Powered by Blogger.

Summer Book Study

This post contains an affiliate link to a great math resource to assist with the maintenance of this blog!

Math teacher friends! I have something so very exciting to share with you! If you haven't already heard, Tammy from Tarheelstate Teacher and I are launching a private facebook group exclusively for upper elementary math teachers! If that's you, we would absolutely love for you to join us and be a part of what will be an amazing community of math teachers!

We know summer is a time to rest. Yes, lots of rest and relaxation. BUT it is also a wonderful time to learn! What better way to learn than to do a book study with your online math teacher friends?! We decided a book study would be a great way for us to learn together, get to know each other as teachers, and step into being the best math educators we can be.

In just a few short weeks we will launch our Upper Elementary Math Teachers facebook group and begin reading Becoming the Math Teacher You Wished You'd Had by Tracy Zager together! I read this book last summer and it is fantastic! This book will challenge your math thinking and help you bridge the gap between the math experiences you likely had as a child and the math experiences you give your students. This book will leave you inspired, encouraged, motivated, and ready to get back in the classroom (well, after your well-deserved summer break of course) and give your students the amazing math experiences they desperately need! I know you will walk away from reading this book with practical teaching strategies to empower your next group of little mathematicians! This truly is a life-changing book for math teachers (because math is life, right?), no matter what stage of your career you are in or how you already feel about teaching math!

Are you ready to get in on the math fun?! Here's how you can learn with us! First, be sure you have requested to join the Upper Elementary Math Teachers facebook group. On May 18th, the OFFICIAL LAUNCH DAY, we will open up the group and throw a little virtual party to celebrate (can you tell we are so excited about this?!).

If you are ready to go all in with us on this book study, start by purchasing Becoming the Math Teacher You Wished You'd Had by Tracy Zager. If you are ready to dive into a summer full of math learning together, check out this timeline below to get an idea of what the next 8 weeks hold!

If you've got other summer PD plans or you just want to join in on the discussion in between all your summer plans, you can get a whole lot out of participating in that way too! We want this to be a time of learning, fun, and community with other math teachers! Tammy and I will be hosting live book chats inside our group to discuss the book with y'all and share our thoughts. We will have weekly challenges and a few giveaways! You definitely don't want to miss it! So, ARE YOU IN?!

A Community for Upper Elementary Math Teachers

GUESS WHAT?! I have something so very exciting to share with you! You know I LOVE all my math teacher friends, right? Whether in real life or online, you can never have enough teacher friends. There's just something about being able to talk math with a group of people who just get you... 

For a while now I have wanted to create some way for math teachers, specifically those who work with 3rd-5th grade students, to connect and grow together. I wanted a place that was completely devoted to #allthingsmath where teachers could come to learn from each other and be inspired by one another. I wanted a place where math teachers could come to support each other on the hard days and celebrate the great days! Teaching math is 100% my passion and I wanted to share that passion with THE WORLD (okay, I may have dramatized that a bit) other MATH TEACHERS!

Are you ready for the EXCITING NEWS YET?! A good friend of mine, Tammy from Tarheelstate Teacher, and I are finally making this dream a reality! We are officially launching our UPPER ELEMENTARY MATH TEACHERS Facebook group! We would love nothing more than if you would join this community of teachers because well, IT IS GOING TO BE AMAZING!

If you don't know Tammy, her mission is to provide a place where passionate teachers + differentiation lovers unite to create classroom environments that get results for our students - socially, emotionally, and academically. She is a rockstar champion for teachers and students and I could not be more excited to partner with her in this math adventure!

We have some really exciting surprises planned for the next few months and we would love for you to be a part of it! If you are ready to be a part of this wonderful community of Upper Elementary Math Teachers, be sure to snag a spot on our VIP list! 

Before your nerdy math brain bursts with excitement, let me share with you our mission and our heart behind this group...

Our desire is to help teachers feel confident in teaching math, understand the standards and how to teach them, with a focus on how to support students' thinking in their many phases of learning. We want you to feel supported and inspired! 

We want this community to be a judgement-free zone by remembering that we all want to improve our math teaching and engage with like-minded colleagues, not because we are already perfect but because we always strive to be better!

If you are ready to be positive, be supportive, be collaborative, be open-minded, and be ever tenacious in the pursuit of being the best math teacher you can be, we want you to join us! 

To kick off the learning together, we are doing a summer book study! Be sure to check out this post to learn more!

Play Dough Fraction Project

One of my favorite things to do in the classroom is to actually make things with my students. I absolutely love throwing on my apron and getting my hands and the rest of the classroom dirty! Creating with kids makes for the best memories! It may take a little extra planning, organizing, and cleaning, but I have never regretted giving my students these types of experiences!

With all that being said, after doing this with my own kiddos, I just had to make this freebie for y'all! You absolutely don't have to actually make play dough in the classroom to put this project to good use, but if you want to give your students an experience in the classroom that will have them talking for days (or weeks or months...) then get your mixing bowls ready!

I decided to make a 4th grade and 5th grade version of this project so all my upper elementary math teacher friends could enjoy it! Click on the link below and grab a copy of this real world play dough fraction project!

We have such a great opportunity as teachers to make moments for and with our students that they will never forget! I hope your students love this as much as mine did! If you do this project with your students, I'd love to hear how it goes! Shoot me an e-mail at brittany@mixandmath.com or tag me on Instagram at @mixandmath! Nothing makes my teacher heart happier than seeing students love the math experiences you create for them!

Problem-Solving: Helping Students Get Unstuck

I think it's safe to say we have all had those students who immediately after reading a math problem raises their hand and simultaneously shouts "but I don't get it!" It can be incredibly frustrating because you know they have not truly taken a reasonable amount of time to think through the problem and try to do something.

Often times we help them get started and move along, until the next problem comes and you hear... "but I don't get it!" So now we are left wondering... Why do some students repeatedly respond like this? What can we do to help them? 

I think there are two reasons why this happens...
  1. They aren't truly stuck. 
  2. They are truly stuck.
Brilliant, right? Let me explain. Sometimes students are so used to struggling and receiving immediate help that they take on this attitude of "learned helplessness" that causes them to believe that they cannot do anything without help.

They don't show the habits of an independent math learner. Instead, they give up at the first sign of struggle. So what can we do to help these students? The same thing you would do to help a student who is truly stuck.

Ask questions. Listen. Ask more questions. It's important that we don't give students the impression that raising their hand and asking for help gets them off the hook from doing any thinking (if that were the case, why would they ever work independently?).

Instead, we need to set the expectation that asking for help will require a little work on both of our parts. We don't want to leave students stuck, but we also don't want to provide too much help and minimize the cognitive demand of the task.

It requires balance and a very intentional line of questioning. Here are some thoughts to help students get unstuck...
  • Get students talking. The more they talk about the problem, it's possible they may get themselves unstuck.
  • Find out what students do know or understand about the problem. Again, sometimes just talking about what they do know helps them get started on their own.
  • Ask students what specifically about the problem is causing them to be stuck. Is it the academic language? Is it the context they aren't familiar with? Is it the math content itself? This will require thinking on their part, but it will help you provide very targeted assistance. 

Having this conversation with students who are stuck is beneficial for them because it gets them in the habit of talking about math, sharing their thinking, and finding something in the problem that they can build on.

For our little friends who aren't truly stuck but always feel that they need help, these questions will help them realize that they CAN do it on their own. The more they feel that they can do it on their own, the more willing they will be to struggle independently in the future.

Remember, learned helplessness is often built over years, so it's not something you can break in minutes.

Solving for Why and Powerful Problem Solving are two books that I absolutely love! Solving for Why is a great book if you work with a number of students who struggle with math. It walks you through understanding their struggles, assessing them appropriately, and then how to teach them for true math understanding. Powerful Problem Solving is a book full of activities that you can do with your students to help grow their problem-solving skills.

I am a big advocate for the habits we instill in our math learners. Positive math habits can be the thing that holds students back or really gives them the strong foundation they need to succeed.

If you haven't grabbed my Mathematical Practice Standards FREEBIE, you can download it here! These questions and posters are a start to building positive math habits in students!

So, what do you think? How do you help students get unstuck?

*This post contains affiliate links to two great math resource to assist with the maintenance of this blog!

More Than Routine

Routine in the classroom is good, right?! Students need structure! Yes, but structure and routine are two very different things when it comes to math instruction. I read a pretty interesting chapter recently in Adding it Up: Helping Children Learn Mathematics about the "routine" of instruction seen in a lot of math classrooms. This "routine" is called recitation and it describes many of the math classrooms we as teachers learned in as children. See if this sounds familiar...

The class begins by reviewing last night's homework assignment. The teacher explains it (or maybe a student does). The teacher then moves on to the content of the lesson by demonstrating a skill, asking a question, waiting for a student response (which typically requires little more than a few words), evaluating the accuracy of the response, and then continuing this cycle over and over again until all the content for the day has been covered or until it is time for students to get a head start on their homework.

In this classroom, who is doing the majority of the work? Is it the students or the teacher? Who is being held accountable for their thinking? It is SO easy to fall into teaching the way we were once taught as students in the classroom in the name of "routine" and "structure." I am not saying that our math classrooms should not be structured. Students thrive in a classroom that is structured. What I am saying is that we have to give our students more. More exploration. More thinking. More talking. More time. More opportunities to experience math and develop their own curiosity about the wonder of math. More patterns. More debates. More excitement. Just more. We need more than a routine to deliver a set of standards. When students leave my classroom I want them to continue talking about what they learned. I want them to feel proud of what they discovered and be ready to tackle something that left them feeling "stuck" the day before. Math, REAL MATH, is addicting! We cannot silence our students' thinking by doing the whole question-answer-question-answer dance.

So what should our math classrooms look like? How do we give our students all this MORE? I think the answer to that is twofold. We engage our students with the delivery of the content and we engage our students with the content itself. Engaging students through the delivery draws them in and hooks them. Following that up with content that engages their mind, sparks their curiosity, and causes them to want more leaves them feeling empowered as math learners. My opinion is that both are needed to give our students an amazing classroom experience that involves learning, community, and a genuine love of math.

*This post contains an affiliate link to a great math resource to assist with the maintenance of this blog!

Which Comes First... Decimals or Fractions?

Let me start by saying I have been meaning to write this blog post for a long time... a very long time!  It was around November of this past school year that I had a revelation (thanks to a fantastic graduate course and professor, the amazing research-based book Extending Children's Mathematics: Fractions and Decimals, and students who were so willing and able to communicate their math understanding and struggles).  The order in which I have been teaching the 5th grade math standards was not allowing students to make critical connections between fractions and decimals.  Here me out... There are certain concepts in math that are pretty obvious in which order they should be taught.  Clearly students should learn to add before they learn to multiply, or divide whole numbers before learning to divide decimals.  What I found is not so clear among many teachers and those district leaders who write our pacing guides is what comes first?  Fractions or decimals?  Both of these concepts play a huge role in 5th grade math and provide an imperative foundation for math learning through high school and beyond.  Don’t believe me?  Hear what Sherry Parrish and Ann Dominick, authors of Number Talks: Fractions, Decimals, and Percentages have to say about the lack of strong fraction understanding in high school students. 

“The National Mathematics Advisory Panel conclude that the most important foundational skill not presently developed appears to be proficiency with fractions... The panel’s findings were corroborated with a survey of 1,000 U.S. algebra teachers, who indicated that a lack of fraction knowledge was the second biggest problem students faced in being prepared to learn algebra” (2016, pg. 2).  

If this is one of the biggest problems students face in learning algebra in high school, it is important that we do all that we can to teach fractions (and decimals and percentages) in a way that allows our students to truly and deeply understand fractions.  Now that you know how important mastery of these concepts is, which should you plan to teach first?  The short answer: fractions.  Then why do many pacing guides do the exact opposite?  Honestly, I have no clue.  I have asked the creators of several different pacing guides for their rationale for teaching all of the Number & Base Ten standards first and then teaching all of the Fraction standards next and nobody could explain to me the reasoning behind this.  Truth moment… For a long time I have taught it this way because that is what the pacing guides have always said to do and I thought surely this was the best way.  It was not until I did my own learning and challenged what I had always done did I realize that decimal understanding is strongest when it builds on students’ understanding of fractions.  See if any of this sounds familiar:
  • Why is 0.01 (one-hundredth) smaller than 0.1 (one-tenth)? Why is 0.2 one-tenth of 2?  To explain this, you need to build on students' fraction understanding of what “one-tenth” truly is. 
  • Where do I put the decimal when I multiply two decimal numbers together?  No matter how many models we used, this question never seemed to disappear UNTIL I got around to teaching multiplication with fractions.  At that point, they could explain why 0.1 x 0.01 = 0.001 or 1/10 x 1/100 = 1/1000.
  • What does it even mean to divide 5 by 0.2 and why do I get a bigger answer?  Why do I get a smaller answer when I multiply 5 by 0.2?  I thought multiplication was supposed to make numbers bigger and division was supposed to make numbers smaller! Yes, technically you can explain this without necessarily getting into fractions, but clarifying this by building on students’ understanding of fractions is much less abstract than attempting to explain this by building on students’ struggling understanding of decimals.  In addition, the models used to teach multiplying and dividing fractions answer these two questions in a visual way perfectly.
Check out the learning progression for decimals and notice how embedded many of the fraction standards are in the learning of operations with decimals in 5th grade!  Believe it or not, decimals are much more abstract than fractions.  The authors of the book Extending Children's Mathematics: Fractions and Decimals state that "children's understanding of decimals simultaneously draws on their understanding of fractions and place value" (2011, pg. xxiv).  I will say, sometimes students find "temporary success" more quickly with operations with decimals than they do operations with fractions if the instruction is focused on procedures rather than conceptual understanding. Procedures for operations with decimals are typically more familiar to students than the procedures for operations with fractions.  But, is this really true understanding? Does this type of learning (procedural rather than conceptual) last and allow them to make critical connections in their growing understanding of fractions, decimals, and percents?

Instead of teaching decimals and constantly jumping ahead into my fraction unit to explain why or how, I finally decided to just take a break from our decimal unit, move right into our fraction unit, and let students discover all the why's and how's for themselves!   By the time we came back to our decimal unit, I could direct students to think about their own understanding of fractions to answer their many questions about decimals. (Side note: You could teach operations with fractions and decimals in conjunction with each other because they have so many connections.)  At the end of my fraction and decimal units, I spent a week or two reviewing and taking time to intentionally highlight the connections many students had already made about fractions and decimals throughout the units. Luckily I have the flexibility to deviate from the pacing guide, so I am excited to use what I have learned from watching and listening to my students' thinking, paired with some great research, to come up with a new plan!

What are your thoughts?  Which comes first on your pacing guide, fractions or decimals?  In what order do you choose to teach fractions and decimals?

*This post contains affiliate links to two great math resources to assist with the maintenance of this blog!

Fractions: Classroom to Real World

Have you ever had a student ask... "When am I ever going to use this?"  Early in my teaching career this question would drive me crazy!  It usually was asked by a student who was capable of doing whatever we were learning, but simply didn't feel like actually doing the work.  This question now makes me realize I have not fully been doing my job as a math teacher...  There should never be a time when a student does not understand the purpose or application behind what they are learning!  When students understand when they would actually use the content they are learning, their motivation is immediately boosted.  Not only do students become more motivated in learning the content, but they are also challenged to apply (Bloom's Taxonomy, anyone?) the content which typically requires more critical thinking.  This is why there has been such a big push for "real world connections" in recent years.  As math teachers, we must take our math instruction from classroom use to real world use and fractions is the perfect place to start!

After visiting the Ron Clark Academy a few years ago, I was totally inspired to use classroom makeovers as a way to engage my students even further in our real world math projects!  As our fraction unit comes to a close, I wanted to share some pictures of all the fun!

We hosted a cooking show to share our delicious dessert recipe with the world! Students got to "bake" and apply their skills adding and subtracting fractions to some real life cooking situations!  I simply threw some plastic table cloths on the tables, brought in cooking utensils, and played some bakery music and we were good to go!  Even though the floor was covered in powdered sugar at the end of the day, it was worth it!

The math cafe was under construction while we used our skills multiplying fractions to build model dog houses!  I added caution tape to every place I could think of around the classroom, put out some safety cones, and added all sorts of construction-like centerpieces to the tables!  I even found an hour long video on YouTube of a construction site (what non-teacher would ever use this?!).  I threw on a pair of safety googles and a reflective safety vest to really get into the construction spirit! :)

Despite the cold weather, we ran our own lemonade stands in the classroom to help us practice dividing fractions!  I reused the plastic table cloths, let students design lemonade stand signs, and brought in yummy treats for them to have at their lemonade stand!  I played some Jack Johnson in the background as kids worked because it just made me think of warm weather (I was impressed that several students actually knew who Jack Johnson was!).  This was the easiest classroom makeover and the kids had lots of fun!

We still have our fraction review project, which is a picnic theme, that we will do some time this week, and then it's off to our next unit!  (Update: If you're looking for a fun review project for all operations with fractions, be sure to check out my Play Dough Fraction Project freebie post!)

I don't makeover my classroom for every project we do, because honestly my students are engaged with the real world scenarios of the projects anyways! But, I do believe the classroom makeovers bring an element of surprise and joy to my students' faces that is just too addicting to resist! :)