Who doesn't love a makeover?

If you didn't notice, I've done a blog makeover!  Who doesn't love a makeover?  Have you ever looked forward to something and it didn't turn out quite how you expected (think of all those Pinterest ideas that didn't look quite like the original pin!)?  Well this is definitely NOT one of those times!  The new look exceeded what I envisioned and I couldn't be happier!

I'm also working on making over my classroom.  Not necessarily my classroom decor (although I am making a few changes), but the "culture" of my classroom.  If you've been here lately, you know that I've participated in the "Minds on Mathematics" book study.  The book, and the discussions the other great teachers and I have had, have really made me think about how I've approached teaching in my classroom and why there is need for a makeover.

First, the classroom and lessons, need to be more student centered.  I feel like I do a pretty good job of this at the beginning of the year and then somewhere around November/December I get tired and slip into bad old habits.  The work of the classroom, i.e. the learning, needs to belong to the students, and the only way for that to happen is for the students to do the "work".  A teenager doesn't learn to drive a car by watching videos or someone else do it; they have to do it themselves.

With this in mind, I sat down the other day to pencil out some plans for the first week of school.  On the first day, we see all of our students, but we have some classes for a bit longer than others.  We don't really do "much" on the 1st day except some introductions.  On the second day, I usually go over my expectations and some procedural "stuff".  I have a letter that goes home to the parents welcoming them to my classroom and giving them information about how to contact me.

As I thought about this second day, I had an epiphany.  Why was I going over the letter with the students?  It was the students who needed the information so wouldn't it be better if they read the letter themselves?  So with the math workshop format in mind, the welcome letter, will become the work time for the second day of the school  During this work time, students will read through the letter with their groups and highlight "important" information.  Our "closing" will be going over any questions that the students have.  By doing this, I'm promoting collaboration (an important 21st century skill!), the students learning about our workshop format from the beginning, and I'm sending the students the message that they are responsible their learning.  

I'm really excited about so many things!  Stay tuned for my next classroom makeover blog-i-sode!

Minds on Math Chapter 10 - Sharing and Reflection

Chapter 9 stressed the importance of students sharing and reflecting upon their work.  Again, I felt as I was reading this, that this was something I did fairly well in ELA, but under-utilize it in math.  It is important for students to think about their not only the mathematics they are learning, but their own thinking.

On pages 162-163, Ward Hoffer lists questions to use in reflection.  As I read these questions, it dawned on me that I really needed to compile some of the great lists of questions that Ward Hoffer shares in the book.  So I set out to find my favorite lists.  I wanted to put them in an easy-to-use booklet that I could carry with me as I circulated the classroom.  This is what I came up with...

I'm going to cut them apart and have them spiral bound at an office supply store.  There were so many useful things in this book and I wanted a way to have what I considered to be the "best" tidbits at my fingertips.  

I really liked the rubric that Ward Hoffer included.  For me, this really helps assess explanations and it gives students some guidelines to consider when penning (or penciling) their explanations.  It also makes the assessment less arbitrary and is more useful than a credit/no credit system.

For those of you interested, we will be having a Twitter chat tonight at 7:00 p.m. CST about this book.  Join us #momathchat!

Minds on Math Chapter 9 - Conferring

When I taught ELA, conferring was just something that we did.  It was a common practice to have a quick conference with students about what they were reading or writing, and the conversations were often very informative.  You could tell who was reading and whether or not they student understood what they were reading.  For writing, you discuss ideas with students and help them further develop those ideas.

When I started teaching math, though, it didn't seem as important to conference with students....until I read this book.  As I read, I thought often of my days in ELA and it dawned on me that, just like in ELA, we also teach reading and writing.  To be successful in math, students have to be able to "read and comprehend" a problem.  Students also must communicate (or write) their thinking and solutions to a problem.  With this ah-ha! and Ward Hoffer's book, I came the realization that I was doing my students a disservice by not conferring with them about their math thinking.  

Ward Hoffer offers three steps to conferring with students.  First is research.  Conferring can be used as a tool for "finding out" what students know, are stuck on, are thinking, etc.  Second, conferencing can be used to coach students.  This entails walking a student through a problem without giving them answers.  Third, help the students reflect on their thinking.  

As I think about my classroom last year, I know that I conferenced with students, but usually when the student came to me.  I was not intentional about conferring with students on a regular basis.  I realize I need to change this.  Time will always be an issue.  Obviously some students need more assistance than others, however, even the "advanced" students in our classroom can benefit from conferencing.  After all, we don't want those students to get bored and lose interest.

I think the list of "Conferring Questions" on page 147 will be helpful.  Maybe I'll put some of these lists/reminders together and spiral bind them so that I can have them with me to easily reference.

Good luck to you all as you get ready for the coming year...it's going to be fabulous!

Minds on Math Workshop Chapter 7 - Minilessons

In chapter 7, Ward Hoffer introduces us to minilessons.  A key to a minilesson is modeling thinking as opposed to showing examples.  The think-aloud concept is not new to me, but I'm afraid it's one that I really haven't used since moving to math from ELA (and since moving from elementary to middle grades).  I can't say that I have a good reason for this, it just is.  This chapter, was a good reminder of the effectiveness of think alouds.  

One thing I really took from this chapter was that thinking aloud doesn't just stop with talking.  Part of the think aloud process is illustrating the thinking and annotating the illustration.  Another important part of the think aloud process that I really hadn't considered was the discussion about what she (the teacher) was doing during the demonstration as well as discussion about what the pitfalls might be.  

The list of "lesson" types was intriguing as I often think of a lesson as the mathematical content or process.  Ward Hoffer suggests that lessons can offer direct instruction, revisit findings from a previous lesson, introduce a thinking strategy, modeling a problem-solving strategy, discussing implementation of a specific math practice, revisiting community agreement, discussing the relevance of a particular concept to learners' lives.  This was a pretty comprehensive list that included some things I wouldn't have thought of as "lessons".  This can serve as an important reminder to us all that math is much more than the content in the textbooks and for it to be meaningful to students, they need to approach it in many ways.

Until next time...

  

Minds on Math Chapter 6 - Opening

Chapter 6 is all about the importance of a good opening.  Ward Hoffer suggests that that there are 4 key aspects to an opening:  welcoming learners, activating prior knowledge, setting a purpose for the lesson, and managing homework.  While most of most of the chapter seemed to be common sense, there were a few points that Ward Hoffer made that made me think about the effectiveness of my openings, which honestly, I am prone to skip as a means of saving time.  

Ward Hoffer poses that an effective opener should set students up for success.  To do this, she writes that the problems posed as an opening must be accessible from multiple entry points because they ensure that "everyone can get started, everyone can experience some success, and you can still gather useful formative assessment data."

Two suggestions for activating prior knowledge were presented:  a problem of the day and conceptual conversations.  The conversations stood out to me for a couple of reasons.  One, it's something different than is probably seen in the typical classroom.  Two, the collaboration required in having a conversation would certainly give students an opportunity to activate and pull out those things that students already know.  

I found homework an interesting addition to this chapter.  While it certainly is part of most classroom's opening routing, I wounder how it would really fit into a 5 minute opening.  Personally, I post my homework answers on Edmodo so that students can check their own as they work.  It serves no purpose for students to work problems incorrectly and more often than not if a student knows his/her answer is incorrect he/she will go back and rework it to get it correct.  Students with questions either post them on Edmodo, or ask them at the beginning of class the next day.  (I post answers only and I only accept their homework if they have the work, this keeps them from turning in a sheet with my answers.)  

As an aside, I totally understand the "limited homework" rationale and I often question our "homework Monday-Thursday" routine.  The reality of it is, though, that when students get to high school and college the demands are intense (at least they are in my district...I'll have a junior this year...I know!).  I feel like if we don't prepare our students for the academic and work-habit/time management demands we haven't fully prepared them.

Until next time...

Minds on Math Chapter 5 - Discourse

In Chapter 5, Wendy Ward Hoffer writes about the importance of time spent discussing mathematical content.  She once again reminds us that "students benefit more from solving and then discussing a few problems in depth, rather than completing numerous practice problems."  While this idea was discussed earlier in the book, it was a good reminder during this chapter because discourse, for obvious reasons, takes time and doesn't fit with the "drill and kill" mindset.

As always, I love Ward Hoffer's lists and there were several in this chapter.  On page 75 she lists ways we can invite students to share.  While I have used some of these in my classroom, the one that intrigued me was "explain your vigilance".  Without Ward Hoffer's example (What were some of the speed bumps you encountered when solving this problem?), I might have glossed over this list completely.  What I like about this is that it validates students' struggles.  It says that it's not only okay to struggle, but it's also normal to struggle.  This is important for all students, because on some level, I think if there's no struggle, there's no gain (the no pain, no gain mantra that coaches use).  As an aside, one group of students who I think need to experience this more is the honors students.  (Mine frequently say that math is too hard (mainly because they've never been challenged before).  I explain to the students and their parents throughout the year that if the student get through the year without feeling a little uncomfortable, I haven't done my job well because they haven't been challenged.)  Working through challenges, whether in the math classroom or in sports or in a career, is an important life skill.

Throughout the book, Ward Hoffer shares the importance of withholding correct answers in order to discuss errors.  One of the things I occasionally do with my students when we are looking at homework answers is post an incorrect answer.  Students often assume if it came from the book, the internet, the teacher, or their parents, it must be correct.  They assume that if I'm giving them an answer, it must be correct and so they mark their answer wrong and never question why they got it wrong.  Students who not only catch the error, but justify their thinking are rewarded in some way.  By working with errors, Ward Hoffer is validating student thinking by recognizing that errors aren't something to be afraid of because we learn from them.

An ah-ha for me was Ward Hoffer's suggestion of allowing students to revise their thinking.  I think this is a natural extension of discussing errors, but one that I think I have missed.  Ward Hoffer writes, "an incorrect answer is the beginning of learning; when we maximize the opportunities revealed by our own and our students' mistakes, we model the growth mindset, the belief that we are all capable of overcoming our difficulties and achieving." (emphasis added)  Allowing students to revise their thinking tells them that our classroom isn't a "three strikes and you're out" kind of place.  Just because they have had some struggles, doesn't mean they're out of the game and unable to recover.  When we allow students to revise their thinking we validate the idea that learning is a process.

I'm off to make classroom posters to help facilitate student discourse.

For the kids,

Minds on Math Chapter 4 - Community

I have, for the last few years, attempted collaborative groups in my classroom.  What typically happens is that the groups work for the first semester, but the students come back from the holiday break and are different creatures (I'm not sure how two weeks does that to them!), but when they come back, I have a hard time being patient with them in groups.  Inevitably, my class ends up in rows shortly after returning from the break.

This chapter on community was important for me in a couple of ways.  First, it reinforced what I believe to be true, students learn better in collaborative community groups.  One of the activities that I start out the year helps students see this.  I have the students list all of the Major League Baseball teams that they can think of.  I give them about 30 seconds to complete this.  Of course, no one ever gets them all.  Then I let them confer with their groupmates and allow them to combine their lists.  What they realize is that they are better as a group than any individual was on his or her own.

Second, I took away from this chapter that perhaps my groups were not working as I would have liked because I wasn't intentional enough at the beginning of the year.  Unfortunately, I cannot wave a magic wand and wish perfect groups upon my students!  Building a community not only takes time, but it takes continual reinforcement of group goals and norms.  Building a community requires work:  reinforcing those things that are going well and correcting those things that need improvement.  

One of the suggestions in this chapter that I really liked and would like to incorporate this year is that of individual preparation time.  Wendy Ward Hoffer writes, "learners often succeed best in community endeavors when they have chances to read, write, and think alone for at leas a few minutes before engaging with others."  I often assign tasks and let the groups dive right in.  Ward Hoffer's statement about preparation time makes me wonder how much better my groups might have been if I had given my students this time to think before beginning.  I think this especially helpful for at-risk and special needs students because it gives them a chance to form their own ideas (something I don't think they get a chance to do when groups start immediately because their voices are overshadowed by stronger students).

I'm off to find community-building activities for my first week of school.

For the kids,

Minds on Math Chapter 3 - Tasks

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Finding worthy tasks...

In this chapter of Minds on Math we focus on finding tasks requiring a high cognitive demand.  Ward Hoffer offers suggestions on where to find high-cognitive demand tasks and suggestions for modifying existing tasks to increase the level of cognitive demand.

Ward Hoffer opens the chapter with a vignette about two seventh grade girls each rolling a dice, and determining whether the sum of the numbers was odd or even.  At the outset I wondered why a seventh grader would be concerned about odds and evens.  Even given the fact that they were looking for the odd/even pattern of sums, I thought that was an elementary task.  At one point during the class period, a student asked the teacher what even meant.  The teacher responded to check the list on the board (which said ends in zero, two, four...)  Ward Hoffer's point, I think, is not whether or not this task was appropriate for a seventh grade classroom, rather, she was pointing out that the task did not have a high level of cognitive demand.  The task did not require students to understand what odd and even meant, they just had to memorize or remember that even numbers ended in zero, two, four, six, or eight.

As I read this chapter, I thought about some of the times I've been guilty of this.  Namely, working with formulas.  Our state (Texas) gives students a mathematics chart to use on the STAAR test.  All formulas are shown there.  Wanting the students to be familiar with the tools available to them, too often I tell the students to refer to their mathematics chart and follow the formula.  While I think there are valid reasons for students to be able to use formulas, I think there's also work that needs to be done to help student understand the formulas.

One of the areas that is very procedural (and is a good argument for students learning to follow rules) is order of operations.  We can work with students to see that performing the operations in different orders results in different answers, but at the end of the day, students need to know that there is a specific order we need to follow so that we all arrive at the same conclusion.

So, those high cognitive demand tasks...what are they and how do we get them?  Ward Hoffer says that tasks should have multiple entry points, various approaches, higher-order thinking required, opportunities to synthesize, and justification and explanation (p. 40).  These are certainly important to keep in mind because our current textbook offers very few of these types of problems.

One of Ward Hoffer's suggestions for finding tasks was to modify existing tasks.  She offered an example problem and then modified it six different ways!

• increase complexity
• introduce ambiguity
• synthesize strands of mathematics
• invite conceptual connections
• require explanation and justification
• propose solutions

I loved that she was able to take one problem and change it in so many ways.  My favorite was introducing ambiguity.  Students hate ambiguity and I think this is the one that could be the most fun to work with because it really gets students thinking about all of the possibilities.

I'm off to find some high cognitive demand tasks for my first unit!

Until next time...

Minds on Math Chapter 2

Wow!  That's what I thought over and over as I read through chapter 2.  There were so many things in chapter 2 that left me feeling as if I had been overlooking the obvious for years.  The chapter was about tools, not the kind in the garage, the kind we use (or should be using) in the classroom.

As a former ELA teacher (and self-proclaimed lover of books), Hoffer's suggestion of using ELA strategies in the mathematics classroom was my biggest take-away from this chapter.   Ward Hoffer refers to the strategies as "Thinking Strategies", but the strategies are the same as what ELA teachers are teaching our students to use when they read.  Can you say genius?

All great teachers know the benefits that cross-curricular lessons have for students and teachers.  So why hasn't it clicked until now that we could use the same strategies?  Imagine the time saved when we can refer to what students already know and do and how students can use that to dive into rich mathematical content! Ward Hoffer writes, "These strategies are far more than sentence stems and conversation starters, but rather learned approaches that can scaffold students' independence as problem solvers" (p. 29).  

I am a Texas teacher, and as everyone knows, Texas did not adopt the Common Core Standards.  In Texas we have content standards and process standards.  The process standards include application, using a problem-solving model, using appropriate tools, communicating, creating and using representations, analyzing relationships, and displaying, explaining, and justifying mathematical ideas.  Our task, and a focus in our district this year, is to purposefully incorporate the process standards into our lessons.  In some ways the Thinking Strategies overlap our process standards (i.e.create representations & mental models) and in others, they work hand in hand.

I have started looking at some of the topics that come up early in the school year.  I want to take a look at what specific strategies and process standards I can use with those topics and how to reformat the class so that it fits the workshop model.  So much to do and so little time!  So much for summers off :)

Thoughts on Chapter 1

My biggest ah-has!

To be clear, some of these weren't necessarily "ah-has" as much of a reminder of things we tend to forget as we battle all of the forces pulling at us as we do our jobs.

• The importance of sharing and reflection - I've talked about this with co-workers, and I know in my own practice that when I take the time to do this, I benefit both myself and my students.  Yet, despite "knowing", and even "believing" this, I find it easy to skip due to lack of time.  I am one of those guilty of allowing "learners to work right up to the bell"!  This was a good reminder that this is an important part of the learning process.
• Work time - "The bulk of a minds-on math workshop is devoted to work time."  Even though I know that this is the way it should be, I often find it easier to "manage" my class if I have "control" over it and am the one doing the work and the students are "captivated" by watching me.  Yes, I'm hanging my head in shame right now, but I think we probably all have those classes that just have a difficult time staying on task when left to their own devices.  

What I'm already doing...

• Community - I think my teaching partner and I do a really good job of building community in our classrooms.    One thing I hear frequently from parents is that their child (who may or may not have struggled in math) now finds math interesting and fun.  (Always a good thing to hear!)  For the most part, our grade-level as a whole does a good job with this and I think it really helps the students understand the benefits of belonging to a community of learners.

Next steps...

• Creating more purposeful openings - Obviously these need to be planned....which is something easy for me to overlook, and why they aren't always as useful as they could be.  I find them difficult to plan because there are times during a class period when I think "I want to review this in tomorrow's opening".  Or, where I do want to spiral a skill previously taught and incorporate a more current topic.  Other times, the dynamics of classes vary and what works with one class doesn't work with another, or what one class needs isn't what another class needs.  (It's all so much more complicated than those outside education realize!)
• Work time - I'm so guilty of "rescuing" students who I feel are struggling.  Instead of letting them struggle with the math, I'm too quick to jump in and help (or even worse, lead them to an answer).  I need to work on questions that will help without giving answers.  Once last year, I asked a question that I knew would be a little difficult but at the same time was not out of reach.  My students just wanted an answer.  They left class without one and were not happy when they left the room.  For my part, I felt a little guilty that we ended on that note, but I secretly smiled inside when one of those students came to me before class the next day with the answer!

Can't wait to see what goodies the rest of the book contains!

For the love of good teaching,

Melanie

Exciting new book study

A fellow math teacher posted in her blog that she wanted to do a book study of Minds on Mathematics Using Math Workshop to Develop Deep Understanding in Grades 4-8. by Wendy Ward Hoffer.  Excited about the title, I quickly went to Amazon and, after reading the description, I couldn't wait to get started.  The premise of the book is that the reader's workshop model that is used in so many ELA classrooms, can also be used in the mathematics classroom.  Furthermore, many of the reading strategies that are taught in reader's workshop can be used in by students in math to take students beyond correct answers and to deepen their understanding of math concepts.

I am truly looking forward to getting started with this book study and can't wait to see how I can incorporate this into my classroom in the fall.  I know this is really going to have a profound impact on how I approach my class next year.

If you're interested, join us by clicking the link to the right.  We'd love to have you join us!

For the love of good teaching,

Melanie