Saturday, March 25, 2017

The National Math Festival

Recently, I received an email letting me know about the National Math Festival.  This is an event I had never heard of before so I quickly went to check out their website and was amazed at what I found there!

The National Math Festival brings together some of the most fascinating mathematicians of our time  to inspire and challenge participants to see math in new and exciting ways. Through a day of lectures, hands-on demonstrations, art, films, performances, puzzles, games, children’s book readings, and more, everyone from toddlers to teens and adults can experience the unexpected sides of mathematics. The National Math Festival is free and open to the public from 10:00 a.m. till 7:00 p.m. on Saturday, April 22, 2017 at the Walter E. Washington Convention Center in Washington, D.C. Those outside the D.C. area can join in via events at dozens of science museums around the U.S. or explore math games, puzzles, books, and other resources available online. For more information check out their full website!

I would love to head to Washington, D.C. this spring to attend but already have plans for that week(I am on spring break!). It is definitely something I would love to bring my entire family to in the future.  If you can't attend, be sure to check out their More Math resources! I found a few new resources there that my students are going to love!  Be prepared to spend a few hours digging through websites!




Friday, March 10, 2017

Assessment for a Growth Mindset

This week we are wrapping up our Mathematical Mindsets book study.  I have loved reading this book and going deeper into the big ideas in my classroom.  If you are just joining us, be sure to check out part 1, part 2 and part 3

Chapter 8: Assessment for a Growth Mindset

Big Ideas

-Teachers are being asked to test and to grade students to a damaging degree
-Often what is easy to test is being assessed rather than valuable mathematics knowledge
-It is common to start a math class with a pre-test to determine what students know.  This gives students a message that math is about performance. 
-Research has shown that test scores demotivate students and convey a fixed messages that result in lower achievement
-Boaler recommends assessing less
-Use more formative assessment 

Impact in the Classroom

Test Less

I am happy to get on board with this one.  We use standards based grading on our report cards so I don't have to worry about giving a percent score.  This naturally reduces the amount of assessing and grading that I have to do.  I never put a grade on classwork or formative assessment prompts. I do grade unit assessments and such but often do not share the percent grade with students.  I have to collect some percent grades currently mostly used during IEP evaluation processes.  I have not yet figured out a way to convince the special educators that a kid is in the lowest 15% of the class without some percentages.  I would be happy to never put a percent grade on anything again and would love to work toward this goal

More Formative Assessment

When I was in graduate school, I read Assessment for Learning and started using many formative assessment strategies.   The following school year, I got even further into formative assessment ideas when all of the teachers in my school had the opportunity to take a formative assessment course together during in-service time.  Reading this chapter brought back a few ideas that we had great success with in our school but have sort of fallen out of practice.  After reading this chapter, I led a staff meeting about formative assessment strategies to remind us all of some of our forgotten favorites.  We also got to have a good discussion about how the assessment practices in our district have shifted and what we have had to give up as a result.

Screeners and MTSS

Since starting our formal work as an MTSS (Multi-Tiered System of Supports) school two years ago, we are doing much more formal testing.  These tests are given 3 times per year and are meant to be screeners to see who is not meeting standards in math and reading.  I work in a small school where I literally know all of the students very well and many of them I work with for 7 years.  I do not need more assessments to tell me who needs help in what area.  These additional assessments have added more to our students' and teachers' plates and seemed to have pushed some of our formative assessment strategies out.  I am really struggling with how MTSS systems effect math mindset and will be having some discussions with other folks in my district about these ideas.

Chapter 9: Teaching Mathematics for a Growth Mindset

Big Ideas

-It is important to set up classroom norms based on research.  Here is the printable poster with the big ideas from Youcubed. 
-Teaching kids how to work in groups is an important step.  Designing Groupwork is an excellent reference to get you started.
-Believe in all of your students and make sure they know you believe in them
-Value persistence and hard thinking instead of speed
-Change praise!  Here is a great list of suggestions.
-Choose tasks with a low floor and a high ceiling!

Impact in the Classroom

The Participation Quiz

What an awesome strategy for encouraging group work!  I am a bit ashamed to admit that I learned this strategy from my mentor teaching when I was student teaching but somewhere along the way I lost it from my repertoire.  Bringing it back to the classroom was just the jolt we needed to re-invigorate our group work.  It is an amazing way to motivate students and share all the skills you value.  

Low Floor, High Ceiling Tasks

Many of the math tasks in this chapter I have tried out with my students over the past two weeks.  It is amazing how much mileage I have gotten out of some of these tasks and how much it has helped move some of my multi-age groups forward.  Another resource for these types of problems that I stumbled upon this week and then spent way to many hours there is Math Pickle. It is an amazing website full of great math problems, puzzles, games and ideas about how to bring unsolved math problems into K-12 classrooms.  

Thanks for following along on this book study!  This book is such a wealth of information.  I am considering doing another book study this spring around Designing Groupwork.  I will let you know the details when I work them out! 



Friday, March 3, 2017

Mathematics and the Path to Equity


Welcome to week 3 of our Mathematical Mindsets book study! If you are just joining us, be sure to check out our launch, The Power of Mistakes and Struggle and Creating Mathematical Mindsets

Chapter 6: Mathematics and the Path to Equity

Big Ideas

-The myth of the mathematically gifted child: This section reminded me of my own math story
- All students should have access to high-level content
-Try to change ideas about who can do well in math
- Make sure students have opportunities to think deeply about math
- Importance of group work
- Eliminate homework
- Encourage minorities 


Impact in the Classroom 

 Eliminating Homework 

The strategy that resonated the most with me is the elimination of homework.  Last school year, I made the decision to stop assigning math homework altogether and it has been great.  The kids who were the most likely to do the homework were the ones who needed it the least.  Having parents and caretakers "help" with homework was leading to procedures I wasn't ready to embrace in the classroom along with negative feelings about math.  I was spending more class time assigning and collecting homework than kids were spending doing it.  Now, I assign no homework.  I do have a class blog that is a curated list of online activities that go along with what we are learning in class.  Families can access this at home if they wish but it is certainly not a requirement.  I also use a lot of games/centers in my classroom and sometimes kids will love a particular game and want to share it with their families.  I let students who wish to take games home to play with family members do this.  I also occasionally will have a student who wants more practice with a particular skill and will ask for something extra.  I indulge this desire.  Since eliminating homework in my classroom, things seem much more equitable and students, parents and myself all seem happier.  I have not noticed a lack of understanding or that we are farther behind than in years past.

Working in Groups 

Another strategy that really resonated with my was teaching students to work together.  In the times that I was most challenged by my math classes, I had a group that I could turn to for help.  I remember spending 6 hours every Thursday night in our University library working on problem sets together.  This gave me the confidence I needed because I could see others were struggling also and because I was able to construct my knowledge with others.  When I was student teaching, my mentor teacher had me read Designing Groupwork which led to a great system for making sure my students work together.  It isn't always perfect and sometimes group work can be a challenge but it is such an important part of my math lessons.

Offering High Level Content to All Students 

The strategy I envision being the most difficult to implement is definitely offering all students high-level content. I think we have done this in our elementary school but I imagine it would be harder and harder to do as students get older and the gap between students widens.  Our school district currently offers accelerated math beginning in grade 7.  I have always been on the fence about whether this is a good idea and this chapter got me thinking that maybe it isn't. 


Chapter 7: From Tracking to Growth Mindset Grouping 

Big Ideas 

-When students are offered high level content they achieve at higher levels
- "We can give no stronger fixed mindset message to students than we do by putting them into groups determined by their current achievement and teaching them accordingly." 
- The importance of providing open ended tasks
- Complex Instruction
-Valuing different types of skills

Impact in the Classroom

Re-Thinking Tracking

Over the past few years, our school has moved completely away from grouping kids for math based on skills.  We teach heterogeneous groups for each grade level and have even moved to teaching some multi-age math groups.  The only exception has been kids who are more than two years behind in math.  These kids are often pulled out of their math class and offered math in a different setting by a special educator.  I would be interested to hear more about folks' opinions on how far behind is to far behind to group heterogeneously. 

More Low Floor, High Ceiling Tasks

When I provide my students with open ended tasks, they are more engaged and invested in their learning.  I feel great about my teaching.  I think I need to do more of these types of tasks but I am still working on juggling doing these tasks with number talks and all of the other things I am expected to do or think work really great for my students.  I will be thinking more about this.

What did you think about this week's reading?!  Please respond in the comments below! 




Tuesday, February 28, 2017

#FractionsFebruary Blog Tour

I am finishing out the #FractionsFebruary blog tour put on by Math Solutions.  I had the privilege of interviewing Julie McNamara, author of Beyond Pizzas & Pies and Beyond Invert & Multiply.  I love reading about teaching fractions and always feel like there is more I can learn.  I read both of these books about a year and a half ago and they brought great changes to my teaching practice, especially the idea of using cuisenaire rods in my fraction lessons.  Beyond Pizzas and Pies is great for grades 3-5 and Beyond Invert and Multiply is great for grades 4-6.  If you teach 4th or 5th grade, I highly recommend you read both of these books! 

What is the most exciting piece of research on teaching fractions that has come out over the last 10 years?

Siegler, Thompson, and Schneider’s (2011) work highlighting the importance of students’
understanding of fraction magnitude provides much needed insight into the importance of the
number line. They found that students who had a good understanding of fraction magnitude (as
evidenced by their ability to accurately place fractions on a number line and to accurately compare
two fractions) were also more successful with problems involving fraction computation. Siegler,
Thompson, and Schneider suggest that the extension of students’ “mental number line” to include
rational numbers is an essential aspect of numerical development - what I refer to as number sense
and fraction sense.

What do you feel is the biggest misconception students have about fractions? 

This is a tough one but one big misconception is that fractions are always considered in terms of
food (pizzas, pies, brownies, etc.) and that fractions are not numbers.

What can teachers do to help students overcome this misconception?

One thing teachers can do is to build on students’ early work on partitioning areas, with explicit
attention to the importance of equal partitioning, and connect this to linear measurement models.
Contexts are very beneficial, especially ones that can be considered on a number line like time and
distance. One of the reasons I use Cuisenaire Rods so much in my work is that they are concrete
enough for students to manipulate and they can be used as bridges to work with number lines.

What was the most surprising thing you learned in the process of writing your books?

I found that I really liked the process and that I LOVE thinking about fraction division.

If you were to go back into the classroom as a teacher, what grade would you choose to teach and why?


This is another tough one. I really love fourth grade, as there are so many opportunities to help
students begin to think abstractly. I also love middle school because there are so many connections
back to the mathematics of elementary school that students are often hesitant to consider. They
don’t know how much they know! One of the best parts of my position at the university is that I have
many opportunities to go into classrooms and work with students in local schools.

You can read the rest of Julie's interview over at the Math Solutions Blog!

Want to win a copy of these books?! Enter the giveaway below

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Friday, February 24, 2017

Creating Mathematical Mindsets


Welcome to week 2 of our Mathematical Mindsets book study! Last week, we looked at the latest in brain research and talked about the importance of mistakes and struggle.  

Chapter 3: The Creativity and Beauty in Mathematics

Big Ideas

- Math gets treated differently than other subjects.  It is much more of a performance subject than any other.
-There is a big gap between real world mathematics and school mathematics
- Students (and the public in general) see math as calculations, rules and procedures rather than creative and beautiful.  

Impact in the Classroom

Fibonacci Numbers and the Golden Ratio

One of the examples given in this chapter was about taking a look at the Fibonacci numbers and the golden ratio with kids.  I have always loved this series of numbers and many years ago was given a copy of Fascinating Fibonaccis which I have now used many times to talk with kids about Fibonacci numbers.  I also love the picture book Rabbits Rabbits Everywhere by Ann McCallum who also wrote Eat your Math Homework.  One more excellent resource is this blog, Fabulous Fibonacci Fun where you can find more background information as well as a great collection of images that illustrate the golden ratio in nature. 

Let Students pose Their own Questions 

Real mathematicians pose and answer questions all the time.  One of the best ways to get our students doing this is to let them have the chance.  Give them mathematical tools or situations and let them come up with questions.  Let them work to find answers to their questions.  This is something I have had some opportunity to do this year in the context of our school wide genius hour.  It is definitely something I hope to do more of in the future.

Chapter 4: Creating Mathematical Mindsets: The Importance of Flexibility with Numbers

Big Ideas

-Kids intuitive joy of math is quickly replaced with learning procedures & rules
-Students need to see math as a conceptual, growth oriented subject.  They should see math as a place to think, not to blindly operate on numbers.

Impact in the Classroom

Number Talks

The single best way I have found to develop a sense of numeracy in kids of all ages is number talks.  Doing number talks with my students has been a total game changer in my students' ability to think about numbers, develop strategies and learn to talk about their thinking.  It is a structured way to spend 10 minutes each day that will give you big results.  If you teach K-4, start with this book, and if you teach grade 5 and up check out this one.  If you have been using number talks in your classroom and are ready to up your game, there is a new number talks book all about Fractions & Decimals. I have dug into this one over the past 2 months and it has really helped move my practice forward and increased my students' understanding of fractions and decimals. 


Hold off on Formal Procedures

When do you "teach" kids the traditional algorithms for adding, subtracting, multiplying and dividing?  Holding off on these formal procedures can really help kids see math as a growth oriented subject where they can develop their own conceptual understanding and design their own strategies to solve problems.  If you are using number talks, you will be amazed at what kids of efficient strategies your students can come up with on their own.  In my school, we have agreed not to introduce the traditional algorithm for addition and subtraction until grade 4.  We hold off on the traditional algorithm for multiplication until the end of grade 5 and division until grade 6.

Go for Depth, Not Speed

Value deep thinking over fast thinking in your classroom. Whenever I talk about not focusing on speed, the issue of math facts comes up.  I think to much emphasis is put on memorization when kids should really be working on knowing facts from memory.  For much more about facts, check out this post

Chapter 5: Rich Mathematical Tasks

Big Ideas

-5 c's of engagement: curiosity, connection making, challenge, creativity, collaboration
-5 ways for teachers to open math tasks and increase potential for learning.  
    1. Open the task so there are multiple methods, pathways and representations
    2. Include inquiry opportunities
    3. Ask the problem before teaching the method
    4. Add a visual component and ask students how they see the math
    5. Ask students to convince and reason; be skeptical

Impact in the Classroom

Rich mathematical tasks are such a good way to generate engagement and enthusiasm in your classroom.  Providing kids with low floor, high ceiling tasks are a great way to get big math ideas, work on perseverance and get kids excited about math. After reading this chapter, I decided to try a little experiment with a very engaging, very open ended task, the 1 to 10 card investigation. If you have never heard of this investigation, head here to check out a 1 minute video. 

I presented the original investigation to a group of first graders who are always looking for a challenge, all of my second graders, the entire 5th and 6th grade classes and a large group of teachers during a PD day. All of these folks were able to access this problem.  The excitement and engagement were just as high with adults solving this problem as it was with first graders.  

Students work together using 20 frame playing cards to solve the problem to 15. 
The best part of this problem was that there really is no end to it.  After folks solved the 1 to 10 card problem, all kinds of extensions were proposed and worked on.  Some kids increased the number of cards while others proposed different arrangements of the cards such as what if we flip one over and then put 2 on the bottom.  Kids challenged each other and me to go further with this problem.  One of my sixth graders must have spent 20 hours on this problem over the last week and was able to generalize a pattern that would work for any number of cards.  Kids asked to take cards home and challenge their families.  Teachers who worked on this problem during PD literally could not stop working on it. 

A student uses cards from my place value to 120 deck to work on solving the problem with 50 cards
 Your turn!  What did you think about this week's reading? What changes are you making or thinking of making in your classroom?  Please respond in the comments below!



Friday, February 17, 2017

The Power of Mistakes and Struggle

Welcome to week 1 of our book study of Mathematical Mindsets

Chapter 1: The Brain and Mathematics Learning

Big Ideas

-Folks who have a fixed mindset can develop a growth mindset.  Their learning approach can become much more positive and successful.
-The students who show the highest achievement in mathematics around the world have a growth mindset.  This can put them a full year ahead of other students. 
-Folks with a growth mindset are more likely to do something perceived as hard. They see mistakes as a way to grow their brain and motivation to keep going.
-Fixed mindsets can develop as a result of praise given by parents and teachers

Impact in the Classroom

Teach kids about brain research.  

Research about the brain and growth mindset has come a long way over the last few years.  I have found Jo Boaler's Week of Insiprational Math to be a fantastic (and free!) way to show kids about how the brain works and get them excited about math.  We started our school year with the week of inspirational math in grades 3-6 and have recently re-watched some of the videos included in the lessons to refresh ourselves on brain research.  We have plans to do a week of inspirational math in our K-2 classes in the near future.  
     Another excellent resource for helping your students understand brain research is a series of short cartoon videos produced by Class Dojo. Recently, we started k/1 math each day with one of these videos which led to some great conversations about how the brain works.  Even if you don't use Class Dojo, these videos are a great resource!  It looks like you can check out the first one on YouTube and the rest are available on their site.  It is free to use and only takes a minute to sign up.




 Change praise

 Praise from teachers can help kids develop a fixed or a growth mindset, it all comes down to the type of praise they receive. Praise has such a strong impact, it can affect their behavior right away.  The praise kids receive in the classroom needs to switch from  you are so smart to you are working really hard. This has been a challenging switch for me because despite good intentions, it is so easy to fall back on the old reliable praise.  Like most things, it is something teachers need to practice.  We spent some time at a staff meeting brainstorming different things that fit into the category of praise and then classifying it as praise that would develop a growth or a fixed mindset.  This is an area where it is so important for kids to get a consistent message and it is definitely worth discussing as an entire staff.  A colleague also shared this Growth Mindset poster with us and posted it in several prominent teacher areas. It has been a helpful reminder and has continued the discussion about changing our praise.

Educate Families

If students are really going to change their mindset than both teachers and parents need to be aware of this research and have practical strategies to help them.  Since our entire school has been working on kids developing a growth mindset, we have communicated with families in several ways.  We started the year by showing a few of the videos from the Week of Inspirational Math at our back to school open house.  This was after we had used these videos with kids so many families had already heard parts and pieces of this.  We also use our school wide newsletter to communicate what we are doing and share growth mindset tips.  The topic has also come up during parent teacher conferences, especially with those kids who need the most work on their mindset.  We have also shared this great little parent handout with families.   It is still a work in progress to educate families about growth mindset but we have made a start and are now developing a common language for kids at school and at home.  

Chapter 2: The Power of Mistakes and Struggle 


Big Ideas

- Mistakes grow student's brains
- When a student makes a mistake, there is increased electrical activity in their brain.  
- Even if you don't know that you made a mistake, it still grows your brain
- After a mistake, brain activity is greater for those who have a growth mindset rather than a fixed one. 
- Successful people are the ones who make more mistakes than non-successful people

Impact in the Classroom

Give students the chance to make mistakes

Giving students a chance to make mistakes is one of the best things you can do to develop their understanding of mathematics.  If they make no mistakes day after day, then the math you are giving them is not challenging enough.  Kids come to believe that being smart means getting the answer right on the first try and with a bit of speed.  I love this video from the Teaching Channel where Carol Dweck author of Mindset: The New Psychology of Success talks about personalized learning and how important it is for kids to make mistakes. 

Teach students that mistakes are positive

I am a big fan of this routine called My Favorite No.  I do a lot of formative assessment in my classroom and doing My Favorite No is a great way to directly address misconceptions with the class.

A few weeks ago, I found these growth mindset posters and put them up on a bulletin board.  In my fifth grade class, I have many kids struggling with growth mindset so I decided to really use these posters with them.  I decided to have them place a sticker on the poster each time they used the "think" bubble.  It struck us very quickly that we make mistakes all the time.  The mistake poster became full of stickers while the others just had a few.  This has been a great way to show how common mistakes are and how important they are to learning.

Test and Grade Less

Our school uses standards based grading for our report cards which means I test and grade a lot less than I used to.  However, there still are times when folks want percent grades, particularly for Special Education Evaluations.  We also have added several "screeners" and other forms of testing as we have moved toward an MTSS model in our district.  I do a lot of formative assessments so I have a really good handle on where kids are.  I am on board with less grading and testing but I am not sure my school/district is ready to change much more in that direction right now.  I am excited that chapter 8 is all about assessment and hope to be able to try some new ideas.

Your turn!  In the comments below, let us know what you thought of these 2 chapters.  If you have a blog and want to post there, just share the link in the comments below. Haven't read the chapters?  Share your ideas about mistakes, struggle, brain research or anything else related to growth mindset!  I look forward to some great discussions! 

Monday, February 6, 2017

Math Love, A Giveaway, A Sale, Book Study Update & More

First Grade Number Puzzles

Book Study Update

Our new book study is getting a great response!  We will be discussing Mathematical Mindsets by Jo Boaler.  This book has the potential to make a great impact in  your classroom regardless of what grade you teach.  It is also super affordable and ships for free if you have Amazon Prime. Get all the book study details here.  

A Sale

Also in the news this morning, Teachers Pay Teachers site wide sale starts tomorrow!  You can save 28% off all of my resources with the code LoveTPT.  I have been window shopping already and currently have 18 items in my cart.  There is nothing like a good sale!

I have been so inspired by my K/1 math group over the last month and have been super busy creating resources to use with them.  I have quite the range of abilities in this group and routinely need to create stuff that spans the K-2 spectrum for these guys.  I am loving teaching math in a multi-age setting and will have more to share about how we structure this very soon.

Math Love

Lots of new Valentine/heart themed math centers for K-2 classrooms!
Counting Puzzle Bundle
Valentine Ten Frames Playing Cards & Activity Set

Teen Number Math Craft
Addition Facts Craft

Kindergarten Number Puzzles
https://www.teacherspayteachers.com/Product/Heart-Number-Puzzles-Second-Grade-3000045
Second Grade Number Puzzles

Math Love Giveaway! 

Thanks for all the love you show me all year long!  Enter below for your chance to win a $10 TPT gift card!  I will send it to the winner before the end of the TPT site wide sale on Wednesday so they can use it during the sale if they wish.

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