Yesterday on Twitter, I took part in an impromptu discussion of fraction multiplication. I’ll be honest. I often get frustrated diving deeply into meaty topics on Twitter because I’m limited to 140 characters per tweet (less when you take into account the fact that the handle of everyone tagged in the tweet is deducted from the total). However, this ended up being a very enjoyable conversation and reminded me of the power of connecting with folks from all over.

Tracey Zager was nice enough to Storify the conversation. If you’re interested to hear how a small group of elementary educators unpacked this topic, take a look. If you’re an elementary teacher yourself, especially an upper elementary teacher, you may appreciate it because you’re likely having similar conversations within your own district or campus.

One question that came up several times during the conversation was how and why the word “of” means multiplication:



As Math Minds’ tweet alludes to, there is a whole issue of teaching keywords and the damage they cause students, but that’s not what I’m focusing on here. Today I want to think through the idea of how the simple two-letter word “of” is related to the operation of multiplication in the first place.

This question made me think of the chapter I’m currently reading in Kathy Richardson’s book How Children Learn Number Concepts: A Guide to the Critical Learning Phases. It’s very timely that I’m reading a chapter titled “Understanding Multiplication and Division”. Richardson begins the chapter with the following quote from Keith Devlin (I like that I’m quoting a quote from a book.):

 “…in today’s world we are faced with a great many decisions that depend upon an understanding of quantity. Some of them are inherently additive, some multiplicative, and some exponential. The behavior of those three different kinds of arithmetical operations differs dramatically…”

Richardson goes on from there to discuss the need for elementary teachers to differentiate additive and multiplicative thinking.

“Central to understanding multiplying is the idea that the two numbers (factors) in a multiplication equation have two different meanings: one number describes how many equal groups there are and the other describes the size of each of the groups.”

And when we describe the relationship between the two numbers verbally, the word “of” can become an essential part of our description. Here’s an example from Ask Dr. Math:

Suppose items come 8 to a box.

If I have 2 of these 8’s, I multiply to find the total, 2 × 8 = 16.

(There are 2 equal groups and the size of each group is 8.)

If I have ½ of an 8, I multiply: ½ × 8 = 4.

(There is ½ of a group and the size of the group is 8.)

Going back to Richardson’s book, she goes on to describe the types of multiplication situations students should encounter in elementary school:

  • Equal groups (equivalent sets)
  • Rate / Price / Length
  • Rectangular arrays
  • Multiplicative comparison (scale)
  • Combination problem (Cartesian product)

It’s the multiplicative comparison (scaling) situations that lend themselves best to understanding fraction multiplication. I found it very telling that in the CCSS grade 4 Operations & Algebraic Thinking domain, there is a standard that says students should interpret multiplication as a comparison. The standard uses whole numbers in its example, but the pump has been primed. Then in grade 5, this idea is embedded in the Number & Operations – Fractions domain in a standard that says students should interpret multiplication as scaling (resizing).

The trouble seems to be that up until fraction multiplication, the act of multiplying two whole numbers has always resulted in a larger number, and it has been easy for teachers and students to view it as repeatedly adding that quantity over and over. However, this idea of a quantity growing larger through repetition is only half of what’s going on. If quantities can grow larger, then they can also grow smaller, and our language to describe this needs to adjust accordingly. Instead of having 3 times as much or double the amount, we can now consider 2/3 of a quantity or half as much.

I don’t think the problem is that the word “of” doesn’t mean multiplication per se, but that as elementary educators, we haven’t opened ourselves up to needing different language to describe something new students are learning to do, namely using the operation of multiplication to decrease the size of a quantity.

Although, after writing all that, I want to revise my thinking. Richardson goes on to describe how children have difficulty grasping the word “times” when they first learn about multiplication. She recommends teachers use phrases such as “groups of”, “rows of”, “piles of”, “stacks of”, etc. There’s that word “of” again, and Richardson is advocating using it with children well before they learn about fraction multiplication.

If students can visualize and make sense of:

  • 2 groups of 5
  • 3 rows of 6
  • 7 piles of 10
  • 3 stacks of 9

Then we should be able to extend to this later on:

  • 1/2 group of 5
  • 2/3 row of 6
  • 1/10 pile of 10
  • 1/3 stack of 9

We come back to the idea that the two numbers in a multiplication situation have two different meanings. The first number in each example is the number of groups, whether it’s 2 groups or 1/3 of a group. The second number is the size of one whole group, whether the whole group is 4 pans of brownies or 1/3 pan of brownies.

So ultimately it seems that the word “of”, and phrases built around it, are mostly there to help students to visualize and make sense of a new kind of thinking. Up until grade 3, most students have been focused on additive thinking, so this is quite the paradigm shift for them, and they will grapple with it for several years. As a result teachers need to use familiar language and phrases, which include the word “of”, to help students expand their understanding of how we operate on quantities.

Interpretation Frustration [UPDATED]

[UPDATE] I wrote an email to TEA and heard back from them within three days. I’m very impressed! The person who wrote me went over each of my concerns one by one:

1. The example for 3(3)(E) in the side-by-side document discusses the partitioning of objects and the fraction as a concept of division, not a numerical representation. The goal would be that a student realizes that each student would receive five half-pieces of cookie. With this basis, students can the develop improper fractions and mixed numbers in grade 4.

Saying that the answer should not be a numerical representation sounds like splitting hairs. The text of the standard says: solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8;

If I look at the phrase “solve problems” I’m led to believe I’ll get a numerical answer like I get when I solve other math problems. Yet I think he’s focusing on the phrase “pictorial representations” to say that their answer is meant to be less formal. All in all, I feel students can solve problems like sharing five cookies among 2 people, but the avoidance of 5/2 as an answer leaves me scratching my head. What purpose does it serve?

2. Much like with 3(3)(E), the focus of [3(7)(A)] is the division of the line segment. In the given example, the mark is ¼ of the distance between the numbers 16 and 17 on the number line.

This is some shady logic. The standards don’t ever mention mixed numbers in any elementary grades, but apparently they are implying that because a mixed number is composed of a whole number (3rd graders should be comfortable with those by now) and a fraction less than one (introduced in grade 3), they are fair game. I’m not against this interpretation. What I don’t like is the vague language that leaves it open to interpretation in the first place. I feel like I need to hire a lawyer to help me make sure I’m interpreting the language of these standards accurately!

3. You are correct; the last stand-alone measurement standard is 2(9)(D). However, students can be asked to measure the side lengths of a polygon in 3(7)(B).With the process code of 3(1)(A), a ruler could stand in for a number line in 3(7)(A).

And yet another example of relying on implication rather than writing standards that were clear and easy to follow in the first place. And he ends with my favorite line that I’ve heard over the years:

4. Please remember that the Texas Essential Knowledge and Skills are minimum standards and are not intended to limit what is taught.

It’s the “Get Out of Jail Free” card. I don’t think the issue is that teachers are scared of teaching beyond the standards. The problem is teachers trying to get a good grasp of what the bare minimum is in the first place. After reading through the TEKS, which are technically the standards, teachers can walk away thinking they know where the bar is. However, based on supplemental documents and email clarifications, the bar seems to be in a state of flux, leaving teachers unsure of how high their students need to jump. This doesn’t seem like a fair position to put teachers (or their students!) in.

Original post follows.


I blame the TEKS formy headache today. Specifically the grade 3 TEKS. They are not on my good side right now.

To give you some background, for the past few years I designed curriculum based on the Common Core Standards. I’ve also designed materials for Texas, but lately it was kind of secondary to the Common Core stuff. I’ve grown to love the Common Core standards. There is a lot of thought and care into the progression of topics from grade to grade. They aren’t perfect, but I value how much they do make sense, especially if you read the accompanying progressions documents.

Several years ago, Texas decided to write some new math standards. They didn’t want to adopt Common Core…because Texas…but it was clear the writing team appreciated those standards, too. The first draft of the new Texas standards had so much Common Core language in them, they may as well have been the Common Core. But then the Texas standards went through a round of revisions and what came back looked like someone had hacked off pieces of the Common Core standards, shuffled them around a bit, and called the final product new Texas standards. Needless to say, I’ve been unimpressed.

However, in my new job, I am working squarely in a Texas district in the state of Texas so the Texas standards (TEKS for short) are my focus from here on out. Lord help me.

Today, while putting together assessment materials for a grade 3 unit on fractions, I started to come across some inconsistencies in the language of the TEKS. It started with 3.3A and 3.3B:

3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines;

3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line;

Remember, I come from a Common Core background. Their standards say this:

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

And this:

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Can you spot the main difference? In Common Core there is no specification that the numerator a has to create a fraction that is less than or equal to 1. You could just as easily make 5/4 as you could 3/4. In the new TEKS, however, there is a clear specification that third graders are working with fractions greater than 0 but less than or equal to 1. (By the way, what’s with the fractions having to be greater than 0? Anything wrong with discussing 0/4?)

Ok. I can handle that. But what’s this grade 2 standard over here say?

2.3C use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole;

Oh, so in second grade it’s okay to count fractional parts above one whole, but we need to stop in grade 3? Apparently that’s the case because improper fractions aren’t brought up again until this grade 4 standard:

4.3A represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b;

Weird. Let’s introduce an idea in grade 2, completely skip it for a year in grade 3, and come back to it in grade 4. Well, at least that’s settled…I think.

Let’s look at another grade 3 standard:

3.3E solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8;

In the Side-by-Side comparison documents provided by the Texas Education Agency, we see the following example provided to help clarify 3.3E:

Examples of problems include situations such as 2 children sharing 5 cookies.

I can buy students solving this problem. That’s fine, but how do you rationalize the answer? You are either going to end up with 5/2 which contradicts the rigidity of 3.3A and 3.3B, or you’re going to end up with 2 ½ which is a mixed number. By the way, did I mention the term mixed number doesn’t appear in the TEKS at all across grades K-5? At all. Can you see why this might make my head hurt a bit?

My guess is that they are cheating a bit in their interpretation of 3.3A and 3.3B. By having students use mixed numbers, they are really only writing a whole number combined with a fraction less than one. Do you get it? The number 2 ½ doesn’t break their rule because the fractional part is less than 1.

So students are likely going to be held accountable for understanding mixed numbers in grade 3 even though they aren’t mentioned in the standards and several of the grade 3 standards explicitly state students work with fraction less than or equal to 1. (Good luck third grade teachers!)

I’m pretty sure this is how they are interpreting it because of how they interpret another standard. In the old TEKS we had this standard:

Old 3.10 The student is expected to locate and name points on a number line using whole numbers and fractions, including halves and fourths.

On this year’s high stake test (STAAR), the students had to locate the mixed number 16 1/4 on a number line. Do you think they would ask the same thing based on the wording of the new TEK? I sure can!

3.7A represent fractions of halves, fourths, and eighths as distances from zero on a number line;

And that’s not all! Looking at the TEKS related to fractions on a number line got me thinking about measuring to fractions of a unit. Guess what! That’s a whole new can of worms. Here is the linear measurement standard from grade 2:

2.9D determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes;

In which grade level do you think they specify measuring to the nearest half, fourth, or eighth of an inch? If you guessed “they never specify it”, you’re right! The standard 2.9D is the FINAL linear measurement standard in the TEKS. The only mention I could find about measuring to fractions of a unit comes from the grade 5 Side-by-Side document put out by TEA. Here’s the standard:

5.4H represent and solve problems related to perimeter and/or area and related to volume.

And here’s how the Side-By-Side “clarifies” it:

Because fluency with the addition and subtraction of positive rational numbers is expected within the Revised TEKS (2012), lengths may reflect fractional measures with perimeter.

So the wording of the standards themselves never brings up fractional measures in grades K-5. The only way you would even know this grade 5 standard uses fractional measures is if you happen to cross reference it in the Side-By-Side document which is available on a completely different website from the standards themselves. I’m not even sure they’re available on the Texas Education Agency website.

Can you see why I had a headache today?

I did email someone at TEA today to request clarification. I can’t imagine I’m the only person who finds these particular standards unclear and confusing. If I hear back, I’ll be sure to share! I don’t want anyone, teachers or students, to suffer as I did today.


One Month In

It’s hard to believe that in 3 days I’ll have been at my new job for a month! I can’t remember if I posted about it already or not, but I left my position at McGraw-Hill Education to become the lead curriculum specialist for elementary math at my old school district.

By the way, my job title is a mouth full and I feel pretentious every time I have to tell it to people. I’ve tried finding ways to shorten it, but it just doesn’t work. If I say I’m a curriculum specialist, then it sounds like I do it all. While technically I can do it all as an elementary teacher, I don’t do it all now. And I can’t just say I work in elementary math because that doesn’t really feel very descriptive. Oh well. As far as problems go, I can live with this one.

Time has flown by, mostly because I’ve been so busy. I’ve been enjoying meeting lots and lots of new people and learning the ropes. My first big hurdles on the job relate to our new textbook adoption. In the spring, our district adopted a curriculum called Stepping Stones. It’s by a company called Origo. It’s a digital curriculum, meaning there is no printed book for the teachers. All of the lesson plans are online.

After a week or so on the job, I was tasked with compiling a list of all the elementary teachers in the district who teach math so we could create their online accounts. Basically we don’t want to spend money buying content licenses for teachers who aren’t going to use the curriculum at all. Making a list sounds easy, right? Just contact HR and get one from them. Yes? Maybe?

No, not so much. HR was able to give me an initial list, but it took communicating with Assistant Principals at our 33 elementary schools and making lots of edits to a spreadsheet to finally nail it down.

The next big hurdle was putting on implementation training for about 1,200 teachers spread out at 6 campuses across the district. Thankfully I have a wonderful partner in crime on my team who knows the district inside and out. She was invaluable in getting everything organized and ready to go. The trainings took place last Wednesday, and all in all, they went amazingly well. Yay!

With those two big tasks under my belt, I’ve moved on to an ever growing to-do list. Currently we’re wrapping up the curriculum documents for the second nine weeks for grades K-5. Then we have to write second semester timelines and unit guides which haven’t even been started yet. We also have Curriculum Based Assessments (fancy name for benchmark exams) to prepare, a department website to update, and preparations to make for upcoming trainings we’re doing with our interventionists.

Whew! Good thing I like what I do.

Math In My Feet #TMC14

After joining the Mathtwitterblogosphere two years ago, I finally got to attend Twitter Math Camp. Yay!

Meg is my TMC Bookend Buddy because we hung out together at the start and end of the conference.

Meg is my TMC Bookend Buddy because we hung out together at the start and end of the conference.

In case you aren’t aware, Twitter Math Camp is a grassroots, “for teachers, by teachers” conference put on by fellow math educators from the US, Canada, and the UK. This year the conference was hosted by Jenks High School in Jenks, Oklahoma. (Thank you, @druinok!) There is no cost to attend and none of the presenters/facilitators are paid. This is very much a DIY conference, and I think that’s why everyone loves it so much. Not to mention I finally got to meet folks I’ve been talking to on Twitter for two years!

One of the things I really enjoy about TMC is the extended learning opportunity provided by the morning sessions. The session I attended all three mornings was called “Embodied Mathematics: Tools, Manipulatives, and Meaningful Movement in Math Class”. Our facilitators, Malke Rosenfeld and Christopher Danielson, helped us begin to explore four questions:

  • What role(s) do manipulatives play in learning mathematics?
  • What role does the body play in learning mathematics?
  • What does it mean to use manipulatives in a meaningful way?
  • How can we tell we are using manipulatives in a meaningful way?

I specifically say we began to explore these four questions because I don’t feel that we came to any solid conclusions, and that’s okay!

The focus of our work together was going through an abbreviated version of Malke’s Math In Your Feet workshop. Here is a blurb about the program from her website:

First and foremost, Math in Your Feet is an integration of two separate but highly complementary paths of inquiry. Percussive dance is a sophisticated, precise, and physical expression of time and space using foot-based dance patterns. Mathematics has been called both an art as well as the ‘science of patterns’ and initially developed to understand, describe, and manipulate the physical world.

Math in Your Feet leads students through the problem solving process of creating their own dance patterns. Along the way, they increase their understanding of mathematical topics such as: congruence, symmetry, transformation, angles and degrees, attributes, pattern recognition, symbols, and mapping on a coordinate grid, as well as deep experience with mathematical practices. The mathematical content of all activities was developed in collaboration with award-winning math education specialist Jane Cooney.

And here is an introduction video because this is a program you should see, not just read about. Actually, you should experience it for yourself, but barring that…


One thing that I really like about Math In Your Feet is that it happens at the intersection of math and dance. It isn’t just math and it isn’t just dance. It makes me wonder what other art forms and activities intersect with mathematics, and it makes me wonder how we can leverage that in our teaching. I think this is important because working in these intersections makes math meaningful. It provides an authenticity to the work teachers and students are doing in the classroom by blurring the lines between “school” mathematics and, for lack of a better term, actual mathematics.

If you want to see some of our work during these morning sessions, I recommend reading the Storify that Malke put together. You can also read her recap of the #BlueTapeLounge, the impromptu math and dance work that continued in the evenings in our hotel lobby.

As for the four questions we started exploring, I’m going to come back to them in future posts. My thoughts on them are still churning in the back of my mind, and I want to take some more time to reflect on them.


[tmwyk] Putting Away Blocks

We’ve had our foster daughter since November 2013. She came to us at 19 months old, and she is currently 2 years 5 months old. One of the things that I’ve enjoyed watching is how she’s become more strategic at putting away her blocks. They come in a box in a 6 by 5 array.

When she first started putting away the blocks after playing with them, she was, shall we say, haphazard about it. She would start by placing the blocks inside the box in any way she pleased.

I tried to recreate how she'd start since I don't have any pictures of early attempts. This is probably even more neat than how she would have done it at ifrst.

I tried to recreate how she’d start since I don’t have any pictures of early attempts. This is probably even more neat than how she would have done it at ifrst.


This strategy worked fairly well until the box started to get a bit cramped. As she pushed blocks into smaller and smaller open spaces, some of the blocks would shift and move into the array configuration afforded by the box. Unfortunately some of the blocks would move in other directions, often ending up turned in ways that made fitting the rest of the blocks much more challenging.

This should give an idea of the troubles she would run into. When blocks were turned, they often made pushing new blocks into existing gaps much more challenging.

This should give an idea of the troubles she would run into. When blocks were turned, they often made pushing new blocks into existing gaps much more challenging.

Despite the challenge this presented, I always marveled at her persistence in pushing and moving the blocks until she would get them all to fit nice and neatly in the box. Sadly, I don’t have any videos of her early attempts at putting away the blocks.

I did happen to take a video the other day showing how far she’s come from her early “trial and error” days. You’ll see there’s a lot more structure to her placement of the blocks. It seems informed by a mental image she’s developed of what the blocks should look like when she’s done.

Unfortunately she is not that verbal, so she can’t really talk to me about what she’s doing. Instead, I chose to sit back and watch. (So technically this is more Watch Your Kid Do Math instead of Talking Math With Your Kids.) Since this is clearly a task that she has always been able to figure out on her own, I’ve felt better keeping my mouth shut anyway. Clearly she’s been doing a lot of meaning making on her own over the past few months.

In some ways it’s excruciating to watch someone take over 3 minutes to put 30 blocks away, but as a parent and educator, I can’t help but be fascinated and wonder how she’ll be putting them away a few months from now.

Pondering Teachers as Curriculum Designers

A few weeks ago I posed the following question:

Is it the job of teachers to design their own curriculum?

I only had one taker, @Mr_Kunkel. Here’s what he had to say:

If there was just one really good curriculum I would say sure. There isn’t. The problem with mass marketed curriculum is that it never meets the diverse needs of all classrooms. I have never found a textbook that was great. They all try too hard to do too much.

I think the power of what we do here on the interwebs, the MTBoS, is that we crowd source the curriculum. We are all capable of coming up with some good lessons. I think the curriculum of the future will be a good indexing of all these lessons that teachers are creating. Some how it would be great to combine them and track them by CCSS. Some people are trying that using their virtual filing cabinets. Actually, a really good virtual filling cabinet would be my ideal curriculum. Forget the books.

I knew I wanted to revisit this topic, but every day I kept putting it off, mostly because I’m still not entirely sure what my own answer is to the question.

While I kept pondering, some of the folks I follow on Twitter serendipitously took up this topic a few days ago. Here’s what they had to say:




And then today I came across (and participated in) this conversation that hit on the issue from a slightly different angle:




It’s nice to see others struggle with some of the same things I do with regards to this issue.

It seems clear that curriculum materials are wanted and needed, whether they are written by publishers or other educators. Many consider them a valuable resource. As @crstn85 points out, “a good book has logical order/units.” Someone has laid the groundwork for the teachers. They’re not starting completely from scratch.

We then get into the gray area of the “implemented curriculum” as @mpershan puts it. What is changing from the written curriculum as the teachers prepare their lesson plans and teach the lesson to their students?

From what I’ve read, the teachers I follow on Twitter couldn’t fathom using curriculum materials as they are written. I don’t disagree with them, but I am curious how many teachers do put full faith in their curriculum materials and use them verbatim. I also wonder if any districts require this.

I’m reminded of Response to Intervention. One of its key tenets is fidelity of instruction. If you have fidelity then it means teachers are “consistently and accurately applying a research-based curriculum.” One implication of this is that teachers need to avoid contamination or pollution, meaning they don’t pull together materials from a variety of instructional resources. In order for RtI to succeed, teachers need to get with the program and stick with the program.

I’d like to add a second question that is of particular interest to me, how much effort is it taking for teachers, individually and collectively, to adapt the materials they are using? As I wrote in the second Twitter discussion, I feel that numerous wheels are being reinvented in numerous classrooms across the country. I felt this within my own school district. No need to even think about the rest of the state or country.

For example, I taught 4th grade in Texas. This is one of the two years that students learn Texas history. The other year is 7th grade. This is important to note because most of the instructional and resource materials available outside of our state-adopted textbook were often written for 7th graders, not 4th graders.

The teachers across my district all had the same social studies standards, and yet each 4th grade team in each school was reinventing the wheel on a weekly basis designing lessons to teach those standards. When I would talk to these teachers at trainings, I would hear about the different types of lessons going on in different schools. It frustrated me because it felt really inefficient that we were planning in such isolation.

My last district had 33 schools. It seems ludicrous to think that the 4th grade teams across the district were creating 33 campus-specific lesson plans for teaching the exact same social studies standards. And I can assure you that these lesson plans were across the spectrum in terms of quality.

Now extend this idea to the entire state of Texas. We have roughly 4,000 elementary schools in this state. Assuming that all of the teachers on a given 4th grade team plan together, which I can guarantee you they don’t, that means there are potentially 4,000 or more different lesson plans being written each week to teach the exact same social studies standards.

Let’s say it takes 1 hour to plan a week’s worth of social studies lessons. That means 4,000 man hours are being spent each week to cover the same standards. A school year’s worth (36 weeks) of lesson plans at one school may be 36 hours of work, but with everyone reinventing the wheel at their own campus, this jumps to 144,000 man hours. That’s a huge jump!

I know I’m making some assumptions here, and my numbers are not precise, but that doesn’t change the fact that when a lot of people duplicate effort like this, it adds up. My motto as a teacher, which I was able to live up to with varying degrees of success, was work smarter, not harder. This redundant time spent lesson planning sounds very much like the latter.

One idea that comes to mind to save time is to do what @j_lanier recommends: put together a crack team of great teachers together, give them time to write, and you will get great instructional materials. Districts have done this. Even the state of Texas has done this. And it has failed.

The state of Texas failed pretty spectacularly in fact. Several years ago, districts across the state started adopting a program called CSCOPE. The idea was to give teachers sets of exemplar lessons for teaching all of their content. However, it was also meant to become a bank of lessons. I’m not sure of the logistics, but the idea was that as other wonderful lessons were written, they could be added to the CSCOPE library. Teachers could then pick and choose which great lesson to use in their classroom.

Unfortunately, this aspect of the program never materialized. There was no choice, just the one set of lessons. Teachers were handed their CSCOPE curriculum, and they were told to teach it the way it was written. These were well written lessons, so why change them? This backfired big time, and in 2013 CSCOPE was eliminated.

So the state level may not be the best place to create and distribute quality lessons. Maybe it should be done district by district? Making 1,000 sets of lesson plans sounds like a lot (this is about how many school districts there are in Texas), but it’s significantly better than the 4,000 sets I was describing earlier. The benefit here is that districts can tailor the lessons a bit more to the needs of their population of students.

At this point I can really only speak to my experience, but I have seen this backfire as well. As I said, my last school district only had 33 elementary schools, a far, far cry from 4,000. The district provided scope and sequences and lesson plans for all subjects, and yet teachers were still resistant to using them. The instructional materials still felt like they were coming from “on high” and didn’t reflect the realities within our own classrooms, even though the people who wrote the materials were skilled teachers from our own district.

So I guess we’re back to the idea of writing lessons plans school by school and teacher by teacher. And then what it comes down to is the amount of time each teacher has to gather materials (textbooks, workbooks, lesson plans found on blogs, etc.), review those materials, and craft lesson plans that meet the needs of their students. And we all know how much free time teachers have to do this.

And it’s not just about time actually. It’s also about how resourceful the teacher is in locating quality materials and how strong the teacher is at making important pedagogical decisions when picking and choosing and tying it all together. This definitely leads to variability in the quality of the resulting lessons. Which leads us back to wondering if teachers really should be curriculum designers.

And maybe there just isn’t a right answer to this question. I feel like I’ve talked in circles and I’m no closer to having a clear idea of what I think the answer is. If you’ve made it this far in my post, thank you for following me down the rabbit hole. The great thing about having this blog is that I can revisit topics again. This is clearly a topic that demands more attention, and maybe next time I’ll be one or two steps closer to an answer.


Public Relations Advice on the Common Core Debate

The other day I wrote about the public relations problem facing the Common Core math standards. Posts from frustrated parents have been popping up on Facebook and Twitter for months claiming to show “Common Core” worksheets that are so confusing an electrical engineer or doctor can’t even figure it out.

Teachers have been valiantly, and sometimes argumentatively, trying to defend the ways in which math education has evolved since these parents were students in elementary school. Where once the focus was on direct teach, a limited set of algorithms, and countless repetition, now the focus is on developing number sense, strategic thinking, and broader reasoning skills.

While teachers have a lot of education research to back up their teaching methods, parents have their children to worry about, and they are scared that the instructional changes brought about by Common Core are going to be detrimental to their children’s learning. And this brings us to the PR problem facing the Common Core math standards.

Frustrated, scared, and angry parents have waged a battle in social media to bring attention to their concerns and scare other parents into action. At the same time, this serves to discredit the experience and expertise of teachers in the classroom. Unfortunately, when the issue boils down to pedagogy vs. children, the human element is more compelling. A parent scared for his child’s education is going to foster more sympathy than a teacher arguing the merits of modern math instruction.

I’ve been wondering what can be done to “fix” this problem, so I chatted with a friend of mine who works in public relations. This topic was admittedly outside her normal scope of work, but she raised a few interesting strategies that I want to share here.

A Singular Message

One of the most effective ways to wage a PR campaign is to have a singular message that is used by everyone involved. I feel that the frustrated parents have been successful with this. Their message is simply: “Common Core math instruction is so confusing, intelligent adults can’t make sense of it, much less our children.” Sure there is a lot wrong with this message, but the fact that it is repeated over and over gives it power, and that matters more than the truth of the statement.

My concern is that educators are too fragmented to develop and deliver their own singular message. We have some arguing with parents about how math education has changed in the past 20-30 years. We have others saying that the parents don’t know what they are talking about and should trust the teachers to do their job. We even have teachers who, for various reasons, are saying that they aren’t fans of the Common Core standards either.

Our message is fragmented and too varied to be as effective as the one put forth by the parents. How do we change that?

An Important Voice

My friend recommended finding someone who can serve as a respected “voice” in education. Someone whose words shine a spotlight and draw attention to issues. They may not create converts immediately of course. However, where we fail as many voices, we might find success by choosing the right person (or several people) to deliver an equally strong message as the one used by the parents, one that is supportive of the modern methods of teaching math in schools today.

I’m not sure who this person should be. I’m afraid that the Common Core standards are very much politicized, so having a politician be the voice would backfire. Honestly, the first two names that come to mind are Bill Gates and Sal Khan. I have my doubts that they would want to give the kind of message that is needed, but I can’t deny they are the kinds of people that these parents might stop and listen to.

A Parallel Message

I spoke about this a bit in my previous post. Whatever message is used to counter the frustrated parents, it cannot be worded so that it is against those parents and their viewpoints. Having an “us vs. them” dynamic is not going to help educators reach the outcome they want.

The message needs to be a parallel message. If parents have the space to share their views on how terrible Common Core math is, educators need to also have the space to share their vision of how math is being taught today and what benefits it has for children.


Long essays on the merits of today’s math pedagogy are not going to win over these parents. First of all, a lot of this writing is ending up in education websites and magazines that parents won’t see in the first place. Secondly, you want to keep your message simple to connect with as many people as possible.

My friend said one thing that might help is some kind of infographic(s) that illustrate the hows and whys of math education today. They need to be published in mainstream outlets so that the general public sees them frequently.

One of the biggest issues with the criticisms by the frustrated parents is that they are based in ignorance. Ignorance of what is going on in the classroom today, and ignorance because that’s how they feel when they are confused by an assignment and it is making them doubt their own math knowledge.

These parents are basing their arguments on how they learned math as kids many years ago. They are not aware of all the research that has been done to help improve teaching methods. So they cherry pick certain math topics, often whole number computation, and construct a narrative that teachers are making these “simple” skills way more complex than they need to be.

However, there are many, many adults who would be quick to tell you they are “bad” at math. If they aren’t confident in their own math skills beyond multi-digit addition, subtraction, multiplication, and possibly division, then what makes them think their math education was so amazing all those years ago? Shouldn’t they want their children to grow up to feel “good” at math?

Finding simple ways to illustrate and educate these parents will go a long way towards warming them up to what is going in schools and the benefits it can have for their children. And they have to see these things countless times. In addition to having a clear, consistent message it is crucial to have that message get out there as often as possible. A drop or five in the bucket won’t solve the problem. It’s going to take lots and lots of drops in the bucket.

One example that I’ve seen shared over and over by @trianglemancsd is 1,001 – 2. It’s a problem that can be solved using traditional methods, but it highlights why we encourage students today to think more critically about what they are doing. Why go to the effort of writing this problem down and crossing out all those zeroes? Just count back 2 and you’re done. I’ve seen a similar idea presented with 100 – 98.

Or better yet, contextualize it. Your favorite basketball team is currently leading 52 to 48. How many more points does the other team need to catch up? Oh, you counted up from 48 to 52. Interesting. Why didn’t you line up the numbers and subtract like you were taught?

I wonder if there is an effective way to present these kinds of problems visually to get parents to think first, and then give them an a-ha. Maybe a simple mental math solution and some tagline like, “There’s always more than one way to approach a problem.”

I would love to have some TV commercials that present a problem and then show various students solving the exact same problem using different strategy after different strategy. And again, end with a tagline that highlights this idea of the diversity in ways of thinking about math. This is what we’re trying to foster in our children. It’s also something they do naturally.

So there you have it. Advice from someone who works in PR about how we can try to overcome the bad publicity dogging the Common Core math standards.

Anyone out there want to take this and make it happen? Summer is starting so you have the next 3 months where parents may not be worrying about this issue quite as much. Use this time wisely and you can be ready on the first day of school next year to kick off your own PR campaign to inform and influence the parents at least in your own school if not farther afield.