Friday, November 3, 2017

Let's Talk About Multiplication Fact Fluency

Earlier this week, I shared this post about memorizing facts versus knowing facts from memory. In this post, I talk about how I used to think timing kids daily on multiplication facts was the backbone of my fourth grade curriculum and how my perspective has shifted over time to one where I believe kids should know their facts from memory rather than through memorization.  If you are not familiar with this idea, here is a video where Graham Fletcher explains it better than I ever could.

After re-sharing this post from last summer on my Facebook page, I received the following comment from Michelle:

"While I agree that strategy is the way to go (it's the only way we teach math facts), I'm second guessing myself when it takes 15 mins to work through a 2-digit x 2-digit multiplication problem bc every 'part' (when using partial products for example) has to be worked out using a fact strategy when kids don't know their facts well. It takes soooo long. I'm so proud when my intervention students get the correct answer but it might take 40 mins to do 3 problems and I start to second guess myself-should I be drilling them more often. I know that they know AND can discuss the fact strategies they used as they go, but I sometimes wonder when is the leap to automaticity going to come. Maybe I need to just be more patient? I'm speaking of intervention students that are seen multiple times per week. Taught the multiplication strategies last year, didn't retain the strategies over the summer, now reteaching but feeling stagnant...guess I'm just having trouble bridging the gap b/t them knowing the various strategies and automaticity. I am supposed to be teaching division to one of them but it is so so difficult when they don't know their mult. facts. This student can complete problems correctly using 100 bead number line or draw a picture and circle groups (divisor) but w/o that are completely unable to make an educated guess bc multiplication facts are not solid. I just hope I'm doing the right thing focusing so much on strategy. Would really love for them to be proficient by the end of the year."

Here is how I would respond to Michelle and to anyone else facing this struggle.

Michelle makes some excellent points!  Their strategies do need to have some level of efficiency.  First of all, are your students fluent with adding 2 double digit numbers mentally?  The ability to do this is the backbone of multiplication fact strategies and is a super important pre-requisite skill.  This is one of the many reasons I hold off on introducing the standard algorithm for addition.  If this is a skill you find is missing in your students, here are some great games that can be done to get your students comfortable with this important skill. Another excellent resource is the Number Talks book which offers a great framework and specific problem strings that can move your students forward with mental addition strategies.

Once you are feeling good about your students' fluency with double digit addition,there are lots of ways to work on building efficient strategies.  I know it can feel like you are moving backwards to have to go back and work on multiplication fact strategies but it will pay off in the long run.  Your work with double digit multiplication and with division will be so much easier if your kids have efficient strategies for multiplication.  Again, I have to say the Number Talks book is an excellent resource that provides a framework and specific problem strings that will move your students forward on fact strategies.  Here are a few of my other favorites for moving kids forward with fact strategies:

Your students are lucky to have you Michelle!  I am sure you will make a big difference for them.

What advice would you give Michelle? Please respond in the comments below

In other news, my blogging friend Tammy from Forever in First recently published an amazing book about teaching!  She has been an inspiration to me for years and I can't tell  you how excited I am to read her book!

Monday, October 16, 2017

Sharing the Good Things Happening In You School

In the past few years, the political make up of our schools has been changing a great deal.  The way schools are funded and the amount of local control in schools has been changing.  There has been a huge push from our state government to consolidate school districts and push some of the local control to the district level.  This has resulted in many fears from parents, teachers and community members about losing their local, small town elementary schools.  They are rightfully afraid that these schools will be closed and our children will be sent to larger regional elementary schools.  I get these fears from the perspective as a teacher who works in a small school and as a Mom who loves the small school her own kids attend. 

In our school, so many wonderful things happen that the general public is not aware of.  Some parents who are well connected to the school have a pretty good idea, but I often think the community in general lacks specifics about the good things happening in their school.  Thinking about the change in political climate and understanding the fears of other teaches and parents about our small school being on the chopping block in the next few years, I have been thinking a lot about how to promote our school and share all the wonderful things happening here. 

1. Video 

Last year, when I was researching ways to get out message out to parents, I stumbled upon Your School Rocks... So Tell People.  This book was full of great ideas that really helped me see the potential to up our game in several areas, including video.  Last spring, I challenged myself to create at least one video a week showcasing something going on in our school and after a few weeks, it got to be part of my routine and the response I have got is amazing.  I use the iMovie app for iPad to edit video clips, add text, etc.  We have been loving using video so much that this year, I have many students so excited to create their own videos that we are doing a trial of WeVideo which seems to be the go to video editing software for use on Chromebooks.  We are working on creating videos highlighting out behavior expectations for PBIS, math how to videos, trailers of upcoming events and so much more.  We share these videos on social media, the school website and on teacher blogs. 

2. Social Media

Our school district has a Facebook page and a twitter account that previous to reading this book, I hadn't paid much attention to.  After reading this book, I immediately looked into who was providing content on these platforms and made sure to send content their was as often as possible.  I am also working on organizing teacher take over days where different teachers get control of the account for the day/week and provide a detailed look into their classroom.  Since I work in an elementary school, we are trying to reach parents on social media, and Facebook is definitely the place where we can find most of the parents.  The book had an excellent chapter on using Instagram to reach your students which I think would be perfect for middle and high school age kids. 

3. School/Teacher Blogs

It is the expectation in my school that all teachers maintain a classroom blog where they share pictures, videos and updates at least a few times per month.  These are linked from the school website and it can be hard to see how much they are getting viewed or how helpful they are to families and the community.  They are a huge asset when someone new is looking into working at or sending kids to our school because they give a great flavor of what we have to offer.  My own blog is also used to curate online resources so it gets a lot of views at school and at home.  When I started adding videos that featured the students and videos that students helped create the engagement on the main page of my blog went up by 500%! Video is so powerful!  

4. Alert the Press

When something special is happening at your school, let the local press know.  Our smallest local paper is always interested in reporting on events happening in our schools.  They sometimes send a photographer & a reporter and other times they ask for more details and a picture that one of us took at the event.  Just a quick email to let them know what is happening in our school has resulted in positive press for us multiple times.  It is free and requires minimal effort. 

5. School Website

Is your school website kept up to date?  For many folks, your school website is the first thing they see when they search for you and you want to make sure you have enough information posted that they can really get to know your school.  Also, you want to make it a place where students and families return to over and over again to get the information they need or to catch up on the news.  Make sure your school website is updated at least weekly to get the most out of it.  Regularly sharing pictures, videos, newsletters, etc is a great way to keep things fresh. 

6. Get Folks Inside the Building

One of the best ways to get parents and community members up to date on what is happening at school is to invite them to come in.  When they are in the building, they not only get to see what is going on, they get to feel the culture as well.  We try to invite parents and community members in at least a few times a year and are now looking for ways to invite them in even more frequently.

7. Class Dojo

Class Dojo is an app that another teacher in my building began playing around with last year and I can't say enough about how much it improves communication with families.  This year, we have several teachers using it in my building and my own kids' school is using it school wide.  I love it so much from the perspective of a teacher and a parent.  It is a communication app that lets teachers and parents share videos, pictures and messages.  A teacher can post to the class board where all families can see it or to each students' individual stories.  It is enough like Facebook, that parents seem to figure out how to use it quickly and it can really improve communication.  I have not yet found a way to use it to communicate to the community at large but it cannot be beat for communicating with parents. They also have GREAT videos about Growth Mindset! 

How do you share the good things happening in your school? Please respond in the comments below. 

Friday, October 13, 2017

When You Don't Agree With Your Child's Teacher

I have known a lot of teachers.  First as a student, then as colleagues and now as a parent   I have been very lucky that my children have had wonderful teachers who I absolutely treasure.  I love their school, the sense of community and the teachers willingness to go above and beyond.  I am trusting these folks with the things that are most important in my life which has really forced me to reexamine my own role as a teacher in other students' lives.  These teachers and my kids' school is such an important part of their life and their happiness there is vital to the happiness of our family.
A situation recently arose where the teacher of one of my children made a decision that I did not agree with.  It was a decision that made me and my child feel unwelcome in their school.  My emotional response to this decision was dramatic and I can't remember the last time I was this upset about something.  I was in the place of the irrational parent rather than the calm and reassuring teacher.  Being in that role was new to me, and I really had to think about the best way to approach this with my child's teacher. 

Talk to the Teacher First

In my case, talking to the teacher was actually done by email.  I did not grasp the entirety of the situation when I picked my child up that day and once I did understand what had happened, I was much too emotional for an in person discussion that day.  In fact, I waited until the next day to begin composing the email and I went back to it several times throughout the day to make sure it was conveying what I needed it to without being too emotional.  The point here is that this was a decision the teacher made, and I needed to talk to her first before complaining to other staff members about this decision. 

Assume Good Intentions

This teacher is one my family has known and loved for years.  I know she has always had the best intentions her students and their families.  I went on the assumption that she was not purposely trying to make families feel unwelcome. 

Think About it From Her Perspective

I spent some time thinking about why she made this decision.  I thought about some of the changes that happened in the school this year and how the number of students in her class has gone up quite a bit.  I also thought about the fact that she seems to have some very challenging students this year and how that might be affecting her. 

Encourage Others

I heard a lot of grumblings from other parents the day I picked my daughter up from school.  I know from experience that parents are much more likely to complain to other parents than to tell the teacher directly why they are upset.  When other parents complained directly to me, I encouraged them to call, email or talk to the teacher about their concerns rather than to other parents.  If the teacher does not know multiple parents are upset, there isn't anything she can do about it. 

Follow Through

In my case, several emails back and forth to my child's teacher was enough to defuse the situation and have her reconsider her decision.  Whatever agreement you come to, make sure you hold up your end of the bargain.  If you get what you ask for make sure you say thank you. 

Mend the Relationship

I can be super challenging to disagree with someone you like and respect.  Even if you come to an agreement in the end, it can do damage to the relationship.  Things might feel a little awkward for a while and you may have to go above and beyond to be friendly and to help repair the relationship. 

Have you ever disagreed with your child's teacher?  How did you handle it? Please respond in the comments below! 

Sunday, October 8, 2017

Fall Math Fun

I am loving the fall weather we have been having this week!  It gave me a chance to get outside with some special Kindergarten kids and do some play based math activities using natural materials.  It was such a nice way to spend some time outside learning together! 

We started by going on a little nature walk with a few buckets and picking up some beautiful leaves, acorns and pine-cones.  Then we dumped our treasures out on the table, grabbed a few fine pointed sharpies and got to work exploring and adding some mathematical details to our fall materials.  We started by writing numbers on leaves.  Some kids wrote numbers to 10 while others wrote some random numbers they knew. 

We have been doing a lot with the 10 frame model recently and I wanted to capitalize on this so I used some of the larger leaves to draw some 10 frames which led to a lot of ordering and matching activies. 

Some kids are ready to look at addition and subtraction facts so we added leaves that had the symbols for +, - and = and they were able to use these with the numeral leaves and natural counters to create equations. 

Many kindergartners need plenty of practice with one to one correspondence and matching objects to numerals.  The acorns, pine-cones and number leaves let them have lots of experiences with this! 

We put everything in a bin and brought it inside to explore for a few more day.  The leaves will crinkle up along the edges and be unusable if you don't put something heavy on them when they are not in use.  I forgot this important step and ended up replacing them with artificial leaves that I had left over from another project. These materials placed in a sensory bin or sand table will give your kiddos opportunities to revisit them over the following week.

To connect our outdoor exploration of natural materials, we made this fun fall themed number craft.  This is a great way to reinforce many models and makes an excellent fall bulletin board display. 

How are you embracing fall with your children or your class?  Please respond in the comments below! 

Saturday, September 30, 2017

Teaching Math With You Tube Videos: Subtraction Facts

In the past few years,  I have posted some of my favorite songs and videos about shapescountingmultiplicationcoinstimefractionsteen 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. These little movement breaks have been super important as we have transitioned from summer vacation back to school 5 days a week.  I forget how busy the back to school season can be and now that things are finally calming down, it is so nice to be back to sharing things with you on my blog. 

This week, I have had subtraction on the brain as we have been working on subtraction in the fact range in both grades 1 & 2. We are are playing a lot of games, using the same deck of cards over and over.  When kids master one deck of cards, I change them out for a more challenging set but the rules of the games don't change.  This really helps me personalize learning! 
Movin' It Math Subtraction Facts to 20 Cards

We have been getting tons of movement in playing Movin' It Math but today I want to share with you some of the other ways we have been using movement and music to practice subtraction facts.  

When You Subtract With a Pirate

This catchy tune from Harry Kindergarten Music gets at two big ideas for subtraction.  It includes the word difference and talks about how you are getting less.  There are some great examples, all with facts in the under 10 range. 

Subtraction Song for Kids

This song from Jack Hartmann is a great way to get kids up and moving.  This song is easy to sing along and dance with.  All examples are facts under 10. 

Subtraction Halving Numbers Math Song

This song is a great way to look at the half facts for numbers up to 24.  It is produced by Dream English Kids which is a You Tube channel that is very new to me. 

My Dog Subtraction

This video uses the "take away" and "minus" language. 

One Less Number Game

Another great song from Jack Hartmann, this one is based on the idea of one less.  Numbers go up to 100.  

Adding and Subtracting

Another Harry Kindergarten Music song!  This one has a lot of different language in it and highlights the differences between addition and subtraction.  

Do you have a favorite song/video for teaching subtraction? Please share in the comments below!

Looking for more work on subtraction facts? This cards can be used in 11 different ways and are an excellent way to increase subtraction fact strategies and fluency! You can use them to work on facts to 10 or facts to 20!

Movin' It Math Subtraction Facts to 10 Cards

Thursday, July 13, 2017

Catching Up and My Summer Reading List

The last few years have been an absolute whirlwind with trying to balance parenting and teaching.  I have been making many changes in my teaching as I move toward personalizing learning.  I continue to prioritize professional reading and wanted to share with you what books I am reading this summer as well as a few life updates.

Taking a real vacation

This past week, I went with my family to Wells, Maine and had my first full week off from thinking about or reading/writing about teaching in at least 3 years.  I didn't take any of my professional reading or even bring my laptop.  I did read 6 books just for fun!  It has been at least 7 years since I have been able to read 6 books for pleasure in a week! My favorite read of the week was the Gilly Salt Sisters.  Despite my attempt to stay away from professional reading for the entire week, the house we rented had several bookshelves full of random treasures, one of which was this interesting looking book by Ron Clark.  I have always been very inspired by Ron Clark's work but have never read one of his books. Despite the fact that I managed to stay away from the book the entire week I was there, I decided I had to read this and have downloaded the audio version using a credit from my Audible subscription. I find audio books are a great way to help me keep up with all of the books I have on my wish to read list.  I often listen to them while cleaning, cooking or driving if I don't have the kids in the car with me. 

Older Kids = More Adventures

My children are 7, 5 and 3 this summer and for the first time ever, I don't have a kid who is 2 and under.  This has opened up an entire new world of possibilities for us in terms of going on summer adventures. They can handle all day excursions and our world does not have to revolve around nap time for a change.  They also all walk well, listen better and have much more endurance.  This has led us to having tons of active summer fun all over our land, our neighborhood and our state.  We can visit many more isolated treasures in the area because our ability to hike has grown exponentially.

Library Time

I am spending a great deal of my time this summer volunteering at our little local library.  This gem is tiny but an important part of our small town.  It is inside an old Baptist Church from the early 1800's.  There is such an eclectic collection of books both new and old.  It is entirely staffed by volunteers and is open a few hours each week.  I have been working to help update and reorganize the collection of books in a way that makes them easier for folks to access.  It is a lot like thinking about how to organize a classroom library and I have very much enjoyed my extra time among the books. 

Staying Out of My Classroom

I have been on summer vacation for almost 3 weeks now and I have managed to stay out of the school building and for the most part away from my school email.  I like taking a break and then slowly easing myself back into the school routine and plans for next year.  Beginning next Tuesday, I will spend a few hours each week in my classroom putting it together for next year and getting this prepared.  Our students start on August 30th and I like to avoid the last minute rush while still feeling prepared.  I find putting in 5-6 hours a week at my leisure over the second 2/3 of summer really helps relieve the back to school rush.

My Summer Reading List

I picked up this book because I saw the author, Steve Leinwand speak at a conference last year.  I was impressed by his ideas about only changing 10% of your teaching practice each year.  

I read an earlier edition of this book when I was in college and student teaching.  After my book study on Mathematical Mindsets, I decided revisiting these ideas would enhance my ability to teach for a growth mindset. 

This is another book I decided to read based on seeing the author speak.  This past spring, I attended a 2 day workshop on grading and reporting with a team from my district.  We have made some excellent progress in this area over the past 10 years but still have a few things we could do to improve the grading and reporting process.  

I ordered this book because I am so inspired by many of the teacher blogs represented in this book.  I am impressed with how these teachers share the happenings in their classroom and ask important questions about teaching math.  

Back in 2014, I did a book study on Teach Like a Pirate and was so inspired by the ideas.  As my job evolves, I get put into leadership roles quite often in my school and my district so it was natural that when I saw Lead Like a Pirate had been published, I knew right away I wanted to read it.  I am almost done and will be sharing some of my thoughts soon! 

This one I picked up on the recommendation of a friend.  Much of my reading over the past 2 years has focused on the intermediate & middle school grades and I like to keep myself up to date with all the grades I teach so I asked a friend who is an expert in primary mathematics which book she recommended and she picked this one! 

The Dyscalculia Resource Book
This book will be coming out in the next few days and looks to be a great resource.  Dyscalculia is something not well understood by most educators and definitely something I want to read more about. 

Two Books I Recently Finished

I read this book during the last month of school, and loved the ideas presented.  I am always looking for ways to improve communication and feel like there are awesome things happening in my school that nobody knows about.  The ideas in this book, especially around sharing with video were things I was immediately able to put into practice.  I passed this book onto my principal and we are working together to make a plan for using some of these ideas building wide next year.  

140 Twitter Tips for Educators
I have officially been on Twitter since the fall of 2013 but have not really used it in any substantial way.  Many fellow educators in the math field and otherwise have encouraged me to use Twitter for professional development and a way to connect with other educators.  Since being the only math specialist in a building can be isolating, I knew Twitter would be an excellent way to connect with the larger educational community.  While reading this book, I began to take many of the tips to heart and was doing a great job with Twitter at least until the school year was coming to a close!  This book definitely helped me feel more comfortable using Twitter and I would highly recommend it to any educator!

How are your plans for the summer progressing?  Feel free to respond in the comments below!

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!

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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!