Minds on Mathematics - Ch3, Tasks {Book Study}

Chapter 3 of Minds on Mathematics considers the tasks that we assign to our students and seeks to answer the following question:

The opening story of seventh graders rolling dice, determining the product, and if that product is even or odd seems below grade level. Grade level aside, Hoffer refers to the task as shallow math where "learners are expected to memorize algorithms and apply them, complete hunt and copy exercises, plug and chug numbers without considering the questions: So what? Why are we doing this? What does this number or equation or concept really mean?" (p. 33-34). Hoffer suggests that we should move from shallow math to deep math.

As in chapter one, Hoffer tells a story of spending an entire lesson on one problem. While the story she tells of the deep discourse her students had with a task on parabolas, seems like a math teachers dream, I am still a bit skeptical. I understand the idea of moving from concept coverage to student understanding. I'm kind of at my own "yeah, but..." here. Where do you find these engaging, thought-provoking tasks? If you spend the entire class period only exposing students to one task, how are you sure they can apply their understanding on a different task that addresses the same learning? If every student doesn't understand after the one task, when does remediation take place? Now, though, I feel like I am missing the point. I'm forgetting about the minilesson and the reflection which I am sure are integral parts of the overall workshop/lesson. I need to keep in mind that this chapter is only defining tasks, not necessarily giving us how to use the tasks in the context of math workshop.

So, it is suggested that shallow math, as well as deep math, can be found in the resources that we already have available to us. "...the really juicy tasks are often printed at the tail end of each chapter, and too often we 'run out' of time for them" (p. 39). Those good tasks are also often the extension activities. In this respect, teachers have to be willing to break away from the prescribed order of things and pick out the ideas that students really need to understand. 

A few things come to mind for me here. In Texas, our math standards have been labeled as either readiness or supporting. Readiness standards make up about 30% of the curriculum, but almost 70% of the state test. If students understand the readiness standards, they should be able to complete anything related to the supporting standards. Therefore, when looking at big ideas of a unit, I have started to look at how readiness and supporting standards are related and relate them to an enduring understanding that is essential for students to learn.

Another thing I have considered recently is essential questions. I know this is not something new, but it is not something I've practiced in the past. I have started to try and flush out what do I really want my students to be able to know, understand and do. 

• Know being memorization type items like vocabulary and formulas
• Understand being those big ideas and essential questions that I want students to have the ability to apply in new situations
• Do are the processes

The "know" and the "do" are easy (which is why I think many teacher teach the way they do). The understand takes considerably more time, thought, and effort. To help me think more about what I want my students to know, understand, and do, I've adapted a unit overview form I found by Bill Ferriter that I feel does a great job of giving student and idea of what they are to learn.

You can read more about what into the making of this form here. And maybe you want this in word format so that you can edit, so here's a link. Hopefully, I haven't gotten too far off track, but I'm really trying to think understanding vs. coverage.
Hopefully, you made it through my rant and slightly off-topic thought process. Now, back to the chapter at hand, the tasks...Hoffer says that when the tasks we have lack the deep math, we have three options:

• resequencing existing tasks
• modifying existing tasks
• finding better tasks

I automatically went to finding and creating better tasks, but Hoffer offers places we may find them. I like the idea of using the challenging tasks that can often be found at the end of a unit or in the extension materials to launch a unit rather than an extension at the end for those students who finish their work. Hoffer also suggests setting a small goal of one to two tasks and to divide and conquer this with teachers on your team. She also provides ways to modify tasks you've found that aren't meaty enough, by increasing complexity, introducing ambiguity, synthesizing strands of mathematics, inviting conceptual connections, requiring explanation/justification, or proposing solutions.

I love blogging as I'm reading rather than at the end. Now, as I read the "Yeah, buts..." at the end of the chapter, I see that all my thoughts are there...

• Time is always an issue so start small.
• Not all students are ready for high cognitive demand, so offer ample scaffolding.
• How do you assess with one or two problems...these problems don't stand alone within the workshop.

I'm really looking forward to getting to the practical examples and logistics in the chapters to come.

Want to read what other teachers think about this book?

 Check out the book study link-up hosted by Sherrie @ Middle School Math Rocks!

Minds on Mathematics - Ch2, Tools {Book Study}

Speaking of tools, I'm super duper excited about my new pencil sharpener! 

Maybe you've seen the Classroom Friendly Pencil Sharpener! It's not quiet like I've seen some sites suggest, but it definitely gives the sharpest point on a pencil that I have ever seen! I lucked up and found this baby on a teacher swap site for 10 bucks! 

Once I bought it, I knew I had to make cans for sharp and dull pencils. I got the labels from Donna @ Peace, Love and Learning and the polka dot pails from the clearance aisle at Walmart.

Okay, on to the tools referenced by Wendy Hoffer in Chapter 2 of Minds on Mathematics. 

These tools are "practices, skills, and strategies best suited for support learners" (Hoffer, p.21). And we, as teachers, must "explicitly offer instruction on these processes with the context of content learning" (p. 21).  More specifically, these tools are:

• Common Core Standards of Mathematical Practice
• 21st Century Skills
• Thinking Strategies

Hoffer opens the chapter with asking a student how he approaches a word that is unfamiliar when reading. The students offers a slew of strategies to figure out the unknown word. When presented the same question in a math problem, the student only knows to start over. Hoffer sass we have to teach students strategies that are transferrable to new situations...encouraging students to develop understanding. 

In the next few pages, Hoffer shows what teaching the processes may look like in the context of the minilesson, work time, and reflection. Using the process standards from the Common Core, there are explicit examples of how to teach students to think. While it is plainly spelled out, we still have to figure out what that looks like for us. I teach in Texas, one of the few states that has not adopted Common Core, but I still found pages 22-23 helpful and I think many of the examples provided are great ways to teach students to think and process material. I can see how creating opportunities for discourse, scaffolding students' independence, allowing ample work time, modeling precision, and welcoming many approaches (just to name a few) can encourage thinking and problem solving.

Still...I see these words and I think I know what they mean in the context of a math lesson, but it really takes planning. While thinking comes naturally for me, it may not for my students. It is hard for studnets to know the thinking that goes into solving a problem unless I explicitly tell them. It's hard to do this "think-aloud" strategy, but it is crucial for students to hear the process going on in my mind. Otherwise, I am just solving a problem and students know none of what went into it other than the steps they see on the paper.

I appreciated the next section on thinking strategies, which really paired down on the plethora of examples provided in relation to Common Core and 21st century skills. Thinking strategies have come from reading research and proven to be helpful across content areas when students are trying to make sense of new information. These thinking strategies are:

• asking questions
• determining importance
• drawing on background knowledge
• inferring
• making mental models
• monitoring for meaning
• synthesizing

On page 27 is a great chart with definitions of each and what students and teachers may say that would use the particular thinking strategies.

...if we take seriously the imperative that students need tools for independent problem solving, not just answers, these three lists [Common Core Standards of Mathematical Practice, 21st Century Skills, and Thinking Strategies] offer us a wonderful array of implements we can hand over to learners as tools to assist them in leveraging student understanding of content for themselves. (p. 29)

We have to teach students the strategies so that they can select and use them as needed. The lesson plan template I referred to making in my review of Chapter 1 has just expanded. Not only do I need to be thinking about what the teacher will do and what students will do, but now what thinking strategy I will offer and how that will be taught. I see this as a "yeah but" and Hoffer states that we don't have to do it all at once. Just consider one math standard at a time and one thinking strategy that can be paired with it when you teach it. Seems feasible to me...I need to not only teach the math concept, but a thinking process that students can use on their own as problem solvers.

Want to read what other teachers think about this book?

 Check out the book study link-up hosted by Sherrie @ Middle School Math Rocks!

Minds on Mathematics - Ch1, Workshop {Book Study}

I'm super excited to be joining a few other math teachers for a book study this month. I've been reading Guided Math by Laney Simmons, but so many of the idea expressed seem to be geared towards elementary and self-contained settings. I was stoked when I read a post by Sherrie @ Middle School Math Rules. She found a book that is about math workshop in middle grades. I immediately scrounged up my duckeys and purchased the book a few days later. So, I'll be joining in and posting my thoughts of the book Minds on Mathematics by Wendy Ward Hoffer. Hoffer explains:

The primary aim of this text is to describe how teachers can organize theirs classroom instruction as workshops that honor the primacy of student thinking, the imperative of student understanding, the key role that classroom discourse plays in achieving both. (p. xviii)

Before I get to Chapter 1, some things stood out to me in the introduction. The statement that "math is memorizing" is one of the reasons Hoffer listed as a "reason we don't get math." She goes on to say:

Although there are indeed math facts and theorems worth committing to memory, students need the gifts of time and space and coaching to construct for themselves an understanding of why a particular algorithm works. (p. xvi)

I love how she refers to giving students time, space, and coaching as a gift. I know my students don't see it that way, but they need to struggle through some things so that they can take ownership of the content, developing an understanding and not just a process.

Another "reason we don't get math" is the belief that "math ability is innate." The book Mindset by Carol Dweck is referred to in this section. I am amazed how much I have seen this book referenced since I read it last year. Hoffer syas that to battle the fixed mindset, we must teach students the growth mindset and some ways that can be done are by "praising motivation and effort, rather than celebrating 'smarts' as some thing intrinsic" (p. xvii).

Chapter 1 is titled Minds-on Math Workshop.

This is a phrase I [Hoffer] coined to describe math learning experiences hat require students to draw upon their intellectual resources as critical thinkers and problem solvers, rather than simply follw a given algorithm; require learners to stretch and think in new ways, rather than rehearse known skills; invites students to communicate their ideas with others, rather than secretly to the teacher, and as a result, offer learners opportunities to attain deeper understanding both of mathematics and of themselves as mathematicians. (p. xvii)

The chapter begins with the problem this chapter seeks to answer and a postulate of how minds-on workshop can be the solution.

Often, as a teacher, I have a hard time allowing students the time to struggle through problems. In an effort to save them from their struggles, I've jumped in answering questions, explaining problems, and guiding students way too much. I'm sure I'm not the only one and that was confirmed in this chapter. Hoffer states that she had to to learn not "to let students do the work of think which led to understanding" (p. 2).

Hoffer states the beliefs that guided her evolution into minds-on workshop:

• Students are capable of brilliance.
• Understanding takes time.
• There is more than one way.

Time seems to be the one constraint that all teachers complain about when it comes to doing something new. Hoffer states there are other constraints such as "curriculum, unit plans, school schedules, department expectations, district and state tests...and the list goes on" (p. 4). I have always been willing to try new things and like Hoffer feel that if students are learning and performing, there are not too many administrators that will object from me trying something different in order to increase student achievement. The focus of minds-on math workshop being "understanding" and not "covering." The keys aspects of workshop are:

• challenging tasks
• community
• collaboration and discourse
• conferring

Book Study Discussion Questions

1. What were your biggest ah ha moments in this chapter?
I need to do less talking and more listening and allocating classroom time accordingly. (p. 5) The idea of me as a facilitator is not foreign to me, but I do not think I do a good job of it. I had not thought that one of my main roles as a facilitator is allocating classroom time appropriately. Hoffer suggests that classroom time should be allocated as the picture shows below:

I can honestly say that this is not what my class time looks like. I imagine that most days, my "minilesson" takes up at least half of the class period, not a minilesson at all. The statement that "those doing the most work are doing the most learning" (p. 5) stood out to me. I can definitely say that I've learned lots, and probably to the detriment of my students' understanding of math.

2. What components of math workshop are already present in your classroom?

Community. I remember looking at a district-provided pacing guide a few years ago and the whole first week was filled with teambuilding activities. I did one day of that, and got straight to the math. This past year, I finally understood the importance of community. Community was a big part of our differentiated instruction focus this past year. I think building community in the classroom made student more likely to take risks.There were other benefits, but I was so happy to see students trying hard, making mistakes along the way, and trying to learn from those mistakes. They were willing to talk about their mistakes with other students and discuss them with the entire class. They didn't shy away from shame of being wrong, but embraced it as a part of learning. I have been thinking a lot about more ways to build community in my classroom this coming school year. I hope to build on what I've done.

3. What are the next steps for planning for math workshop in your classroom this coming year?

I want to be mindful of how I allocate classroom time so that my students are doing the work, therefore doing most of the learning. Hoffer offers a lesson plan template on p. 17 that breaks the day into opening, minilesson, work time, then sharing and reflecting. I think the more important part of that template is that within each section there is space to detail what the teacher does and what the student does during each part of the workshop. I think focusing on what students do will be easy, but I need to be more mindful of my role during each portion.

I am also looking forward to the chapter on conferring. "Conferring describes a particular sort of discourse that takes place between a teacher and student focused together around understanding a concept" (p. 7). I instantly think of a structure for this and how I'll record it. I'm sure I'm probably trying to be too structured and it's as simple as having conversations with students and assessing through those conversations.

Alright, I'm starting late on the book study, so it's time for me to read chapter 2.
Want to read what other teachers think about this book? Check out the book study link-up!

{Monday Made It} VistaPrint Frenzy

When I saw a Groupon for $70 of VistaPrint products for 17 bucks, I immediately started building items that I've been wanting for my classroom! I didn't go too crazy, but here are the items I ordered.

My first purchase idea comes from Shae @ Kindergarten Cupcake Crumbs. On orientation night, she had cute litte gifts for her parents.

Source

You can download these tags for free from Shae's TpT store. I'm not completely positive that I'll do this, but I am very tempted. I imagine that lot of 6th grade parents will attend open house since it's their child's first year in middle school. So, I went ahead and made a similar tag using business cards from VistaPrint. I think it would be a great last stop during my open house stations I hope to do. For an idea of what I mean, check out this post by Kim & Megan @ KinderGals. Of course, I'll be making open house stations appropriate for a 6th grade class.

I hate to admit it, but if a parent doesn't have email, I'm horrible at communicating. After reading a parent communication post by Tina @ Drawing on Math, I was encouraged to make these simple postcards and I hope to send notes of kudos and concerns home to parents.

I always have trouble with allowing students to use the restroom during class. I imagine that 6th graders will need to go more than my 8th graders who I rarely let leave the classroom. I saw a teacher who used a punch card to allow students three bathroom passes per grading period. Thanks to Mrs. Hester's Classroom, I'll be using free VistaPrint business cards for my restroom passes. Each edge of the business card will be for a different quarter i.e. left side will be hole punched during quarter one, the bottom during quarter two, etc.

This Facebook Like stamp is courtesy of Sarah @ Everybody is a Genius. You can head over to her blog to get the picture I used to upload and make this small self-inking stamp.

Source

I also ordered a small self-inking stamp that says "Checked for completion only," which was free!

I really want to send home a brochure to all of my students' homes before school begins, but all the information provided is on my classroom website. I really want to promote the classroom website this year. I've decided that instead of getting brochures printed, I am doing magnetic business cards. I figure they have more chance of not being lost if they're magnetic and parents/students will have my contact information and website at stuck something metal (hopefully the refrigerator or a file cabinet). I'll include these in a welcome letter that I hope to send home before school starts.

I'm super excited about these items and can't wait for them to be delivered!

What items have you purchased from VistaPrint for use in your classroom?

Currently July

I'm link up with with Farley at Oh' Boy 4th Grade for the monthly Currently post!

A few explanations:

Loving - I just recently started meal planning using eMeals.com. It's awesome! I love the recipes that are provided and the app makes my weekly grocery shopping trip so easy. You can read more about my experience withe eMeals here.

Thinking - I've been non-stop thinking about next school year and working on little projects, which I plan to share on the blog soon. But, I seriously need to stop and enjoy the summer a bit!

Wanting - I'm joining in on a book study with Sherrie @ Middle School Math Rules and my book is finally order and on its way! We're studying Minds on Mathematics by Wendy Ward Hoffer. I'm excited because this book is about using math workshop at the middle school level.

I'm also excited about my new personal blender that I ordered. I already have a Magic Bullet, but I'm thinking this Oster My Blend will work well since most of the time I make Smoothies, I'm on the go! I love how the blender cup has a lid. I bought an extra cup too!

Ooohhhh! And I just remembered that I hav ea couple of VistaPrint orders on the way too! Can't wait to share...

Okay, I think all the others are self-explanatory! Head on over to the link-up to see more Currently July posts...

New Classroom...EEK!!!

I am super excited and super overwhelmed about my new classroom! I can't believe I have a room with windows and it's so large! Today, I dropped by school to drop off some things to get them out of my house and to possibly do a little cleaning while I was there.

To my surprise, all the furniture was along the walls and the things I had already brought to school were staked on top of cabinets and desks. While, I didn't get any work done today, I am excited about how it looks like a blank slate (other than the stuff the previous teacher left in the cabinets and on the shelves).

Window & a SMART Board...Woot!

...and another window! Woot! Woot!

I've already shared my classroom decor inspiration once before. If you haven't seen it already, check out this post! And I can't wait to give you a classroom tour once I have it all set up!

{Monday Made It} Teacher Toolbox

So, this teacher toolbox has been all over Pinterest for the past year or so. While, I loved the idea from the moment I saw it, I was not compelled to make one because it looked too tedious. That is the furthest fromt the truth. This project took me about 20 minutes and $20 and I'm so glad I did it!

I bought the Stack-On 22-Compartment Storage Cabinet from Home Depot. I'm not going to post directions because you can find them multiple places. I used the directions provided by Leslie @ Jack of all Trades and printed my labels from a free template provided by Elizabeth @ Fun in Room 4B. I used scrapbook paper that I already had at the house and inspired by my current classroom crush from Melanie @ Inspired In Style.

I debated on painting the frame of the toolbox and I'm glad I did! Here's the final product!

As I'm cleaning out and packing up, I've been dropping things in the appropriate drawer of my toolbox and it makes me even more excited about this project.