Building Mathematical Comprehension Chapter 2

Mathematical Vocabulary, that's the focus of Chapter 2 of Building Mathematical Comprehension.

There are several ideas on graphic organizers and some bulletin board ideas offered in this chapter.  To be honest, I didn't do as well with vocabulary this last year as I had in the past.  As I reflected on the year, vocabulary building and instruction was an area I let slip.  I know how important it is to teach proper vocabulary to students, especially in mathematics.

One thing that I think was very helpful to me was a professional development where we collaborated vertically with the grade level teams below and above us specifically in the area of vocabulary.  We discussed the vocabulary that was currently being used and then suggested vocabulary we'd love for the grade level below us to begin implementing and using.  This was very eye-opening to my team as we spoke with the 6th grade team.  We learned that there were some key vocabulary terms that if we used in 5th grade, would be tremendously helpful to students in 6th grade as they deepen their level of mathematical knowledge.

I would strongly encourage you to get with the grade level teams ahead of, and behind your own and have a vocabulary conversation.  It can be informal and take just a few minutes.  You might be surprised at what you discover either about your own instruction or the instruction that might be happening before your students arrive in your classroom.

I think it's extra important for primary grade teachers to use correct vocabulary.  As a first grade teacher, I was certainly guilty of using "simple" names for math terms because I thought the true vocabulary words would be too difficult.  I soon realized that if taught correctly and used over and over, young students can understand the vocabulary just fine and it sets them up to be more successful in the future.

One of my summer tasks is to create a template/master of a student interactive math notebook to guide me through next year.  Vocabulary will be a strong part of that notebook.

How do you make sure your students get explicit math vocabulary instruction?  Be sure to check out the other posts on Chapter 2 linked up below.


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Notice and Note Post 10: Contrasts and Contradictions

Heather at 2 Brainy Apples did a great job of sharing the ideas from Notice and Note: Contrasts and Contradictions and Aha Moment.  I wanted to share with you my reading notebook entry that I planned for my students.  To help me do better with notebooks this next year, I'm planning entries and writing them down myself.  I realize that they may end up a bit different when I actually teach them, but they'll be planned and I'll have a good idea of what will be helpful for the students.  

Two page spread of C&C notebook entry.

I started with an overview entry so students will have the main idea of each of the signposts in their notebooks.  I included a section briefly explaining what the signpost is, then the question that should be asked.  I also included a sentence connecting the signpost to comprehension strategies. 

Left side of notebook.

The second section of this notebook entry is the responses for the lesson outlined in this chapter based on the short story Thank YOu M'am by Langston Hughes.  I didn't want to waste half a page, so I just sectioned it off with a colored squiggle line.  The lesson basically stops 4 times to ask the question " Why is the character doing that?"  In my notebook, I wrote the responses I had at each stop.  Students will include their own responses as we move through the lesson.  

Right side of notebook with a peek at the text. 

Part of the lesson includes having students mark in the text.  I debated on whether to include the text in their notebook, but finally decided to include it.  I wanted the text there for reference since this was an anchor lesson.  When students go back to remind themselves of Contrasts and Contradictions, they'll have the text as well to see how the signpost worked here.  So, I just folded the short story in half and glued it in along the top edge of the back page.  

Right side of notebook under the text glue in. 

Since this signpost focuses on character, I decided my next mini-lesson would be on characters.  I'm debating whether to teach this lesson before the signpost, we'll see in August,  The character cut-out and page idea is from the Reading Notebook by Nicole Shelby.  I also have her Language Notebook set that I'll be using in writing lessons throughout the year.  

I'll continue with my notebook entry for Aha Moment in the next post and link it here when it is live. How will you be teaching your students about Contrasts and Contradictions? 

Teach Like a Pirate: What's in it For Me?

This section of Teach Like a Pirate is all about answer the age old student question... "What's in it for me?" Dave Burgess offers 5 hook types to help answer this question for your students.  Here are the five hooks and how I have either used them in my classroom or see myself using them as I plan for next year. 

1 - The student hobby hook: Get students interested by using hobbies and interests that appeal to them and connect with the material being taught. I'd like to get to know my students better in the first couple of weeks of school.  I was crushed last year when it took me until January to know that a student had lost his father the previous spring.  That would have been super important information to know in September! I realize that some students and families aren't going to be super forthcoming about things like this, but I'm thinking that a combination of an interest/get to know you inventory and an individual interview with each student at the beginning of the year will give me a great start.  We do reading benchmark assessments at the beginning of the year and I'm thinking this would be a great opportunity to add a little personal interview conversation with each student.  My assessments will take longer to get through, but I will know my students better.

2 - Real world application hook: Show students directly how knowing this content will be helpful to them in their life. This is a tougher one for me.  Not everything I have to teach students will be helpful to them in their life.  I try to connect it as much as I can, but sometimes I have to look to means of engagement in other hooks.

3 - The life-changing lesson hook: Touch students in a way that changes their lives.  It might change their feelings, perspective or reflection on themselves. This works really well for me in our literature and history lessons, especially when we discuss times of discrimination.  The stories of slavery and genocide and escape and hiding that riddle U.S. history really touch students and give them new perspectives and cause to reflect.

4 - The student-directed hook: Get student buy-in and interest by allowing student choice. I try to give students choice within "have-to's". It might be required that students complete a science project, but what they choose to do is completely up to them.  I give choice constrained choice in reading when students choose their literature circle books from several options.  The leadership team at my school read the book Drive this last year.  Much of the ideas in that book focus on motivation through choice.  I think the thing to remember about choice is that it doesn't mean free for all and choice can be had within parameters.

5 - The opportunistic hook: Use current events, trends, fads, movies or music to grab student attention and connect to relativeness. I LOVED the idea with this hook to post pictures of current events with a corresponding QR code.  When scanned, the code would lead students to more information about the event and/or topic.  Technology combined with what interests students is sure to engage.  I love this idea and plan to use it not only for current events, but the historical events we are learning about as well.  Students will be hooked by the picture, code and information they learn.

Reading in the Wild Summer Book Study Chapter 1

I'm also linking up with the Reading in the Wild by Donalyn Miller book study today.  Since this is the first time I'm linking up, I'm going to share my thoughts and reflections on all of chapter 1.  To see the schedule and read the posts from last week on the first half of chapter 1, see the book study landing and information page here.  It's hosted by Catherine at

Reading in the Wild is the perfect companion read to Notice and Note.  Notice and Note is all about helping students understand and comprehend the text and Reading in the Wild is about building students as readers; a perfect pairing.  I really appreciate all of the experience that Donalyn shares.  It's all about how it's worked for her in her classroom and she's not shy to admit that it might work differently for other teachers.  She shares examples of the forms she uses and blank ones, however she encourages teachers to adjust the forms to fit their style and needs.  This first chapter concentrates on noticing student reading habits and supporting students in developing better ones when needed.  I'm thinking that a reading inventory might be good for my students to do around late October and again maybe in February.  It would be great to compare the differences over time.  Donalyn suggests perhaps doing this in the spring, but I fear that's too late for students to recognize some patterns about themselves as readers.  In October, we're established enough in routines and expectations that I think it might be a good time to inventory, reflect and make some goals. 
I loved the idea of the reading time observation.  Making it more concrete by recording observations is just what I needed to hear.  I feel like I do a lot of anecdotal observing and assessing, but it would be so much more helpful to me to record it.  I've gotten away from that and this was a good reminder to me, not only for those I suspect of being fake readers, but in all aspects of my classroom and teaching. 
I also had an aha when Donalyn shared how she worked with "Nathan" after observing him.  Not only did she talk with him about specific ways to change and improve, they wrote the goals down.  Again, writing it down is key.  She says, "With students who struggle to complete books or set attainable reading goals, writing page goals into their planners or reader's notebook holds them accountable and helps them see that they will finish a book if they read a little bit each day."
She also validated my plans to have students respond and write about their reading using edmodo.  She mentioned doing exactly what I was planning to do, which really helped me know that I was going in the right direction.  
The final section of chapter 1 is about scheduling.  She shares her schedule and some additional options.  Again, she really iterates that you have to create a schedule that works for you.  Here's the schedule I had last year, including my language arts time.  I'll post about my schedule for next year when I have that figured out.  It all depends on when my principal schedules specialists and intervention times for us. 
Schedule in my classroom: 
9:00-10:10 Guided Reading and Literature Activities 10:15-11:25 Math 11:30 Specialists (Rotated among P.E., visual art, library, math extra, drama/music) 12:00 lunch 12:40 Shared reading (lesson from our basal text, Journey's) 1:10 Read Aloud 1:20 Writing 2:00 Recess 2:15 Science / Social Studies 3:15 Dismiss
What is your basic daily schedule?

Teach Like a Pirate: Ask and Analyze

Welcome to Teach Like a Pirate.  A book study on the book by Dave Burgess.  This section, Ask and Analyze Questions, is all about how to use questioning to steer yourself as you plan and to engage students as you teach.  

Each week as we're studying this book, there's a twitter chat on the chapters that are the focus of the week. Last Monday, we chatted about this section.  You can join us with the #tlap2014sbs tag on Monday, Wednesday and Friday of each week.  Usually around 9:00 Central Time, but check twitter for exact time as each host chooses the time that works for their schedule.  During our chat on this section, these are the questions I asked:

• What was your reaction to those six words: "It's easy for you, you're creative."
• What questions do you ask yourself as you sit down to plan to help you include creativity?
• Where/how do you record your ideas? You know the ones that come to you in the shower and dissppear when you're drying off.
• How do you reflect on and improve your lessons/teaching?
• How do you incorporate your interests/hobbies into your teaching?

The second question is the most difficult for me.  I'm going to start asking questions like: 

• How can I incorporate any of the "the arts" into this lesson? 
• How can I incorporate technology that will enhance the lesson and engage students? 
• What is the best place for this lesson? 
• What question or problem can I pose to students that will get them conversing on topic to come to an answer or solution?

These questions will help me find more creative ways to excite and engage my students in the lessons I plan.  

In addition to asking these questions as I plan to incorporate Genius Hour in my classroom this year.  This is a way to allow students to explore and learn about their own passions.  What better way to engage and excite student than to let them choose a topic to learn more about or an area in which they want to improve.  You can get some information about how to implement this in your own classroom here. 

There's so much I want to do this next year, I'm working on letting some things go so that better things can be let in.  Head on over to

to get her thoughts on the Transformation section.

(Actually, head here to get the rest of this weeks insights.)

Share your thoughts.  I'd love to hear your reactions and thoughts in the comments of this post or link up with us.  Please consider joining us on twitter as well. #tlap2014sbs.

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Notice and Note Book Study Post 4

Welcome to part 4 of our book study.  Brenda at Primary Inspired wrote about Chapter 7: Do Text-dependent Questions Foster Engagement? and I'll be focusing on Question 8: Must Everyone Read the Same Book? I love the short answer that the authors give of: "...yes, at least from time to time."  

I read books with my students in a variety of ways.  We begin the year with a whole class novel.  This allows me to model and teach all the students how I want them to respond in their notebooks and to introduce comprehension strategies, etc.  I'm excited to add teaching the Notice and Note signposts to this beginning novel.  I'm planning to use the book Maniac Magee this year.  Last year I used Witches, but a 4th grade teacher used it as her end of year book and I just couldn't bring myself to start with a book many of them will have ended on last year.  My teammate also does a class novel in December and we all do one again in May.  I think I may add the December class novel to my plans as well.  

We all read the same text daily from our text, Journey's.  We term it shared reading in our district and the point is for every student to be reading the same text together.  They are grade level so every student, regardless of reading level is exposed to grade appropriate level and instruction.  This is the time I introduce sills to the whole class.  We discuss comprehension and reading skills at this time.  This is also the time I do some close reading with our basal story.  It is my "to students" time of reading.

After the first class novel, students start literature circle groups.  I choose 6 books, usually on a similar theme.  I give a book cover intro to the class and let students choose.  I only allow 8 in a group and usually start with my lowest readers so I can direct them to the books that are better suited to their levels.  Once all 8 in a group are taken, students coming after have to choose a new book.  Students who are disappointed they didn't get their first choice are often pleasantly surprised at how much they end up liking the book they get "stuck" with.

Then I have my guided reading groups, I usually choose shorter texts or articles for this instruction so we can focus on comprehension skills, close reading and fluency. I also try to do a lot of non-fiction.  They get their novels and fiction in literature circles and choice reading.

I have a decent sized class library and students are always expected to read if they finish an assignment or feel like they have nothing to do.  Of course I'm always looking to build my library, but my students seem to find some great treasures there and for the most part, they do choose to choice read when they have extra time.

I'm going to work more on the idea of becoming a community of readers this next year.  I'm planning to have each literature circle group comment and converse in an edmodo group about their reading sections each week to help them be better prepared for the group conversations on Friday.  I'm also planning to participate in the Global Read Aloud Project.  You can find more information about joining that here.  I'm looking forward to connecting with classrooms from around the world who are all reading the same book.  We'll be reading The Fourteenth Goldfish by Jennifer L. Holm.  It's a brand new book coming to print in August.  You can view and purchase an advance copy of it by clicking the cover below.

I'd love to connect with any classes that decide to read along as well.  The other choice that might be appropriate for fifth grade is One for the Murphys by Indy Mullaly Hunt.  I understand that this one is a little more serious in nature with more heavy themes.  I didn't think that was what I wanted to read near the beginning of the year.  If you're interested in looking at this one, click on the cover below.

I did get the book though and will read it myself and consider it as a read aloud later in the year.

What is your way of balancing that everyone in the class gets some experiences all with the same book while still providing choice and accommodations to meet everyone's learning needs? Please add your comments or link up with us below.

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Notice and Note Book Study Post 3

Welcome to Section 3 of our book study.  I spent yesterday at a state organized professional development focused on supporting teachers in implementing the common core in English Language Arts.  I was so excited to share how wonderful Notice and Note is and and some insights that pertained to our topics that have come from my learning by reading this book.  I get to spend the next three days in PD as well.

Since it's nearly midnight as I'm writing this and I have to get up to attend more PD tomorrow, I'm going to make it short and sweet. I'm sure you'll gain some great insights from the other participants who link up or leave comments.  

Question 6: What is the role of talk?

I marked on page 29 the sentence "Authentic questions, by contrast, are questions for which you really don't know the answer." The best conversations we've had in my classroom have revolved around authentic questions.  Students return with their own questions, and answer and question one another.  Unfortunately, most of these happen unplanned when a question pops into my mind spurred by a reading or comment from a student.  Purposefully planning such questions would probably be more meaningful and would make them occur with more frequency. 

Question 7: What is Close Reading? 

In the PD I'm attending, we discussed what close reading is.  Many teachers want a formula or outline to follow. Then they can say, I did such and such, therefore I'm going close reading.  Close reading is more than just an outline to follow.  I think a term that might better describe it is deep(er) reading.  It's what I call looking more closely at the text in my classroom.  I love this sentence on page 36: [Close Reading] "It should imply that we bring the text and the reader close together." It's not a step by step, formulated process.  It is reading several times, for different purposes each time with the ultimate goal being to bring the text and reader together.  Additionally, the repeated readings don't have to be of the entire passage over and over.  You can purposefully choose specific sections to drill down into and examine closely. 

Please join us by linking up below or commenting your thoughts on this section.  Late to the party? Visit here to see the schedule and all the details. 

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100 Minutes...Chapter 5

I have loved this book, 100 Minutes: Making Every Minute Count in the Literacy Block, so much.  It has validated much of what I already do and has given me some ideas and things to think about as well.  I hope you have been reading along with us as well.  If you missed chapter 4, you can read about it here.  If you need to start at the beginning, start here: 

I wanted to host this chapter because honestly, writing instruction is one of my personal weakest areas.  So, I signed up for Chapter 5: Writing Around the Literacy Block to selfishly help myself.

There's so much within the scope of teaching writing that it can be overwhelming.  Where to start? What to teach? How to teach it? How to grade it? When?

I realized as I read that I need to start with the basics. For me, the basics are good, thought-out, direct instruction lessons on writing topics.  This is where the heart and base of students' writing improvement lies.  Although often the more a student writes, the better he/she gets, it is not always true.  And, with instruction based on what students need, improvement is nearly guaranteed.

I love the quote from Nancie Atwell on page 74 about needing to ask ourselves how we get students to take charge of their own thinking and writing.  Her answer is through direct lessons.  Donohue mentions her frustrations with students asking about low grades and not taking responsibility for their learning.  She says the solution to that problem is "beginning with the end in mind."  During lessons, the teacher demonstrates and instructs on expectations for a particular style or assignment.  Students work together and individually on writing that, through revision, meets the criteria that has been set together.  I think most of us have been taught to always give students the expectations for any assignment or behavior, but this goes a step further to show and work with students to set that expectation and example.  Then, students slowly move to independence.

My goals for writing instruction next year include the following:
1. Become familiar with many mentor texts and their best uses in teaching students and acting as exemplars.
2. Plan keystone lessons that students will need throughout the school year based on our scope and sequence.
3. Plan lessons that correspond to difficulties I see in students most years.
4. Review student writing throughout the year as we work together and plan lessons based on student need.
5. Stick to planning and teaching direct writing lessons, don't set them aside for other lessons. (That means a commitment to being prepared.)

This is where I think I need to start to help me be a more successful writing teacher.  What are your thoughts on this chapter?  What is your next step in being a better writing teacher?  I'd love any of your advice and tips for me as well.  Feel free to leave a comment or link up your own post on Chapter 5 below.  You can also ask questions directly to Lisa Donohue, just add them to this form. 

On June 13th, be sure to visit 


For thoughts on Chapter 6. 

Notice and Note Book Study Post 2

This section of the Notice and Note Book Study is being hosted by 

Be sure to head to Heather's main post here.  You can join the fun too and link up your post or comment or ask questions in her comment section of the post.  

Question 3: Where Does Rigor Fit?  I recently heard some ideas about the word "rigor" that really resonated with me.  I am pretty sure they came from a presentation from George Couros at the Utah Educational Technology Conference I attended a few months ago.  He pointed out that the word rigor seems like such an unlikely word to use for what we mean when using it recently in education.  The etymology of the word is from Latin meaning to be stiff.  It is most often used to describe the state of a living thing after death and the body stiffens.  It also has the meaning to be harsh, strict or extreme.  In what way do we desire these attributes for our readers? We desire to increase the difficulty level with which our students are able to work with a text in order to deepen their understanding.  Perhaps we could find a different word to describe this act?  I simply use the term "Deeper Reading" with my students to encompass the ideas of close reading and offering rigorous and meaningful lessons.  

The authors of Notice and Note also pointed out a similar notion in the section of this chapter titled "It's Rigor, Not Rigor Mortis" I appreciate these sections of text from the chapter that really resonated with me: 
"Rigor is not an attribute of a text but rather a characteristic of our behavior with that text.  ...rigor resides in the enerty and attention given to the text, not in the text itself." (pg. 20)

"The essential element in rigor is engagement.  The rigor has to be achieved by engaging the readers in a process that is sufficiently interesting or rewarding that they'll invest energy in the work." (pg. 22)

A question that has come to mind in this notion of rigor being about the interaction, is how does text leveling play a role in this?  Of course students must be able to access the text in order to dig deeper, but what about a text that might usually be considered too easy for a student?  I feel that sometimes students are able to easily read a text and understand surface comprehension, but miss all of the deeper, underlying meanings that can be gained from the text.  I am thinking that for digging deeper, it may be a fantastic idea to bring forward "easier" texts and increase the expectation for engagement and commitment to the text.  Then, slowly increasing the difficulty of the text while continuing the expectation of engagement and commitment. 

Question 4: What do We Mean by Intellectual Communities? 

This idea of having an intellectual community is one that I have desired, but not quite learned how to foster.  This last year, more than any before, I realized how willing my students are to do the bare minimum.  They weren't engaged in learning and didn't have that intrinsic desire to work hard and do more.  A small handful out of the 33 students in my class ever went above and beyond the minimum and many did just enough to brush the minimum and yet now quite reach it.  I would love to hear your ideas on how you achieve an Intellectual Community in your classroom or school!

Notice and Note Book Study Post 1

Welcome to the first post in this summer blog book study on Notice and Note by Kylene Beers and Robert E. Probst.  I had been eyeing this book for a bit and wondering how helpful it would be among the sea of many other professional development books.  I asked some fellow bloggers for ideas on good summer book study books and this one came up.  So, I decided to give it a go.  I'm so very glad I did!  I'm about half way through, and LOVE it!  I hope you'll join us this summer and read along.  Please make comments or link up your own blog posts to share your ideas on each section.  Be sure to stop by our information page here to get the details of this book study and a calendar of posts. 

Post 1 will cover Chapter 1 and Chapter 2 (through page 19). This first section of the book reviews the questions the authors asked as they were seeking information on what is helpful to students as readers and consider how to change their teaching based on current theories and practices. 

Question 1: Is Reading Still Reading? As technology continues to become more integrated into our way of life, we have to re-examine what we consider to be reading.  In tandem with thinking about what we consider to be reading, we have to consider the way we are reading and whether we are adequately preparing students to access and understand these various texts. The skills it takes for a student to navigate and read a website, blog, text, etc. are very different than a book which differs from a newspaper or magazine as well. 

At the end of each chapter, the authors offer some questions to consider and discuss with colleagues... that's all of you.  I do think the nature of reading is changing and as teachers, we have to be aware of that and willing to change what texts we teach and how we teach students to access and comprehend them.  I don't think reading will ever become obsolete, I do think the way we read will change and evolve. 

Question 2: What is the Role of Fiction? There is such a push lately for students to read more and more non-fiction.  So what place does fiction have in our classrooms now? I love this quote from Notice and Note: "Indeed, it is imaginative literature that offers readers a chance to think about the human issues that concern us all: love, hate, hope, fear and all the other emotions, problems, situations, and experiences of living."  How many of us feel that in addition to the content areas, we have also become teachers of societal norms, manners, behaviors, etc.?   I know that I have felt this way, and feel increasingly so with each school year that passes.  Fiction is a perfect way to teach literacy and integrate social skills.  The authors also write: "Living for a time in the book's imaginary world may make us better able to live in our real world."  What a wonderfully profound statement to consider!

As the summer continues, I hope to share how I structure and run my reading time in my classroom.  I've had several bloggers ask about how to effectively run guided reading, literature circles and reading lessons from a basal in the time they have.  With the help of a fabulous colleague, I have a solution.  One of the questions asked at the end of section 2 is how to strike a balance.  I hope that my posts about reading in my classroom will help to answer that question as I feel it very important to find that balance. 

What are your thoughts and reactions to these first two sections of Notice and Note? Add the link to your blog post to the linky below or share your thoughts in the comments of this post. 

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Summer 2014 Book Studies

I'm so excited for this summer!  I'm excited for several reasons, a break from school, time with my family and vacations.  I'm also excited for this little blog.  I have lots on the to-do list in posting and creating and getting organized to continue the pattern throughout the school year.  The biggest thing going on this summer right here is Summer Professional Book Studies, bloggy style.  I'll be participating in several book studies this summer which means I'll be writing posts about my reactions and plans of implementation as I read along with many other great bloggers, including readers.  You can join the fun by creating your own posts if you have a blog, or commenting your thoughts on the blog posts.

The first one has already begun! 100 Minutes: Making Every Minute Count book study is up and going.  You can find all of the introductory information here.  And the first post on Chapter 1 here.  I'll be posting on Chapter 5 on June 9th.  I'm hoping I can also link up with some of the other chapter posts.  If you need a copy, click below to get yours on Amazon.

The majority of my summer will be spent with a WONDERFUL book, Notice and Note.  I've been wanting to learn more about close reading and make informed decision on how I best accomplish it with my students. This has been the perfect book to do that for me.  I'll be hosting this book study and linking up with each chapters leader as often as I can.  We'd love for you to join us!  You can get all the details and schedule here.  It all starts on June 3 and posts go live most every Tuesday and Thursday through mid-July.

The last two books are professional development on mathematics.  Guided Math Conferences is a new book from Laney Sammons of Guided Math fame.  This book is available on TpT.  It does take a bit of time to ship, so I recommend ordering it ASAP.  Remember you'll earn reward points for your purchase on TpT.  Amazon is not currently carrying it.  This study will start June 19 and will be hosted by Brenda of Primary Inspired. 

Good Question for Math Teaching comes in a K-6 version or 5-8 version.  I picked up the K-6 version and am really loving it.  It has really helped me re-frame my thinking and the types of questions I'm asking my students.  This one starts on June 10th and you can find a calendar and info here. 

If you cant tell by now, I'm a bit of a PD junkie.  I love learning best practices for teaching.  I recognize I can't do everything, but I can take the best and implement it into my own practices to improve upon what I'm already doing.  I hope you'll join us for one or all of these great book studies.  There are several others that will be going on around the blogosphere as well, so keep your eyes open and come join us!

If you plan to join a blog book study, I'd love to know which ones.  Please leave your plans in the comments below.  If you're hosting a book study, feel free to leave the information as well. 

Making Inferences and Predictions in Math

It's time for chapter 6 in the book Building Mathematical Comprehension by Laney Sammons.  You might be familiar with her other book, Guided Math.  If you don't have these books, I would highly recommend them both.  Click on the covers below to order them or take a look at them.

If you missed the first five chapters, head over to this post at Primary Inspired or this one at Thinking of Teaching to start at the beginning.

****I know it's a bit of a long post, but I hope it's full of information you'll find helpful.  There's a giveaway at the end of the post, so be sure not to miss that!!*****

This section is all about using the skills of inference and prediction in math.  The two concepts that really struck a chord with me are:
1~"When mathematical concepts are taught by teachers and then problems are assigned, versus using problems as a way to teach concepts and build conceptual understanding, students have few opportunities to practice thinking inferentially about mathematics.  ...In classrooms where students are expected to assume a major role in their own learning, they are encouraged to go beyond the literal mathematical information they encounter." (pg.178)

The district I work for have been very supportive of the task oriented mathematics.  Giving students open-ended problems to work through is so very powerful as they learn through struggle, inference, and logic.  I think there are 2 big road blocks in using tasks.  First it takes some training to get students to work in groups and to have the stamina to work through the problem.  Second, finding tasks.  Here's a few resources:

From Meg Anderson ~
     Open Ended Math Challenges Grades 3-6 
     Hands On Common Core Fraction Unit
     Hands on Decimal Sequencing
     Intermediate Math Journal Prompts
     Place Value with Large Numbers Activities
From Teaching with a Mountain View ~
     Division Project or Math Center *Movie Marathon* (Long Division)
     Multi Digit Multiplication Project for the Common Core *Resort Report*
     Breaking Up the Bakery: A Fraction Project , Center , or Assessment 
From Primary Punch ~
     Math Movers: Back to School Edition
     Math Movers: First Week of School Edition
     See all the items in the Math Movers Series here

Check the linky at the end of this post (under the giveaway) for more links to products and other blog posts on this topic.

2 ~"Think-alouds allow students access to the thoughts of their teachers.  To truly meet the needs of students, you must access their thoughts as well.  One-on-one conferences provide a portal into student thinking. ...Focused conversations with individual students allow you to see each student's strengths and weaknesses.  These insights allow you to specifically identify the instructional needs of each student..."

My first grade team the last three years did this really well.  We gave students a 10 question paper pencil assessment at the end of each math unit, but also did a 5 question interview with each student.  It was amazing the information I learned about students as they performed tasks in front of me or explained their thinking and understanding about a concept.  This information really helped guide my teaching.  It was especially helpful for our Re-teach and Enrich groups.  After each assessment students were grouped based on their performance for either further teaching on the concept, review, or extension.  This all took place during a dedicated half hour 4 times a week.  During our regular math session, we continued to move on to the next topic.  The burning question you're asking yourself...How did you have the time?  To create the tasks we worked on them collaboratively and based them from our objectives.  To administer, once I had a little practice, I was able to do all the assessment interviews in two days while students did review/extension math centers.  I tried to schedule a parent helper or two to help with the centers so my focus could be on the interviews.  It was well worth the time to get the information for improved instruction.  Now, if you're not going to use the information to guide instruction, then it's totally not worth your time.


Miss Nannini of the blog Young Teacher Love has amazing sets to help you in assessment.  She has the assessments ready for you and a system to have the students be accountable for their learning.  I've got all the 5th grade sets and am excited to implement them this fall as I move to 5th grade.  Many of her assessment items could be turned into a conference question.  You can see all her assessement products for grades 2-6 here.  And her accountability systems here.

Do you have information on this topic to share?  Leave a comment or link up below the giveaway.

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