school.  It is certainly a routine that students, teachers, and this math specialist love due to its visual qualities, critical thinking elements, and engaging ways!

But the master behind Splat! has many other great resources available to teachers.  They are opportunities to expose our students to many concepts and to encourage some rich discourse in our classrooms.  And, best of all, Steve Wyborney shares his wonderful creations with us in the form of free downloads.

These resources are good in a normal year, but this year, they are especially nice to use in a virtual learning format.

Here is a run-down of some of the things you can find from Mr. Wyborney:

Splat!:  Beginning with concept of missing addends, the Splat slides move from primary concepts to fractions and algebra as the slides become more complex.  Students benefit from the visual nature of the slides, and they love the game feel of it all.

Esti-Mysteries:  Another popular routine with students, esti-mysteries merge the skill of estimation with critical thinking.  One clue is revealed at a time so that students can narrow down their choices.  In the end, they still depend upon their estimating skills for a final decision.  One thing I like about this routine is that once it has been taught, I think it can be used in many ways including revealing a clue a day with the final discussion occurring at the end of the week.

Estimation Clipboard: This is one of my favorites!  This routine again builds off of the concept of estimating and makes it fun for students to take the risks when making an estimate.  An image is shown, students make an estimate, and then the answer is revealed. Another slide is shown with a change in the image, and the students adjust their estimate.  This simple routine has hidden sophistication in that it often has hidden benchmarks for students to use to be able to make a better estimate.  Many of the images are about number, but I especially recommend the slides that deal with length.

Cube Conversations:  These 3D images are a great way for students to get an introduction to volume and to build their visual and grouping skills.

Tiled Area Questions:  Beginning as general area problems, these develop into more complex relationships between whole and fractional numbers.  Again--an opportunity to stretch our students' thinking and their abilities to justify their thinking.

His animated multiplication chart is a nice tool for students to explore patterns and be exposed to their facts.

I know that for many of you Splat! is a common routine used in your classroom, but I wanted you to be aware of some of the many other treasures that you can find on this website.  If the past proves anything, I would bet we can look forward to other great ideas to be created by him in the future!  Have fun exploring this awesome sight, but more importantly, have fun watching your students think, engage, and discuss mathematics in such fun ways!

Thursday, September 17, 2020

Looking at Data

While the post title might lead you to believe that this post is about looking at student data, that is not the case in this situation.  Let's look at some resources for students looking at data!

Last fall, I met with some representatives of a major company in my community to discuss math education in our schools.  The number one take-away:  We want workers who know the answer to the question, "What does the data tell you?"  

It is common for teachers to present math pictures or problems to students and ask them "What do you notice? What do you wonder?"  But this post focuses on true data and how we can get students to look at it more thoughtfully, with the ultimate goal being that they can use the information to be better informed about the world around them.

Jo Boaler and youcubed have come up with data talk images!  Here is a link to their page of images (which I am sure will grow...)  Displaying these data images to students not only is great practice with graphs and infographics, but it also allows them to be better readers and understanders of data.  While these might make a great start to a math lesson, they can also be wonderfully embedded into content areas such as social studies and science--all with the simple questions, "What do you notice?"  "What do you wonder?"

Another resource that I often lead teachers to is numberless graphs.  Much like numberless word problems, numberless graphs force students to think and make relationships about the things they know from the graph while still missing key information.  Also much like a numberless word problem, the data is slowly revealed to them to help them make sense of it all in a thoughtful way.

No matter the grade you teach, what are you doing to engage your students in reading and understanding data?  Consider trying some of the links above, and watch the lightbulbs go off!

Friday, July 31, 2020

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!

  


Friday, July 3, 2020

Individual student toolkits for CRA instruction


If students are in your classroom in August, it will be worth your time to have some sort of math tool kits prepared for your students because it is not recommended that students share resources, and you don't want to be cleaning them every night. What you are able to put in the kits will depend on your resources.  

We know that CRA instruction is vital for conceptual understanding of mathematical concepts.  Just because we will have some limits in place (for everyone's safety), doesn't mean we should abandon best practices.  We just need to adjust and do what we can for our students.

As I have said before, the use of virtual manipulatives will probably increase in your instruction even if you are seeing students in person.  This is especially true for those manipulatives where students usually need a lot of them to do their work--like pattern blocks and base ten blocks. I recommend that you use the virtual versions some in the classroom so that students are comfortable with the websites if they should need to use them from home without your direct support.

You might also consider paper versions of some of these tools to have in students's toolkits.  Not only can you get them easily and cheaply for the classroom, but you can also send them home if you need to without the worry of losing valuable manipulatives.

You may not start the year with all of the items in the toolkits.  You might add some as students are introduced to new concepts. Here are some things you might consider putting into individual toolkits for your students:

K:
hundred grid from nrich.maths.org
number path  1-20 by Berkeley Everett
ten counters (unifix cubes?)
rekenrek
real or paper pattern blocks by Mathwire
+/- Math Flips cards (+/- 1) by Berkeley Everett
Quantity Cards from Erickson Early Math Collaborative
pair of dice

1:
hundred grid from nrich.maths.org
number path  1-20 by Berkeley Everett
twenty counters (unifix cubes ?)
rekenrek
beaded number line
small clock face paper version
real or paper pattern blocks by Mathwire
pair of dice

2:
hundred grid from nrich.maths.org
number line 1-20 by Math Salamanders
twenty counters (cm cubes?)
rekenrek
beaded number line
small clock face   paper version
play coins, dollar bills
ruler
real or paper pattern blocks by Mathwire
real or paper base ten blocks from Tim Van de Vall
+/- Math Flips cards by Berkeley Everett (Doubles/Near Doubles) (make 10 with 2 addends)                        (make 10 with 3 addends) (2 digit + 1 digit) (2 digit + 2 digit) (subtraction within 20) (subtraction within 100)                                                                       
pair of dice

3:
twenty or more counters (cm cubes?)
beaded number line
small clock face   paper version
play coins, dollar bills
ruler
10 x 10 array (laminate)
real or paper pattern blocks by Mathwire
real or paper base ten blocks from Tim Van de Vall
paper Fraction Strip  from Math Salamander (blank version)
paper Fraction Circle Pieces Page 1   Page 2  Page 3
+/- Math Flips cards by Berkeley Everett (if needed from previous grades)
 x Math Flips cards by Berkeley Everett (2s,5s, and 10s) (4s, 6s,& 8s) (3s & 6s) (9s & 4s)
pair of dice

4:
thirty-six counters (cm cubes?)
beaded number line
ruler
10 x 10 array (laminate)
real or paper pattern blocks by Mathwire
real or paper base ten blocks from Tim Van de Vall
paper Fraction Strip  from Math Salamander
paper Fraction Circle Pieces Page 1   Page 2  Page 3
+/- Math Flips cards by Berkeley Everett (if needed from previous grades)
 x Math Flips cards by Berkeley Everett
pair of dice

5:
thirty-six counters (cm cubes?)
beaded number line
ruler
real or paper pattern blocks by Mathwire
real or paper base ten blocks from Tim Van de Vall
paper Fraction strip from Math Salamander
paper Fraction Circle Pieces Page 1   Page 2  Page 3
Math Flips cards by Berkeley Everett (if needed from previous grades)
pair of dice

If you laminate many of the paper tools, students could use a dry erase marker to create representations.

What am I forgetting?




Sunday, May 17, 2020

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.






Friday, April 3, 2020

In These Uncertain Times...

The world is so unsettled now, as we try to maneuver through these scary waters. As teachers, we are doing all that we can to help our students feel safe even though we have to do this through technology. I think what unsettles everyone the most is not knowing how long this will last.  We hear different predictions and ideas every day about the length of this stay at home world.  We just want to see our students and have some closure to our school year.  However, this is not in our control either.

What is in our control is offering some normalcy to our lives and our student lives.  As we do this though, we may sometimes become overzealous and expect things from our students that they don't have the support to complete from home. Give yourself some grace.  You can't make up for the interaction that would have happened if we were in our schools. If you are meeting with your students online or giving them tasks to complete, keep it simple.  Read a book, write a letter, solve a puzzle, play a game, help fix dinner tonight...these are all appropriate assignments that keep our students and their parents from being overwhelmed by school as well as by world events.  

I hope this ends sooner rather than later.  I hope that a vaccine is found.  I know that when it is found, teachers are some of the people who helped to develop the doctor who finds the vaccine. This has always been true because teachers believe in their students. 

I also know that the entire world is holding its breath right now.  Do what you can to help your students feel safe.  Don't feel obligated to have them complete large amounts of work.  Believe in them and that they will be okay when this is over. All will be okay. 

Tuesday, March 10, 2020

Math is Visual


Our students need access to math visually as much as possible.   This can come in different ways.  Drawing, manipulatives and online components are some places to start.

I spend a lot of time in classrooms working around word problems.  One of the things I find myself constantly coming back to with students is "Think like a reader:" use schema, make predictions, infer, VISUALIZE...that is what good thinkers do.  Asking students to draw what they are seeing happening in the problem is an important step.  That drawing can be a true drawing, a number line, a tape diagram, or anything else that helps them make sense.  Are they thinking through the problem or are they just pulling the numbers and computing without making sense? 

I also use numberless word problems a lot. Numberless word problems give students the opportunity to see the problem as a story and to make sense of it without worrying about the numbers.  Once you have practiced this strategy in class, it is a strategy they can refer to independently when they come across a word problem that confuses them.

Manipulatives are important, too.  CRA instruction helps us to build the visual into the child's mind by using tools to represent the math.  This is important for all students and provides equity in instruction.

There are many websites with visual representations.  One of the best is Math Visuals.  Berkeley Everett has created a treasure trove of visuals for the K-5 classroom.  His short videos to accompany skills like counting and computing are a fabulous resource, but they are just the beginning.  He brings visual supports to understanding mathematical properties and making connections through visuals, too.  In addition, his Math Flips cards are well worth the time to cut out and use with all of your students.

Many other awesome websites exist, too, that are very visual.  Math is Visual, Fraction Talks, Same or Different, Number Talk Images, and Slow Reveal Graphs are just a few of the visual resources that may help you and your students make more sense of mathematical concepts.

Visual math is for all students.  We have to be careful not to assume they can see it in their heads.  We have to help them see it in their heads...Visuals help students to make sense.  They help students to look for patterns.  Visuals help students to answer the question, "What does the data tell us?"

In what ways can you provide your students with more visuals?  This is an important area for all of us to grow.

Thursday, February 20, 2020

Counting Connections

I love choral counting! This is confirmed every time I participate in one in a classroom.  It doesn't matter if it is a Kindergarten or 5th grade.  Choral counting gets everyone thinking--including the teacher!

One piece to choral counting that I have found to be important is the connections that can be made between different choral counts.

For example, this was an eye-opening choral count for some 2nd graders.  We began with the confidence builder of counting by 5s.  We broke it down by looking for patterns.  A lot of good talk and discussion here, but it really kicked up a notch when I challenged them to count by 5s off-decade.  We began slowly, but then the students were able to idenify patterns and get going.  We looked for patterns in this count, too, and then I pulled the two counts up side by side.  The ahas! that the students had were quite exciting!  So important for students to make these connections.

I did another one recently in a 5th grade classroom where we counted by 21s.


Students stepped up to the challenge of counting by 21s and looking for patterns.  But the real excitement came when I asked them to do another count by 2.1.  (I had copied the first count onto a clean page before we had found its patterns.) Students kind of gasped, but then I pulled up the clean screen of our previous count.  They counted by 2.1 as I added decimal points into the numbers.  When we were done, we made connections between the two counts and place value.  We also discussed what would have happened if I had asked them to count by 210.  These place value concepts were things that they "knew," but when we put it on paper, it really clicked for them!

Because I am in and out of classrooms, I did these "double-counts" in one session making the choral count a little longer than usual.  I certainly think that it would work for a teacher to do one one day and the second one the next day.  The importance is the time taken to connect the two counts, and following-up in later days with similar counts in order to help cement the counts into students' minds.

Beginning with choral counting is your first step.  Give one a try!  Once you get past that hurdle, you will feel more comfortable moving into a double-count!