Tuesday, October 25, 2016

Teaching Math With You Tube Videos: Halloween Fun

In the past few years,  I have posted some of my favorite songs and videos about shapes, counting, multiplication, coins, time, fractions, teen numbersarea and perimeter and addition facts.  I try to keep these posts up to date with the latest songs and videos I am using with my students.  They are a great way to get a little movement break while still working on important math concepts. Today I want to share with you some fun Halloween themed You Tube Videos that are a great way to review math topics while having some holiday fun and movement.  


I have several kindergarten friends this year who are still struggling with one to one correspondence, counting to 20 and recognizing single digit numbers.  The following few videos are a good way to work on these important ideas.  I like to sing along with them and work with them to make up finger plays or dances to go with them.  

First Grade

I love the 10 in the bed rhyme for working on combinations of 10 and basic subtraction ideas.  This is a fun Halloween version of the classic song. 

Another great basic subtraction song/video!

Can you tell my first graders are working on subtraction?  This isn't a Halloween song per say but it is all about pirates (and subtraction!) so it fits in well with out theme!

Do you have a favorite Halloween song/video for teaching kids about math?  Tell us about it in the comments below!

Sunday, July 31, 2016

Back To School Math Tips: Organizing Online Resources

It's time!  Teachers all over the country are thinking about back to school.  Whether you are going back to school this week, next week or not until the end of the month, I am sure your mind is on back to school.  My math blogger friends and I have teamed up to bring you our best tips for back to school.  Check out my tips below for organizing your online resources, enter my giveaway and be sure to check out the other back to school tips.

Organizing Online Resources

I love starting the new school year with everything organized and ready to go.  It is the time of the year that I feel like I have everything in its place.  I am a math teacher who uses many games for practice and for differentiation so naturally I have a lot bins full of manipulatives, game pieces, card decks and dice.  As the years have progressed and online math games have developed, I have added them to my repertoire but have always struggled with how to keep these resources organized in a way that made them easy for my students to find.  For every good math resource available online, there are 3 bad ones and I really wanted a place to organize the good resources for each unit where my students could find them. 

At the beginning of last school year, I decided to get my online math resources organized in a way that made them easy for my students (and me!) to find and use at school and at home.  I decided to create a classroom blog that linked to all my favorite online resources.  I went with a blogger blog because it is easy to use and my school already uses google email and other products.  It is super easy (and free!) to set up a blogger blog.  

Because I teach multiple grades, I decided to create a page on my blog for each one.  On the home page, I added a little welcome message and directed students to click on the tab for their grade across the top of the page. I work with 7 grades but decided to start with 4 grades for the first year.  If you are a classroom teacher, you can create a page for each content area.  If you want to start small, just create one page for one subject and add more as you get comfortable. 

When kids clicked on their grade, they were taken to a page that had resources on it that went with their current unit of study.  They were a mixture of online games, you tube songs and math literature book read alouds.  It takes just a few minutes to learn how to add links and embed you tube videos in your blog posts.  

Here is an example of what was on the grade 2 page when we were working on telling time

Having my favorite online resources in one place where kids could access them from home or school was fantastic.  I probably spent less than 15 minutes a week keeping my pages up to date with what we were working on.  If you are new to blogging, it will definitely take you longer when you start out but it is certainly a skill worth learning.  Having your favorite online resources organized when the school year starts will certainly help to make this the best year ever!  If you have other tips for keeping online resources organized, be sure to share them in the comments below!

The TPT Back to school sale will take place Monday and Tuesday August 1st & 2nd!  All of my resources will be 28% off with the code BESTYEAR.

Want some extra money to spend during the back to school sale? Enter the giveaway below.  I will choose a winner early Tuesday morning and email the gift card to the winner so they will have it to spend during day 2 of the sale!  

a Rafflecopter giveaway

Check out some other great back to school math tips!

Wednesday, June 22, 2016

Memorizing Facts Versus Knowing Facts From Memory

I used to think one of the most important things I did with my fourth graders was to make sure they were fluent with their multiplication and division facts.  My definition of fluency was synonymous with fast.  To me fast = fluent.  To ensure my students all had "fluency" with their multiplication and division facts, we had daily timed tests which some kids loved and others dreaded.  We used a boxed program that was on my self when I started teaching.  

As much as I thought I was doing the right thing, there were a few things that bothered me about this process.  There were a few kids who were very proficient mathematicians who just were not doing well with these timed tests.  I also had some kids who were doing really well with the timed tests yet they were really struggling to multiply larger numbers.  

After more and more of these concerns popped up over several years, I started doing some more research into what exactly fluency meant.  I stumbled upon the work of Catherine Fosont and read her Young Mathematicians at Work series.  I learned about models for multiplication, using equal groups, arrays and the open area model.  I learned about helping kids develop strategies for multiplication facts.  Strategies based in understanding and the properties of multiplication. Strategies that will help kids develop number sense.  

I still focus on fluency with multiplication facts in fourth grade but fluency has a completely different meaning to me now.  The way I work on fluency now does not involve timed tests.  It does not involve kids being anxious or feeling unsuccessful at math.  Instead I focus on developing number sense which helps kids learn and remember strategies that make them fluent with their multiplication facts.  To the untrained eye, it often appears as if my fourth graders have memorized their facts when they actually know their facts from memory. 

This short video does a great job of explaining the difference I am talking about:

How do you think about or teach fact fluency? Please share your ideas in the comments below! 

Saturday, April 30, 2016

Math Workshop:Sharing & Reflection

Welcome to the final week of our Minds on Mathematics book study.  If you missed them you can go back and read Understanding Takes Time,  Shallow Versus Deep MathStarting Class and Mini Lessons & Work Time.  

This week are going to take a deeper look at ending class with sharing and reflecting when using a math workshop model.  


Perhaps the most important part of a math workshop model is the time for students to share.  It is so important to stop work time before the end of your math class period and give kids a chance to share.  This is the part that helps to solidify their comprehension and gives them a chance to practice metacognition which is thinking about their own thinking.  They get a chance to synthesize their understanding, check on their progress and make goals for the next day.  Teachers can gather important formative assessment data about what strategies kids are using and where to go next.  By communicating their thinking and listening to a variety of peers' solutions and ideas, students make connections and deepen their own thinking.  

My favorite way to structure sharing time is by bringing the whole group back together.  As I have been circulating during work time, I choose a few pairs to share their thinking.  I pick pairs who have different strategies and ideas to share.  Then I have students present their work while classmates ask questions or make connections.  When multiple groups present different ideas, we take some time to synthesize the learning and talk about which strategies were most efficient.  To add some variety to our days, I sometimes will mix the pairs up and have them share with another person or another pair.  With clear expectations and a lot of practice, my students have become more efficient at this portion of math workshop and it is easier for me to fit it all in to one class period.  In the rare case where work time extends beyond where I intended, we will start the next days class with sharing time.  


I love how kids can learn from each other during sharing, but I also love how kids can learn from themselves during reflection.  This is usually a quick but important part of math workshop.  I don't get to this every single day but at least a few times per week.  On any given day, we might reflect on behavior, or our skills as mathematicians, or what we have learned, or the process of solving problems.  We never do all of these at once, we usually just choose one.

The reflection I enjoy the most is the time at the end of a unit or a semester or school year when we have time to look a little more in depth at progress.  This is often when we will do some writing or comparing work from the beginning and end of a unit.  This is the deep reflection that makes all of my students feel like they are really learning.  It really helps to make their learning personal.  It also really helps with setting goals in an authentic way.

I love the reflection prompts printed on pages 162 & 163 in the book.  I think these would be well worth posting in my classroom to help us bring our reflecting to the next level.  I don't often do quick written reflections but with the questions and sentence frames presented here, I think I could get some valuable information from my students without adding a lot of time or stress to our day.

Thanks for following along as I read this great book!  Please share your thoughts about sharing and reflecting in the comments below!

Saturday, April 23, 2016

Math Workshop: Mini-Lessons and Worktime

Welcome to week 4 of our Minds on Mathematics book study.  If you missed them you can go back and read Understanding Takes Time and Shallow Versus Deep Math or Starting Class

This week are going to take a deeper look at the mini-lesson portion of math workshop and talk about what work time looks and sounds like. 


Mini-lessons during math workshop should be
- Short and focused (under 10 minutes)
- Whole group instruction
- Goal is fostering independence

"The more I explained the less my students seemed to understand.  The more sample problems I did for them, the sleepier they appeared." (Hoffer page 103)

This quote from the book perfectly sums up my past experience with teaching rather than listening. As I have shifted my practice from that of an expert giving out knowledge to that of a facilitator helping kids build their knowledge, this quote is no longer true.  Many of the ideas presented in this chapter were ones that I have been comfortable with for the past few years.  My mini-lessons look a lot like these.  As I read, I kept coming back to modeling thinking as something I really wanted to work on. 

My Own Experience with Modeling Thinking

 I immediately thought of my second graders and solving multi-step problems.  We are finishing the year up with more practice adding and subtracting 2 and 3 digit numbers and I wanted them to get the chance to practice these important skills while working on solving problems that involve more than one step.  I find that with second graders, story problems can be tricky because there are a lot of words on the page for those who are struggling readers.  I decided to use modeling thinking to help these kids out with multi-step problems.
In the spirit of keeping my mini-lesson mini, I presented one problem to students.  It was: Jonathan had 172 baseball cards.  He spilled his drink on part of his collection and had to throw away 58 of his cards.  For his birthday, his friends decided to surprise him with 75 new cards.  How many baseball cards does Jonathan have now?
I put the problem on the screen and had a student read the entire thing.  I then thought aloud about how overwhelmed I was with trying to figure out what happened to Jonathan and what I was supposed to do.  I decided aloud to tackle the problem one sentence at a time and to stop and think after reading each sentence.  I switched to a new slide on my screen that had one line come up at a time.  After reading each line, I stopped and thought aloud about what I knew.  I would then reveal the next line and repeat.  I did much of the thinking aloud but also had some students contribute to my think aloud.
When the problem was solved, kids shared what I did to make a challenging problem easier.  Then I sent them to work with a partner on 2 additional multi-step problems involving some combination of addition and subtraction.  They did an amazing job and really focused on what strategies made it easier. They finished by writing their own multi-step problems. Tomorrow I will start class with a think aloud on one of their problems and then they will pair up again and solve another few examples.  

Work Time

The postulate and question of the day at the beginning of this chapter really helped me think through the big ideas about work time.

How can we facilitate thoughtful and productive work time for math learners?" 
Facilitating thoughtful and productive work time for math learners is something I have worked hard at developing over the past five years.  I think this is a strength in my classroom and in my school.  My challenge for next school year will be to make this thoughtful and productive work time work in a multi-age setting.  With our declining enrollment over the past few years, we have had multi-age classrooms but have been separating kids by grade for math class.  Next school year it is my goal to work with teachers to build capacity for truly multi-aging.  I think it will be a fun challenge to see how we can structure thoughtful and productive work time for such a diverse group of math learners.  
"Students learn most when they spend math work time thinking, talking, and making meaning of mathematics for themselves."
This quote sums up my teaching philosophy in one neat sentence.  To me, this is where the fun and the learning of mathematics takes place.  I know in my own education the math classes where I did the most talking were also the ones I did the most thinking and the ones where I finally had a chance to construct the meaning of mathematics for myself.  This nicely summarizes the constructivist ideas around learning and is what I strive to do each and every day in my classroom.  
"pages of mindless computation do not foster the construction of new knowledge. Learners need the opportunity to collect, generate, and frame their own problems and inquiries. The learner must be in the drivers seat." (Hoffer, p. 116)
This used to be so challenging for me.  I was very afraid that giving up the drivers seat meant giving up control of the situation and of my class.  It took years of seeing how other teachers managed their classrooms and employing the best management strategies before I was able to step back and really let my students be in charge of their own learning.  It is my goal to give the illusion of the classroom running itself.  I have high expectations for behavior and being on task and I am not afraid to spend the extra time making sure the backbone of classroom management is there.  Without excellent management skills, you can never be an excellent math teacher.  

Join us next week for the final installment of the Minds on Mathematics Book Study! 

Saturday, April 16, 2016

Math Workshop: Starting Class

Welcome to week 3 of our Minds on Mathematics book study.  If you missed them you can go back and read Understanding Takes Time and Shallow Versus Deep Math.  

This week are going to look at how to start a day of math workshop.

The Opening

The first part of math workshop is the opening.  This is a time to invite learners to make connections and establish purpose.  The book outlines 4 parts to a successful math workshop opening.

Welcome Learners

If you are teaching a self contained classroom, this is your chance to make a transition to math class.   You might play a math song, check out a math you tube video, have kids share a favorite memory of math class or have some way to get kids pumped up that math is about to start.  If your students switch rooms for math and this is the first time you are seeing those students that day, this is your chance to greet kids at the door and work on making those connections with students.  It is your chance to work on developing community.  

 Activate Prior Knowledge with an Opening Exercise

What do your students already know that can help them with the day's problems?  How can you ask questions in such a way that students are engaged and feeling capable?  You are trying to convey that students already know some thing that can help them and that they are capable of being successful mathematicians.  "Offer students problems that invite challenge by choice; Let the first question be something everyone will likely know, followed by questions of increasing complexity that may feed into one one another, reminding learners of the concepts behind the mathematics."  I love how the book presents these tiered openings and it is definitely one of my goals to be more intentional with choosing questions like these for my openings. 

The other way to activate student knowledge is by having them consider a concept.  They might write everything they know about division or provide examples of vocabulary words that are likely to come up during the day's problem.  

My struggle with the opening of math class is always making sure it doesn't take more time than I allotted or take over the class entirely.  This is something I am still working on.  

Learners Setting Purpose for this Lesson

This is more than just writing your learning target on the board and having students read it.  It is about having students set goals for themselves.  What are they good at? What do they need to work on?  It might involve the topic for the day such as fraction division or it might involved one of the math practices such as attending to precision

Managing Homework

I have stuck to my resolution this year and not given any homework.  This is a decision I am quite happy with and have no plans to return to giving homework.  If you do give homework and want to work it into your opening, the author offers several suggestions.  

Your turn!  How do you open your math class each day?  What are the essential components for you?  How do you make sure your opening doesn't take over the entire class?  Please respond in the comments below.

Join us next week as we look at the mini lesson and work time in our Minds on Mathematics book study.  

Saturday, April 9, 2016

Shallow Versus Deep Math

Welcome to our second week of looking closely at math workshop.  Get more details about my math workshop book study here.  

Deep Versus Shallow Math

In this week's reading, I was struck by the difference between deep and shallow math.  Here are some characteristics of each type of math.

Shallow Math

- Memorizing algorithms
- Applying an algorithm (usually a word problem found on the bottom of a page full of practice for that algorithm.
- Hunt & copy exercises
- Plug and chug numbers
- Not considering what the numbers mean
- About covering the content
- Teacher gives out knowledge

Deep Math

- Engaging, exciting, exhausting & inspiring
- Pushes learners out of their comfort zone
- Mental models
- An understanding of a concept that can be built upon later
- Discourse
- Challenging tasks
- Students wrestling to make sense
- Content understanding
- Teacher as a facilitator of learning

When I was in elementary and middle school 99% of the math I did would be classified as shallow math.  I was the queen of the plug and chug.  I thrived on algorithms and hated "word problems".  When I was in high school, it was more of the same until I got to Algebra 2 and was faced with new and challenging problems that no one had "taught" me how to solve.  This took my enthusiasm for and understanding of math to an entirely new level.  Math class became exciting and invigorating and for the first time I got to invent my own strategies for solving problems and compare them to my classmates.  It was such a dramatic and marked change for me that it really is what sparked my interest in becoming a teacher.

Now when I teach math, I try my best to keep most of what I do with my students at the deep level.  Math workshop provides me with a vehicle for giving kids support solving challenging tasks.  

Your turn!  Can you think of anything that is missing from these lists of shallow and deep math?  Where did most of your own learning take place? Please respond in the comments below!

Come back next week for part 3 of our Minds on Mathematics book study!