# Book Study: Teaching Numeracy, Preface and Introduction

### Welcome!

I love the excitement that this book studyย series has generated! I was tickled that we cleaned out Amazon’s supply of the book in about two days. Luckily, one of the authors, Margie Pearse, has contacted Amazon and more are on the way.

*This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.*

If you don’t have the book in your hands, you’ll see from the format of the book study that it’s not a problem. Over the next seven weeks we will be reading Teaching Numeracy, 9 Critical Habits to Ignite Mathematical Thinking. Each Monday, I will write a blog post with my thoughts on the reading, and I hope you all will participate by adding your comments. In the Preface, the authors state,ย “Research mixed with practical ideas is, in our opinion, a magical brew for teachers.”ย I couldn’t agree more, and that’s exactly what you’ll find in this book. My hope is that we all think deeply and make concrete plans for implementing these important instructional practices in our classrooms this fall. Push yourself to put your thoughts in writing by commenting as we read each section!

### Reading Schedule

- Preface and Introduction
- Critical Habits 1 & 2
- Critical Habits 3 & 4
- Critical Habits 5 & 6
- Critical Habit 7
- Critical Habits 8 & 9
- Essential Components 1, 2, & 3
- Essential Components 4 & 5

### Preface and Introduction

There’s no way you could read the Introduction and notย come away with a good understanding of what is meant by numeracy. The authors cite numerous studies and resources about what it means to be numerate. To put it in my own words, I’d say that numeracy is not just doingย math, but *using* math. In other words, if you can’t apply the math you know, you’re not numerate. Here’s a thought I hope you’ll comment on: I have always thought of numeracyย and number sense as being interchangeable, but now I’m not so sure. Are they the same thing? If not, how are they different? The idea of connections between literacyย and numeracy is not new to me, but I think it’s typically thought of from the perspective of using literacy strategies to teach math. Books such as Laney Sammons’ Building Mathematical Comprehension: Using Literacy Strategies to Make Meaning are a good example. And of course, we’ve all realized that most math tests are actually reading tests–if you can’t comprehend what the problem is asking, you can’t solve it. But the authors make a very strong case about the far-reaching importance of numeracy outside of the classroomย through quotes such as this:

Evidence shows that poor numeracy skills are a greater impediment to life chances than poor literacy skills and that by raising standards of numeracy we will be improving the career prospects of our pupils (Groves, 2001).

Which brings me to my final thought/question: My experience has been that thereย is something of a “literacy versus numeracy” mentality (pg. 2). For example, in my district, we have had reading interventionists on our elementary campuses for as long as I can remember, but only in the last four years have we added math interventionists. And I think teachers are still largely drawn to the primary grades (K-2) because they want to teach children to read. I do feel, however, that slowly the scales are balancing. I appreciate the talking points provided in this Introduction regarding the need for stronger numeracy instruction. Looking forward to lots of active participation as you all share your thoughts in the comments!

I think having strong number sense is a critical piece of being numerate. Numeracy fail example: A highway sign stated: 2013 TN Highway fatalities- 51% with seat belt, 49% without seat belt. Is the goal of this message to encourage or discourage seat belt use?

Some K-2 teachers are not comfortable with numeracy. In fact, I have heard a few K-2 teachers say that they couldn’t teach above 2nd grade because of “the math”. I am glad that there is more talk about the foundational years being just as important in numeracy as literacy. I am thankful for the CCSS because of the balance of mathematics content with the Standards for Mathematical Practice. Mathematics is more than calculating. The term conditionalized knowledge was new to me and I like it!

Your numeracy fail example seems to be exactly what the authors are talking about in the Introduction. Great section of text on the top of page 5 that starts out, “When you’re numerate, you understand how to navigate through the world with a practical sense of how and why numbers affect you.” The rest of that paragraph speaks to exactly what you’re saying about data analysis.

I’m with you on the Standards for Mathematical Practice. It’s that balance between content and process that essential.

That is my observation as well – and my soapbox – that math intervention needs its own people. Many schools the ELA doubles to also do math. Different animals. We need to equalize math coaches /specialists / interventionists eps at the elementary level.

I think they are using Numeracy as the verb (action) that takes place as a result of having number sense. In other words, Numeracy is the acting upon mathematical ideas – in such ways as Math Talk.

Finally, a pure interpretation and implementation of the Practices and CCSS is to me the process to developing math LITERACY. in the language arts world literacy has its meanings and connotations. In the mathematics world the implications are HUGE, the potential enormous. Mathematically literate people are problem solvers, critical thinkers, perseverant, etc., and can use all the elements of language literacy to express their Numeracy.

Some early thoughts. Looking forward to this read!!!

I can’t believe I haven’t read this book already! Only a few lines in Pearse says, “our students have a weak number sense. Many students know how to do the math but do not know how to think through the math. There is an enormous difference. “ If one of my students or fellow teachers were reading this book, they would think I wrote that myself. I am constantly saying to students “you need to think about the math, not just do it.” I have spent countless hours arguing my case with teachers, students, parents and administrators of the value of having students construct their own understanding of concepts rather than just teaching procedures. When I blog about the way I help students understand concepts like multi-digit addition and subtraction without teaching them “how to do it” I get such great feedback about the way my students think about math.

I also love the quote “research mixed practical ideas is, in our opinion, a magical brew for teachers. “ When I read a professional book based on research that is presented in a teacher friendly way with plenty of examples and ideas for activities to use in the classroom, I become a better teacher. When I am struggling with a student on a particular topic, I find going back to the research always gives me new ideas. I am looking forward to reading this book in more detail and I can’t wait to see what new ideas it gives me. Great choice Donna!

Tara

The Math Maniac

I absolutely share your belief about teaching critical thinking skills, Tara. Like you, I’m looking forward to lots of great ideas from this book!

I completely can relate to your comments about the battle to help move kids beyond just getting an answer to understanding the idea of really thinking. I really want my students to understand that math is so much more than finding answers..I want them to be true problem solvers.

Is numeracy a more general knowledge of “using and applying math” and number sense a more specific number knowledge of understanding numbers and their relationships? But, you have to have number sense in order to have numeracy.

We have reading specialist that work directly with students but not math specialists. I wish we did.

I like your analysis of the difference between numeracy and number sense, Beth. I have always thought of number sense as understanding the relationships and connections between numbers, so that makes sense to me. Numeracy is definitely something much larger.

I think the lack of math specialists is pretty common. Maybe I’ll do a Facebook poll and gather some data.

In my area a math specialist is very rare. I have been working as a math specialist for 9 years now. Over the last 2 years I have been in two different buildings part time. They are very small schools but there are 3 literacy specialists in one of the buildings and 1.5 in the other. When you have 3 literacy specialists and only a 60% math specialist, things are definitely not balanced.

Tara

The Math Maniac

In our building the Title 1 teachers work with reading and math, though more time is given to reading. Sue

Thanks for sharing that, Sue!

I am so excited to be a part of this book group! After 13 years teaching grade 5, I will be the newly created Math Specialist K-5 Title 1 Teacher. I have been snagging every freebie of Donna’s as well as Tara’s as I prepare for my new role. One quote that I loved in the introduction was on pg 4, “Numeracy is “braiding” together mathematics, language, and thinking.” I think that is perfect!!

One issue that I come across constantly was mentioned in the Foreword…namely the fact that we have a culture of math instruction which emphasizes teaching students how to get the right answer rather than the underlying conceptual understanding of the skill. I think immediately of the shoelace cross-multiply method when comparing fractions. Also, when I was teaching some assistants how to draw a grid and shade it in with two colors to show the product when multiplying two fractions, one assistant genuinely asked me why we need to go to these lengths when all we need to do is multiply the numerators and the denominators. I wonder how often I will need to justify the methods for conceptual understanding to students and parents (and perhaps some teachers) alike?

Thanks again for this wonderful opportunity. I am so grateful to you for creating this blog to share your ideas and materials beyond your school community. You are a wealth of knowledge!!

Ann Elise

First, congratulations on your new position! What an exciting opportunity to make a huge impact. We should become good friends, because I’m stepping out of my math coach role and into a K-5 intervention position like you.

Like you, I also taught 5th grade for many years, and it’s very hard to undo the mentality of getting the “right” answer after it’s been ingrained since Kindergarten. I feel like we are making great positive strides in the primary grades–and all grades, for that matter–and that the idea that we need to teach for conceptual understanding is becoming more commonplace. Change is coming!

You are going to love being a math specialist! It is great to have blogs like Donna’s out there to help you. When I started my role as a math specialist, I assure you I had no idea what I was doing. Teacher blogs didn’t exist then and there were not a lot of other math specialists in the area. I took a teaching fractions class and found a great mentor who suggested I read all of the research mixed with practical ideas that I could get my hands on. Reading helped me become a much better math specialist.

Tara

The Math Maniac

Your new gig does sound exciting!

I’ve applied for a position as elem math coach to travel the state and provide pd as well. It will be my first pure coaching position (without my own classroom) if I get it. Any advice? I feel I really need a mentor and some training which I hope will be provided!

I am very excited about this book study this summer and have been equally excited as I have begun reading the book. I love the powerful message of the importance of true understanding the true meaning of how this connects to being numerate.

I completely agree with Beth about her interpretation of numeracy and number sense. Numeracy in a way, reminds me of an umbrella and how it serves as the overarching understanding of numbers and the application of numbers…it is the idea of being confident and being able to actively bring together, language, math, and thinking in a variety of situations. Number sense is underneath this overarching idea of numeracy and is more specific to the relationships and patterns that exist between numbers.

There was a quote that kind of connects to yours Donna that I liked, “…individuals who lack the ability to think and reason numerically can neither make wise decisions nor participate fully in civic life” (p.2). This idea of literacy vs math has been a battle or a difficult balancing act in my building. My administration and teachers all see the equal importance of math but have a difficult time keeping all the “balls in the air” professional development and maintenance wise. How can we continue to support teachers to help their true understanding? My building just got a literacy and math coach for the first time and our biggest struggle is supporting a building of almost 1,000 students (9-10 sections of each grade 2-5). Having been a district math coach before, the power that math coaches have in a building are incredibly powerful.

Laurie

I agree that math coaches can have a powerful effect on a building. I really think there is a huge need for them. As important as math is, there really isn’t enough emphasis placed on making sure teachers are competent mathematicians. I know several primary teachers who are not proficient with fifth grade math concepts. It is hard to see why the math you teach is important if you don’t know where your students are going. Imagine if a school hired teachers who couldn’t read at a fifth grade level….

Tara

The Math Maniac

I think the need is probably even greater for GOOD math coaches than literacy coaches. Many of us are proficient at teaching reading or can find enough resources to meet our needs. Math is a whole other story. So many teachers see to only touch the surface of math concepts, even at the primary levels.

Sue

Excellent point, Sue. I think (hope?) the winds are changing though. I present at conferences to a mostly K-2 audience, and I have seen a huge increase in the knowledge base of primary teachers–especially related to numeracy.

I am so glad to have this opportunity to improve my practice. Thank you so much for doing this as part of your blog!

My pleasure, Lauryn!

I sincerely have goose bumps just reading all your insightful comments. I feel so blessed to be part of this book study. Thank you, Donna, for organizing this group!

I am wondering about reasonableness in relation to number sense. Do students need to develop good number sense before cultivating reasonableness and sense making in problem-solving? I have been researching a bit on whether or not reasonableness, sense making, number sense, and numeracy are hierarchical? I am not exactly certain but I sure know our kids need lots and lots of experiences with all of it!

We’re excited to have you contributing, Margie!

Your ‘chicken or the egg’ question is thought provoking. I think that some amount of number sense has to precede reasonableness. For example, how would a Kindergartner who doesn’t know that 5 can be decomposed into 3 and 2 or 4 and 1, etc. or the relative magnitude of numbers, such as 20 or 100, determine reasonableness. Ask a Kindergartner if it would be reasonable to eat 100 cookies and I imagine they would say “yes” with a big smile!

I totally agree.

Love your way with words! I hate to admit it, but if someone asked me to eat 100 cookies, unfortunately I’d give the same answer. ๐

Haha! I get that!

I am excited to be a part of this book study. I cannot count the number of times I have heard a teacher say, “This child has no number sense. Everyone recognizes the problem, yet they struggle with how to correct the situation. I am looking forward to sharing this book with the staff.

I was not surprised to hear that the development of initial numeracy by young children ages 4 to 9 is absolutely critical to later mathematical success. Yet, in our primary grades, the entire focus seems to be literacy. I do believe this is changing, but now I can have some research to back me up!

Numeracy needs dialogue to develop. Discussion needs to be encouraged in the math classroom. This will help students think through the math. I get frustrated when I see students sitting in rows doing calculations worksheets in a classroom. Students without numeracy have not idea if their problems make sense. They can do the process without understanding the math behind the algorithm.

I am looking forward to helping teachers develop critical thinking and foster behaviors that enable students to grow mathematically. To be able to help students develop numeracy, the ability to adapt math ideas to new contexts in everyday life, will be a great goal for the next year.

I agree with the author that literacy has been in the “TOP SPOT” for quite a while, now it hopefully is time for math to have its turn.

Ellen

Ellen, I love your paragraph on the necessity of dialogue! Our students absolutely must engage in deep mathematical discussions. I think many teachers argue that they don’t have time to allow students to talk, but that is very short sighted. I’d rather have students do one, rich problem and discuss it, than 10 computational problems in silence.

Micah, I had been teaching 2nd grade with the tricks and formulas that I myself had been taught. Three years ago I embraced mathematical thinking and discussion in my class. Now when my students solve addition problems they have their own strategies and have a clear understanding of what addition is. Word problems come alive in such a setting. My second graders impressed me with their capability to do mental math. Obviously the changes in my teaching led to better number sense which leads to improved numeracy. My point is…you are on the right path.

That’s the thing, Connie, that is how WE were taught, so that’s our comfort zone. And I think that’s probably why I never really liked math. Boring. Rote. It’s only when you begin to really see the connections and patterns that it comes alive!

My main thought when reading the Preface & Intro was; “How do we help society realize that being ‘numerate’ is equally as important as being literate?” Too many people think it is acceptable, even cool, to say they were never good at math (even some teachers). Yet they would never say that about reading. Mathematics is the gatekeeper for too many pathways in our society…want to be a nurse, you need mathematics; want to be in IT, you need mathematics; want to go to college, you need mathematics. In the Foreword by Arthur Hyde, he tells the story of his daughter whose college path required only the most basic math class and that could have stopped her from going any further.

My quote was from the Introduction: “In an age dominated by numbers, individuals who lack the ability to think and reason numerically can neither make wise decisions nor participate fully in civic life (Shoenfeld, 1994). I think the main reason people feel it is okay to be bad at math is because they think math is arithmetic (as mentioned in the Foreword) and you can use calculators to help you do arithmetic. But calculators can’t do mathematics…only humans can. We need to change people’s view of what mathematics entails in order for us to change the stigma that it is okay to be bad at math.

I like your point about math being more than arithmetic. In an age where people walk around with a calculator in their pocket, it is important for kids to recognize that math is so much more than arithmetic. It drives me crazy when teachers or textbooks give kids a page of rote practice on addition or multiplication and then have 2 story problems at the bottom that need to be solved with that operation and call it problem solving. Math is so much more than that!

Tara

The Math Maniac

It’s a HUGE paradigm shift to move away from the thinking that it’s okay to be bad at math. I remember reading something from a book (although I can’t remember which one) about a cocktail party setting. If someone says they are really bad at math, everyone in the group would probably laugh and tell their own stories. If, however, someone said, “You know, I can’t read. Just never been good at it.”, it would be a totally different (shocked, horrified) reaction.

I love you line: “calculators can’t do mathematics, only humans can”. With the work we have been doing in our school I think our students are starting to understand this. The bigger challenge is getting our parents and the larger community to understand. This is ‘not the way we were taught’, and understanding the changes can be challenging.

I am excited to be part of this book study. I’m hoping that I can become numerate in order to help my students. Math has always been difficult for me and I tend to teach it the way I was taught. In the preface it says “Students, when numerate, do not simply do math; they are taught how to think through the math.” I spent the last year taking an intensive math class to help me better understand how to think through math and while I’m still learning I no longer have the fear of math that has always haunted me. I’m hoping to come away from this book study better prepared to help my students develop their thinking skills.

Micah, this is great! It will be very hard at first but you will not regret your decision to teach kids to think rather than just do the math.

Tara

The Math Maniac

I love your honesty and passion for learning, Micah! The only way to improve is to recognize that something needs improvement. And, honestly, who doesn’t need to improve?

I recently moved from Michigan to Australia. When I began teaching in Australia, I truly thought “numeracy” was simply a different term for “math.” This has really opened my eyes to the difference! It also enlightens much of my thinking over the past few years. My district (in MI), like many others, has focused on literacy for the past EIGHT years, with little PD or focus on math. My new school is also on a literacy focus, but I am working on my own to build my math skills, as I feel it is necessary.

I agree that number sense is more related to numbers and the quantities they represent, as well as patterns with numbers. Numeracy is applying math to the world. When we first began to look at Common Core math, that is what really stood out – students must be able to apply math concepts to a wide variety of situations. They must know when to do what, and must recognize a math problem in their every day life.

When reading I was also struck by the critiques of methods such as teaching kids to notice key words – “The teachers do not realize that the message kids get is, ‘don’t bother reading the problem or thinking about what is going on.’ ” This was quite powerful for me, as teaching “key words” is such common, well respected practice. It really made me reflect on how I am teaching math.

I also took note at this: “Only when they have an inner conversation (questioning, visualizing, and making connections) will they notice when their answer is illogical or where they went wrong in their calculations.” These strategies are EXACTLY what I have been teaching my students in reading. It further demonstrated the strong relationship between literacy and numeracy. I think it is fantastic that these strategies can help students to see the connections between the two! If they can visualize or make connections in multiple scenarios, they will see how math and literacy are not distinct.

Such a powerful start to a book! Can’t wait to dig deeper.

First things first…YOU MOVED FROM MICHIGAN TO AUSTRALIA?!!? That’s awesome! As the authors mentioned, Australia and New Zealand are way ahead of the numeracy game. What a great opportunity for you!

I haven’t read all the comments yet so I hope I’m not too redundant.

Thinking about numeracy and being numerate is the equivalent to literacy and being literate. We all believe that being literate is vital. Now I’m wondering why anyone would think that being numerate is any less vital for a successful career and fulfilling life.

“…individuals who lack the ability to think and reason numerically can neither make wise decisions nor participate fully in civic life.” Those words really resonate with me. I think we see that in many adults around us (especially if you read comments on news websites).

As a primary educator, I love to teach reading. And I do it well. For years I thought I wasn’t very good at teaching math because I had so many students struggle while teaching strictly through the text series our district purchased. So many times a lesson fell flat and I blamed myself. Then I began to doubt the series as an ‘end all be all’ and began reading more about teaching math. My gut said many of the same things I read in the introduction. This past year was my most successful, mostly because our series doesn’t match up with CCS and we need to develop many of our own lessons and activities. With the attention on CCS and data driven instruction, this books study is good timing for me.

Sue

I think the fact that we are all saying many of the same things is validating, Sue. Like you, I never taught out of a math book. The teacher’s edition can be a good roadmap and can provide ideas, but “open your book to page 75” is just not engaging in any way, shape, or form!

“I don’t need to know fourth grade math, I teach second grade” Is something that I have heard over my 24 years of teaching, and more specifically my past 7 years as a math specialist. It is frustrating to hear teachers say things like that – It is OK to be “il-numerate” but not OK to be illiterate.

I really loved reading about about numeracy and the research around it! I am so excited to begin reading this book. We are starting a new Curriculum in out district, and Numeracy and Number Sense seems to be huge in it! I am looking forward to putting the two together.!

Il-numerate! Love it, Terri. I think just having the word numerate to go with literate is a big step, don’t you think?

At the end of the Preface it refers to students with numeracy as deep-thinkers, meaning-makers, and sense-builders. These students are taught to think through the math not just do it. I feel that all three of these components are important for out students to be numerate. I have found at our school that a lot of students just want you to tell them how to do math, and they don’t want you to let them figure it out and make sense of it.

Two years ago my principal had an extra teaching position open and decided to create a Math Coach/Math Interventionist with the open position. She asked me to take the job and I jumped at the chance. She knew the importance of this position and allowed me to find my own way with the job description which was none existent. I found in the position that a lot of students and teachers struggle with the conceptual understanding because they rely more heavily on the procedural understanding. “Building conceptual connections is at the heart of numeracy. Meaning is not passively received; it is actively constructed.” The math initiative in our state has greatly helped this issue but I still feel like our teachers need to provide the students with more conceptual understanding for true numeracy to take place. I recently went to a two day workshop where they addressed this topic. I hope that with the knowledge from the workshop as well as this book I can provide the teachers in my school new insight on numeracy.

Tiffany, that’s exactly how I initially got my math coach role–a forward-thinking principal used creative staffing to make a campus-based position. A year later, our district put coaches on all elementary campuses.

Waiting for the teacher to give you the solution is a learned response. I read a study once that revealed that teachers in the United States let students struggle far less than teachers in Japan and Germany. It’s part of our teaching culture in the US to jump to a student’s rescue at the first sign of difficulty. I love the idea of productive struggle, which goes right along with constructing meaning.

Tiffany, what state do you work in? I’m curious to hear (read) more about your state’s math initiatives. Sue

Alabama. We have AMSTI- Alabama Math, Science, and Technology Initiative. The website is amsti.org. If you click on the About Tab it has a lot of information about it! ๐

Thanks, Tiffany, for providing this site. It’s very helpful for my pre-service math teachers.

I live in Idaho and our tiny little school has the privilege of working with some amazing people from Boise State University.

Just ordered the book. Looks like it’s on back order as they cannot promise when I will receive it. Looking forward to the book discussion.

Welcome, Gale! The format of the book study makes it easy to jump in at any point. You can actually read the whole Introduction (which is what we discussed this week) using the Look Inside feature at Amazon.

Hi, I also just ordered the book. They allowed me to read the intro for free until my book arrives. I hope it will be in time to join this blog.

I think the discussions about numeracy are of great value and we all can deepen our own understanding of what it is and learn more about what are the best practices for teaching it when working with elementary age students.

Hopefully me copy will arrive in time for me to “catch up” on my readings and join this discussion group, thank you, Donna for offering the book study. I look forward to reading thru the posts.

Comparing the challenges teachers encounter when teaching math”numeracy” to ‘illiteracy’ is an oversimplification in my experience. Even the very young students I have encountered that struggled with reading had sufficient oral language skills to provide a basis for remedial reading instruction. Children use language quite successfully. It seems to me that students struggling in math lack a similar skill set to build on.

The instruction given teachers about teaching reading in our state(AZ) through the Reading First Program has teachers who used to feel like they were better at teaching math than reading feeling far more confident in their reading instruction. In fact, our school has flipped from students’ test scores being higher in math, to being higher in reading! We are desperate for tools and instruction on locating, diagnosing, and remediating students’ math problems.

Reading instruction focuses on the “Big 5 Ideas”

Phonemic Awareness

Alphabetic Principle (Phonics)

Fluency with Text

Vocabulary

Comprehension

These are easily assessed, diagnosed, and allow for prescriptive and timely intervention.

What are the ‘Big 5” or 6, 7, or 10 for math? I am hoping this book study will help break these down for me.

You make some excellent points! My reading coach counterpart and I have often discussed a similar concept–in reading, students have a reading level, determined through testing (Fountas and Pinnell, Rigby, etc.). It’s easier to say a student is either reading on-level or how much above or below. In math, there is no such data, so identification of remediation needs becomes more complicated. There are certainly commercial math diagnostic tools available, but I don’t feel that their availability and use is as wide-spread as the reading tools. I’m not even a reading teacher, and yet I know the names of the reading diagnostic instruments.

You might want to check out these resources, which are excellent for diagnostic purposes:

How Children Learn Number Concepts: A Guide to the Critical Learning Phases, by Kathy RichardsonTeaching Number in the Classroom with 4-8 Year-Olds, by Robert WrightThanks, Donna, for these titles. I just ordered both!

I am always intrigued by the math rankings on the TIMSS. It was important to me to include this data in our Introduction to Teaching Numeracy.

I just read a study by Erling Boe, an educational researcher from the University of Pennsylvania, that I think you will find really interesting.

Before starting the actual tests, students are asked to fill out a questionnaire asking them questions like their parents’ education level, their feelings about math, etc. It is 120 questions long (Wow!). In fact, it is so time-consuming, many students leave almost one-fourth of the questions unanswered.

What Boe discovered is there a correlation between the number of questions answered on this questionnaire and the actual score on the math test. Countries whose students are willing to take the time to answer all the questions on the questionnaire are the same countries whose students do the best on the test itself.

That discovery blew me away and wanted to share it with all of you.

Fascinating research, Margie! Thanks so much for sharing. It makes total sense, though, right? It’s interesting how culturally influenced work ethic and perseverance are.

Assessing math is so complicated, as students can excel in certain areas, but really struggle in others. I suppose the same can be said for decoding and comprehension, but math topics are so much more varied. In Michigan we always had simple assessments based on what we taught (in kindergarten). Number ID, counting objects, etc. In Australia, as students enter school, we administer the Early Years Numeracy Assessment. It is a test where you continue asking questions until students are no longer successful. It starts with things like counting, one to one correspondence, adding, etc, and continues on to multiplication, division, calculator skills, etc if students are able. Having administered the test, I have to say that it gave me a base level understanding of students’ skills, but not much else. The questions certainly were not open ended or requiring much depth of thinking, and once it was administered we did little with the results.

I live in Ontario so we have slightly different systems than in the U.S. The past couple of years our PD focus has made a dramatic change of focus from literacy to numeracy. We have moved to MLC (math learning cycles) and I have been very fortunate to be on our school’s team. I have attended a number of trainings but the one thing I have found very valuable have been the co-teaching opportunities. We did one very cool day where we taught a similar lesson in my room (Kindergarten), grade 2 and grade 7. It was fascinating to see that similarities (and differences) about how students are communicating and discussing the reasoning at different grades and ages. It also reassured me that I know more than I thought I knew about math at the higher grades. Many of you have commented how they frequently hear that teachers don’t feel their math ability is sufficient to teacher higher grades, and in some cases this may be the case, however from the experience I had I feel that maybe sometimes because we don’t feel we are using the skills every day we don’t think we have them. Just a thought.

I got started a few days late waiting for my book to arrive but was so excited to start reading. In our school wide discussions and developing our school plan for improvement in math achievement the one theme that keeps coming up is that student are all too often lacking basic number skills. I feel that this is a combination of both numeracy and number sense. I appreciated the quote in the introduction about numeracy in that “it requires understanding of the number system, a number sense”. Students need to have number sense to develop numeracy. It is tricky to differentiate between the two terms but maybe number sense is an understanding of number concepts and ‘knowing the mathematics’ and numeracy is ‘what the student can do with the mathematical knowledge’.

Wow, is all I can say about your school system’s approach to PD! We’ve been doing a lot more cross-grade observations on my campus, but I love the vertical spread of your co-teaching day.

I like your descriptions of number sense and numeracy. I’m just curious, in developing your school plan, did you discuss these terms? If not, do you think you will now? Is there value in all teachers on a campus having common definitions for number sense and numeracy?

When we were doing our plan I don’t think these specific terms came up. After reading the introduction I am confident that this is what we were talking about but I definitely want to introduce this book to others in September.

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I am so excited to participate in this book study and to learn from each of you. I have thoroughly enjoyed reading everyone’s comments so far! I am an instructional coach at my school and am starting my second year in that position. I absolutely love what I do! I love to read anything math related and can’t believe I haven’t heard of this book. My friend Mindy, who is also a coach, and I are working on developing a PD that combines reading (her strength) and math (my strength) in a way to help our teachers understand the connection. I always find it amazing how things we need come into our lives at just the right moment! I told her we can’t build this PD until I am done reading this book!

One of the major things that stood out to me is the connection between being literate and numerate and the importance our society places on each one. When I began my career as a math teacher, I saw the discrepency of the amount of money and time that was spent on reading interventions vs. math interventions. I have seen a shift in closing the gap within my district, but there is still a long way to go.

Another point the author makes that resonated with me is “Many students know how to do the math, but do not know how to htink through the math. There is an enormous difference.” As a teacher I always sought to help my students understand the math they were doing. I told them I never wanted them to say because Mrs. Walden said so. If that was the only way they knew an answer, then I had failed them. I wanted them to be able to explain their reasoning and understanding. When the 8 mathematical practices came out with Common Core that empowered me to help my students focus on the bigger picture. They embraced the practices and that became our focal point while learning the “skills and procedures”. They were making connections and that was very exciting to me. I have done a lot of work in our district to help teachers see the importance of embedding the practices into their lessons.

As we continue this book study I am so excited to gain more strategies that I can share with my teachers to truly help our students numerate!