Guided Math in Action Book Study: Chapters 5 and 6

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Welcome to my guided math book study!  It is not to late to join in!  Every week, I will provide the links to past posts so if you are just finding this book study you can jump right in!

July 2   Chapters 1 and 2

July 9   Chapters 3 and 4

July 16 Chapters 5 and 6

July 23 Chapters 7 and 8

July 30 Chapter 9

Guided Math in Action

Chapter 5: Balanced Assessment: The Key to Grouping Students for Guided Math

This chapter has lots of information about assessments and how they pertain to guided math.  The importance of formative assessment is stressed as well as using pre and post assessments.  I feel like I do a great job assessing my students with a variety of assessments and using the results of these assessments to inform my instruction.   I love the focus in this chapter on trying to do individual interviews with students.  These give me such good information about a students' understanding.  I know they can be incredibly difficult to find the time to do, but I would encourage teachers to do these interviews with kids when at all possible.  The information you gain can really help you target your instruction. 

One thing I would like to work more on that I read about in this chapter is getting kids involved in their own math learning.  I would like to spend more time going over assessment results with kids and working with them to set goals for their learning.  "The research show that when students are involved in their learning they do better." My goal for this year is to empower students to become involved in understanding what they know and are able to work on next in their math learning.                                                                                                                                 I also think it is important to have a balanced assessment system.  Dr. Newton stopped by our book study last week and left a comment about beginning of the year assessments that got me thinking about the importance of giving a variety of assessments to get the full picture of a student's skills.  It is important to check for fluency as well as problem solving ability and the big idea skills that kids should come into a grade with.  I think I am guilty of skipping some of these types of assessments sometimes because I work with my students over a period of years, I tend to assume I know their abilities pretty well.  I want to be sure I am not making assumptions though and will be more thoughtful in balancing different types of assessments going forward.  

Chapter 6: A Framework for Guided Math Lessons

This chapter is all about how to structure your small group lessons.  There are 8 steps that each guided math lesson is supposed to follow.  It can seem a little intimidating if you think about having to write out a plan for all 8 steps.  Don't let the fact that there are 8 things you need to do scare you.  Some of them seem more complicated than they really are and during an actual group time take less than a minute.  For instance outlining a learning expectation can be as quick as telling kids you are working on combinations of 10.  The biggest thing to remember is that all of this gets easier with time.  After many years of working with small, intensive math groups this is second nature to me and I very rarely need to create a written plan at this point. 

I think the most important things to remember when you are working with small groups are

1) Have a purpose.  Why did you put these students together?  What skill are you going to target?

2) Keep it focused.  Work on the learning intention in a purposeful way.
3) Keep it moving.  This is small group time and you have other groups to meet with.  Keep the lesson moving, make it short and sweet.  Kids will stay engaged and you will be maximizing your instruction time.


I look forward to a great discussion on this week's reading!  

QR Code Scavenger Hunts: Using Technology to Practice Math

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We all know how important it is for kids to have basic arithmetic skills.  Whether you teach all algorithms or help kids construct their own strategies their comes a time where they need a little more practice with a skill to work on accuracy or fluency.  You can go with a traditional worksheet or you can make it super engaging with a QR code scavenger hunt.  

You have probably seen QR codes around.  They are popping up on cereal boxes, business cards and subway stations.  Here is a look at one if you are not sure

You need a smartphone, tablet or other digital device with a camera and the ability to install apps.  You need to download a QR code reader app (there are many good free ones!) and then you are set to go.  Simply scan the QR code and it will take you to a website or display text or a phone number or even show you a coupon.  There are many options and more are being added each day.

So how do I use QR codes in the classroom?  My favorite way is with a QR code scavenger hunt!  

I use my laptop and a QR code generator to generate QR codes with math problems and then place the QR codes onto task cards, add some text and a border, design a record sheet and an answer key and then they are ready to use.  If I don't have time to commit to doing all that, I jut head over to Teacher's Pay Teachers and browse my options for QR code scavenger hunts that are already made.  For a few dollars, I can usually find what I want and be ready to go.

My favorite places to do QR code scavenger hunts are in the gym or outside on the track.  Although they work fine in the classroom or a hallway, kids get really excited to do math in the gym or on the track.  

My sixth graders doing a decimal QR code scavenger hunt in the gym

In my school, we have several iPads and older smartphones as well as a few iPods.  All of these devices work great for this activity.  I also let my older students (grades 4 and up) bring in their own devices when I know we are going to do a QR code scavenger hunt.  I usually have kids work in pairs and share one device. (Update: we went 1 to 1 with Chromebooks in my school and we love using this free app with our Chromebooks. Now that I curate online resources with a school wide math blog, I just leave the link to this free app at the top of each grade level's page. )

A student uses an iPod to do a fraction QR code scavenger hunt

The students start by scanning the start card.  The first problem will appear on their device.  They use their record sheet or a piece of scrap paper to figure out the answer.  Once they find the answer, they go out and find it on another card.  If they can't find the answer on any of the cards, they know it is wrong and try the problem again or get some help.

A student uses partial products and area models to solve a double digit multiplication QR code scavenger hunt

A student uses multiple strategies to solve a double digit addition qr code scavenger hunt

A student uses partial quotients to solve a division QR code scavenger hunt

They continue in this manner until they get to the card that tells them they are done.  Then they bring their record sheet to me so I can check for accuracy (this is usually not an issue) and types of strategies used.  

QR code scavenger hunts can be a fun way to practice routine skills during math.  I have used them with kids in grades 1-8 and they work great at all levels.

Here are a few free QR code scavenger hunts if you are looking to try them out!

Multiplication Facts

Addition and Subtraction Facts

Types of Lines and Angles

100 days of school

You can browse the entire collection here!

Math is About More Than Number Crunching and Formula Writing

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I have been participating in a book study over at the Math Coach's Corner on this book.  

Teaching Numeracy

It describes 9 habits kids (and adults!) need to support mathematical thinking.  I was reading about habit 3 which is identifying similarities and differences and recognizing patterns and I saw this quote:

“If identifying similarities and differences is basic to human thought and boosts student achievement, why, then, are we still content to settle for number crunching and formula writing as the dominant form of instruction?”

This got me really fired up and as I was leaving a comment over on the book study, it turned into the story of my own mathematical education and why I think there needs to be a shift in teachers' focus from teaching kids how to do math to helping kids think about math.

Here it is!

I was taught arithmetic in elementary school and didn't find it particularly interesting but was always quite good at it.  When I think about my own instruction in math, it is amazing that I didn't completely hate it.  We used Addison Wesley style textbooks and everything was taught as a procedure.  Nothing was ever connected for us at all.  In fifth grade I remember we had a wide range of ability levels in our classroom.  The teacher allowed another student and I to start from the back of the fifth grade text book and work our way forward.  I don’t think we ever got any teacher time, we just did page after page of rote practice.  We even checked our own work and graded our own tests with the teacher’s edition.  I thought it was a great adventure then but now it seems like a recipe for disaster!

In middle school and for algebra 1 and geometry, I was able to follow the procedures that had been taught and relied on my great memory to “plug and chug” my way through these classes with excellent grades.  Looking back, I see that I didn’t really understand the math but I could do it.  I was never taught to think about the numbers I just operated on them.  It wasn’t until tenth grade when I stepped into an Algebra 2 class that I ever started getting the connections between things.  I had a fantastic teacher who helped me to see connections and challenged me to live up to my mathematical potential.  Luckily I had the same teacher twice more before graduating from high school and he really helped foster my love of mathematics.

As an undergraduate, I had a dual major in elementary education and mathematics and took some very challenging math classes.  I had the widest range of professors you can possibly imagine ranging from the very good to the completely inept.  I had a dynamic, inspiring teacher for my combinatorial theory class and to this day I get so excited about combination problems and I love doing them with my students.  I also had some of the worst professors imaginable and I think now looking back it is because they couldn't or didn't connect what they were trying to teach me with what I already knew.  I don’t know if they actually understood the connections themselves.  I remember one professor who taught a class on groups and rings would have the entire class show up at his office during office hours because none of us could figure it out.  Finally he told us all that if we showed up for class and tried our best, he would give us all a B. 

It wasn’t until I began teaching and started working on my master’s degree in K-8 math instruction that I finally really understood the connections in math.  Being introduced to things like the area model for multiplication and finally getting that multi digit multiplication, fraction multiplication and polynomial multiplication are all connected by this model changed the way I view math.  Instead of a list of disconnected procedures, I had a visual model that could help me solve ANY multiplication problem.  Through my master’s program, I also finally got the connection between algebra and geometry.  When I was in high school they were taught as two different subjects but through the problems I worked on in this program, I got to see that you can solve many problems with algebra or geometry.  I also learned that I tend to favor solving problems with algebra and really had to open my mind up to see how the same problem could be solved with geometry.  It made me a better mathematician and a better teacher. 

When I think about my own math education, I can see why I teach the way I do and why I am always annoying my students with my sayings like “think about the math, don’t just do it!”  I spent many, many years just doing the math and was quite successful at it.  However, I was missing the passion, understanding and beauty of mathematics.  I could not solve novel problems.  I could only plug numbers into formulas.  If I forgot a formula or a procedure, I had no way to go back and re-create it for myself.  I have a great memory so I did well in general because I tended to not forget.  As my deeper understanding of mathematics developed, it helped shape me into the teacher I am today.  I get the connections now.  I know if my answer makes sense.  If I forget a formula or a procedure, I can rely on other things that I know that are connected to it to help me out.  I love nothing more than jumping into solving a novel problem.  I thrive on trying new math and applying my new knowledge to what I have learned in the past.  I love math. 

I want my students to feel about math the way I do now.  I want them to have the connections and be passionate about using what they know to solve new problems.  I don’t want them to settle for being taught how to do it!  I want them to construct their own knowledge and learn to think instead of just applying procedures.  I am not willing to let my students learn math the way I did.  I want more for them.  It is time to stop teaching kids how to do math and start helping them learn to think about math!

How do you make math about more than number crunching and formula writing?  

Monday Math Literature Volume 51

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If you missed last week's post about using the Princess and the Pizza to practice adding decimals and money, you can check it out here!

I continue to be very inspired by the Math and Literature books written by Marilyn Burns, Stephanie Sheffield and some other great authors.  They have opened my eyes to finding math lessons in other children's literature.

Today I want to share with you a lesson I thought of when reading to my children.  I have not yet used this lesson in the classroom but tried it out with a few nieces and nephews.  I think it would be great in grades 1-4.  It is all about 3-D shapes!

The Little Red Hen Makes a Pizza

This book is super cute!  It stars the little red hen who is working hard to make a pizza.  She doesn't seem to have what she needs on hand and has to make several trips out to pick up supplies.  She asks her friends if any of them would like to help her prepare the pizza or run errands and they keep saying no.  Finally the pizza is made and is very large!  She asks her friends for help eating it and of course they say yes.  Then she asks for help cleaning up and her friends finally agree to help.  It would make a great story to use in a lesson about helping out your friends and doing your part also.  

The best part of this book to me is that it features a lot of 3-D shapes in the pictures.  Take a look at these:

See what I mean?  This is the perfect book to use in conjunction with a lesson on 3-D shapes.  

Here is a fun way to record the 3-D shapes you identify in the book!  You will notice there are not a lot of examples of pyramids.  I find this to be true quite often when going on 3-D shape hunts.  You can grab this record sheet for free from Google drive.

 When I do this lesson in the classroom, I plan on using my shape posters to have kids do a 3-D shape hunt around the classroom.  I will spread out the posters around the room and have kids bring examples of each type of shape back to the poster that it matches.

My 3-D shape posters are available in red, green, purple and blue!

Does anyone have any other recommendations for children's literature that can be used to for a 3-D shape hunt?

Check out other great books over at Mrs. Jump's class

You Oughta Know About.... Push-in Versus Pull-out Intervention

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As a math specialist I often get asked which is better... push-in or pull-out interventions.  Today I am linking up with a bunch of great bloggers to share with you all kinds of things you might like to know about.  You can check out other blog posts by checking out the links at the bottom of this post. 

Let's take a look at the pros and cons of each intervention method

Push-In

Pros

      To me, the best part of the push-in model of intervention is that I really get to know all of the kids in a class. When I am there for co-teaching whole group lessons and available for small group instruction I get to know and work with a wide range of kids.  The groupings can be more flexible and there is a great sense of teamwork with the classroom teacher.  There is a great opportunity to follow a guided math structure and having two adults in the room makes things run very efficiently.  It is also a great way to learn from another professional and see new teaching strategies.  When I do push-in interventions, I am the person moving between rooms rather than the students which certainly saves transition time.  Push-in instruction also means all the materials kids need for that subject are in one place.  Finally, it provides more consistency in terms of classroom rules and routines.  

Cons

     There are several things that can be very challenging with a push-in model for intervention.  If the classroom teacher and the interventionist have different ideas about classroom management, it can present a challenge.  If one teacher is very laid back with management while the other is very consistent and on top of things it can be tough to co-teach and co-exist in the same room.  Also, noise and distractions can be more of a problem especially as class size increases.  

Pull-Out

Pros

     The very best part about pull-out intervention is having a quiet, focused place to do it.   It is a small group of kids and at least in my case, I have my own mini-classroom to work in and there are not any distractions from other groups, students or teachers.  If I am using specific materials for a particular intervention I can leave them in one place and know they won't get moved by another teacher or kid.   Many of my favorite intervention materials like my place value decks and number puzzles are also used by teachers in the classroom so I can access most of my favorite things regardless of where I am.  When kids come to my room, they get a change of scenery and a quick break as they walk to my room which is always nice.  I also am in control of classroom management in my own space and I have to say, I really like having things my way.

Cons

     The thing I miss most when I do pull-out interventions is the co-teaching relationship I have with the classroom teacher.  I also have a very packed schedule and if I am not in a teacher's classroom, it can be hard to catch up with how students are doing and what we are working on.  I also find during pull out interventions the groups are much less flexible and I tend to end up with the same kids over and over again.  There also seems to be a bit more of lost instruction time waiting for kids to come to me or having to go to their classrooms and wait for them to be ready to go.  There are also some kids who seem to get lost on their way from their classroom to my room.  

My General Rules for Intervention

     In general, I find push-in intervention to be the most effective way for me to deliver math services.  I love getting to know all the kids in the school and I really enjoy collaborating with other teachers.  Co-teaching and sharing kids can be a great way to increase the learning of all students.  I am very good at getting along with other educators and have spent a lot of time developing relationships with the folks I work with.  When you first start with a push-in model there is certainly a learning curve as you figure out the other teachers styles, preferences, strengths and weaknesses.  After a decade of working with many of the same teachers, I have strong co-teaching relationships and can be very effective teaching with the people I know so well.  Our school also tends to have smaller class sizes which really help make push-in instruction less distracting and more effective.

    Despite the fact that I really love push-in interventions, I still do some pull-out interventions.  There are some days that the push-in model is not effective and there are some kids whose needs are so specific that they need to be in another room or near different materials to have their needs met.  The best part about my job has been the flexibility I have to move between the push-in and pull out models.

     I work almost exclusively with math but feel that many of these pros and cons still hold true for literacy interventions as well.  If you are looking for the perspective of a literacy person on this matter, you might want to check out Amy's post over at Eclectic Educating. Amy is a reading specialist who has had experience with both kids of interventions.    

How does intervention work in your school?  What method do you prefer?  Please respond in the comments below! 

Check out these other great blog posts about things you oughta know!  Tell them the Math Maniac sent you!

An InLinkz Link-up

Teach Like a Pirate Book Study Part 1: Passion and Immersion

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Welcome to part one of Teach Like a Pirate Book Study!  It is not to late to join in, so if you are looking for some inspiration for your teaching, grab a copy of the book and join our discussion!  Feel free to leave your discussion in the comments or if you have a blog and want to do a post about it, leave a link in the comments.  

Teach Like a Pirate

Here is the posting schedule

July 12 Passion and Immersion

July 19 Rapport and Ask and Analyze

July 26 Transformation and Enthusiasm

August 2 Part II: Crafting engaging lessons

August 9 Part III: Building a better pirate

I want to start out with these two quotes from the beginning of the book:  

Clip art by Amanda Wittenborn

"Teaching like a pirate has nothing to do with the dictionary definition and everything to do with the spirit.  Pirates are daring, adventurous, and willing to set forth into uncharted territories with no guarantee of success.  They reject the status quo and refuse to conform to any society that stifles creativity and independence.  They are entrepreneurs who take risks and are willing to travel to the ends of the earth for that which they value.  Although fiercely independent, they travel with and embrace a diverse crew.  If you are willing to live by the code, commit to the voyage, and pull your share of the load, then you're free to set sail.  Pirates don't much care about public perception; they proudly fly their flags in defiance."

"We need mavericks and renegades who are willing to use unorthodox tactics to spark and kindle the flame of creativity and imagination in the minds of the young."

These quotes got me fired up about teaching and excited to read the rest of this book.  I love reading books like this in the summer time, I find it is an excellent way to recharge my batteries and get me excited about teaching again.  

Passion

The first section of the book is all about Passion.  There are three great questions that Burgess asks that you are supposed to answer before reading the section.  I am usually the type of person to glance at the questions and go on, but I found these questions to be good ones and in the interest of making a good book study, I answered these in writing before starting this section.    

Within your subject matter, what are you passionate about teaching?  

      I have 2 topics in math that I am most passionate about.  The first is algebra.  I am not talking about that big heavy text book you had in eighth grade.  I am talking about the patterns and conjectures students make starting in Kindergarten.  I am talking about the moment when a student realizes that knowing 8 + 9 = 17 helps them know 17 - 8 = 9.  I love seeing these magical moments when kids get the big ideas of mathematics.

     I also have a slightly unhealthy obsession with fractions.  I think this is because I was taught fraction in such a strict methodical way that I am always surprised and delighted when I find a new way to look at fractions.  I remember sitting in my first math professional development after graduating from college and the instructor told me that her research was showing that kids had 5 different strategies for comparing fractions.  I thought common denominators was the only way!  When I was a sixth grade classroom teacher, I remember waking up one night thinking about how to use the area model to multiply fractions.  I feel like there is always more to learn about fractions and that is exciting to me.

     

Within your profession, but not specific to your subject matter, what are you passionate about?

     I am passionate about seeing kids gain knowledge.  I love seeing that spark kids have when they have worked really hard at learning something and the self-confidence boost they get when they master it.  I love how that confidence can translate into a better attitude, a willingness to work hard and a passion for learning. 

I love the focus on making sure you have identified your professional passion because, "On all of the days when you don't have passion for your content, you must consciously make the decision to focus on your professional passion."  I may be one of the freaks Burgess mentions who is passionate about everything they teach (almost) but I have days where I am just not feeling the love for the content.  When that happens, I need to make a conscious effort to focus on my passion for teaching and seeing student growth.

When you combine your content, professional and personal passions you get an unstoppable teacher!  "Teaching is no longer about relaying the content standard... it's about transforming lives.  It's about killing apathy.  It's about helping the next generation fulfill their potential and become successful human beings.  It's no longer about memorizing fats; it's about inspiring greatness."  Reading quotes like that get me so fired up for the new school year!

Immersion

This section focuses on being present in the moment.  I love the analogy of the swimming pool and the person watching from the sides versus the person in the pool.  As a math specialist, I spend a lot of time in other teacher's classrooms and I think the difference between a good teacher and a great one can be their willingness to jump right in the pool.  Their students really benefit in both engagement and academic success from their willingness to completely immerse themselves in the lesson.  

As much as this section focuses on being present in the moment and making sure you are not distracted by other things, it still shows the importance of sizing teachable moments.  "I'm a firm believer in having structure and definite plans for the direction of lessons, but sometimes things happen that demand a change in direction and a "letting go" of the plan.  The teachable moment is called that because if you wait it will be gone!" Even if it means you are not "covering" the curriculum you are supposed to, it is important to seize these teachable moments!  "At some point in your career you have to decide if you care more about teaching to tests or teaching kids." I know the reason I became a teacher was to teach kids and not to teach to tests! 

Your turn!  What are your thoughts on Passion and Immersion?

I bought the kindle version of this book and have been reading it on my iPad and my desktop using the free kindle app. This is my first time using a kindle version and I am still not sure how I feel about it.  What is your opinion on e-books versus real books?

Guided Math in Action Book Study Chapters 3 and 4

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Welcome to my guided math book study!  It is not to late to join in!  Every week, I will provide the links to past posts so if you are just finding this book study you can jump right in!

July 2   Chapters 1 and 2

July 9   Chapters 3 and 4

July 16 Chapters 5 and 6

July 23 Chapters 7 and 8

July 30 Chapter 9

Guided Math in Action

Chapter 3: Managing the Math Workshop

This chapter starts out with this GREAT quote " We must spend 40 hours a year dealing with students' pencil problems (dull or broken tips, wanting to use the sharpener, running out of eraser, and so on). To solve all these problems ahead of time, just prepare a few hundred sharpened pencils at the start of the year." I love this quote because I have been in many classrooms over the last few years where it feels like 25% of math time is consumed by kids looking for pencils or trying to share an eraser with another student.  Do yourself, your sanity and your class a favor and get a great pencil sharpener,  a few huge boxes of good pencils and spend an hour or two getting them sharpened and ready to go for the school year.  Make it your mission to not lose any precious minutes of instruction time on pencil issues.

The meat of this chapter is the discussion on how to set up your classroom and establish routines and procedures.  Many ideas are similar to those outlined in The First Six Weeks of School and are a great way to set up a responsive classroom situation where kids know the expectations and contribute to a positive classroom environment.  Central to this working well is the idea that you have to teach kids how you want them to behave, treat materials and treat each other.  I love this section's focus on teaching kids to work independently so that the teacher is free to run small groups.  Independence is such an important skill for students to develop and it is important to teach it.  

There are also great ideas on scheduling and setting up for guided math.  It is all about organization and does take some time up front to have materials that you will need prepared and organized in a way that is easy to access them.  I find this is the most intimidating part of getting started with guided math.  There is quite a bit of prep work up front but I feel this really pays off in the long run!  "Staying organized is going to help you keep your sanity.  There is so much going on in math workshop, you don't want to be running around looking for stuff that you need to do your lesson.  Keep your stash stocked!"

Chapter 4: Forming Guided Math Groups

This chapter focuses on the importance of making sure you are meeting with ALL students and meeting them on their level. I love the quote from the beginning of the chapter, "when a teacher tries to teach something to the entire class at the same time, chances are, one-third of the kids already know it; one-third will get it; and the remaining third won't.  So two-thirds of the children are wasting their time."  That is pretty strong evidence that you should be doing at least some small group work in your classroom!  I also like how this chapter emphasizes the importance of meeting with kids below, at and above the standard.  It can be challenging to make sure all kids are getting what they need, especially since so much time is given to kids who are behind to try to help them catch up.  All kids deserve to have teacher attention, even if it isn't always fairly divided.

Depending on your class size, you might have 3-4 groups of kids.  The book does a nice job detailing the different levels of learners you may encounter.  The most important thing to remember is that these groups need to be flexible!  "Guided math groups are organized according to the common needs of a specific group of students in a certain place and at a certain time."  This does not mean they are ability grouped for the year!  The key to all this working is a good formative assessment system.  I feel that if you don't have a good understanding of formative assessment, guided math groupings are not going to be effective.  There are some great books and blog posts out there about formative assessment if you need some help getting started!

I am really enjoying reading this book and discussing it with all of you!  It is not to late to join!

What are your thoughts on this week's reading?  Please respond in the comments below!  If you have a blog and would like to write a blog post about it, leave your link in the comments below.