Composing and Decomposing IS NOT adding and subtracting

I remember when the NEW TEKS first released, I was super confused about the composing and decomposing language. It sounded like "putting together" to me, so I naturally associated it with addition. And decomposing means to break apart numbers, so I naturally associated it with subtraction.

But after surveying many of the the state's supporting documents and reading one of my now favorite books, Teaching Student Centered Mathematics (by John Van deWalle) and Developing Number Concepts by Kathy Richardson; I began to get a deeper understanding of the concept of composing/decomposing.

"To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers." (Van deWalle 2006, pg 26)

This was such a great quote that helped me make the connection that composing and decomposing is the conceptualized foundation that helps support students understanding for addition and subtraction.

So bottom line is composing and decomposing is NOT addition and subtract, but it lays the foundation for students being able to fluently add and subtract, mentally!




Watch this video:

Does McDonald's Sell Cheeseburgers? Well,...does it?

Of course McDonald's serve cheeseburgers- what kind of question is that right?

I mean isn't this the thief we are referring to?

Or perhaps THIS is the thief that we should really be addressing. I must raise my hand and be the first one to admit that I was the preacher for this riddle/rhyme when teaching my students long division. I cared not about students' frustration with learning acronyms, giving them steps that had no real mathematical meaning and thus robbing them of whole number- number sense and more importantly robbing them of the true meaning of division! For me, the vocabulary for this unit was:

• Outside number
• Inside Number
• Number on top
• Divide
• Multiply
• Subtract
• Bring Down
• Check
• Answer

Did you count the true academic vocabulary in that list? I did not hold my students accountable for academic vocabulary, mathematical thinking nor articulation of repeated subtraction with efficient methods.

Research says that division isn't only similar to subtraction in that it involves the separating mechanics, but that it is (just like subtraction) a difficult concept to grasp for students. And difficult concepts should NOT be approached, tackled nor attempted with abstract methods. If not all concepts, those which are most complex should be gradually approached with concrete manipulatives and connection to pictorial representations. Consistency in practice should take place at these levels before we make the connection to a more abstract algorithmic method.

So I share this video (based on approaches that I've read are more developmentally appropriate for students) and I wish I would have used when I was a classroom teacher. Now, I get chances to work with students in small groups and I claw at every chance I get to expose them to these strategies and raise the level (bar) of mental math for them. After all, students can learn at high levels if we simply embrace those methods and take the risk of exposing them to those strategies! Will you try it?

To Coach...or not to Coach?

Serving as an Instructional Coach can be a very daunting and overwhelming task. It can also be varied and uncertain in terms of tasks and expectations. Have you ever heard that joke about the "fine print at the bottom of a contract"? If any position in Education relates to this joke, it's that of an Instructional Coach (or Specialist).

A colleague came to me not long ago and expressed their interest in returning to the classroom from their time as an Instructional Coach. I must say, having spent some time investing in this colleague as a mentor, I was a bit devastated.

*Side Bar* I take pride in being able to spot a servant-hearted person; one who takes ownership of their professional learning by spending their time studying research-based practices (rather than searching TPT and Pinterest for activities) and seeks chances to turn such learning around immediately. That's worth admiring and when I observe such qualities in someone I'm inclined to move on such a hunch, by investing time and energy modeling, mentoring and maturing said person into their potential. But hey, it's not about me, right? *Okay I digress*

So I asked this colleague why they were considering returning to the classroom (which there is NOT a law against, by the way). Their response to me was that their true passion lies in working directly with kids and that they miss the classroom. Now, at face value, I took the response to mean that they had this aching desire to be in the classroom where they felt they could have the biggest impact! Few words/ideals are more true than that and I wouldn't dare fight such a theory and noble desire.

But after some thoughtful consideration, I mauled over their statement and proceeded to dig a bit deeper. Could this person mean by "they miss the classroom", that they feel as if they don't get enough time in the classroom? So after a series of probing questions, I hit gold! They were trying to articulate that the position of a Specialist/Coach was super overwhelming and inundated with so many other tasks that being where teachers needed them (modeling and supporting kids) was near impossible.

This is true in some settings. I remember my first year as a Specialist even though it was a blur. It was filled with trivial tasks that had nothing to do with Math, busy tasks that helped teachers but may or may not have been content related, included pulling data, being in meetings and helping teachers plan. I rarely sat with a kid or put into practice what I preached (so a teacher could see my value). The following year, my job title was protected by leadership as boundaries and expectations were clearly set and consistently held to. But this didn't take away the urge to sit behind my desk and complete tasks for teachers. I had to plan for our PLCs, plan to be prepared for our planning sessions, amongst the normal data pulling, analyzing, program coordinating (GT, testing, RtI, etc). So when was I going to do all of this AND be in a classroom for 70-90 min with a teacher and students? If perhaps a teacher did nail me to model or co-teach, I had to spend time preparing...more time away from classrooms.

But I learned that some things needed to happen "off the clock" and I needed to MAKE TIME for teachers. So I organized my schedule by placing priority on a specific few grade levels (supporting K-6 meant I needed to pick both a testing and primary grade to focus on).

1. After my PLC and planning times were set, I put my office hours during the lunch block (11am-1pm) and filled everything else in with classroom time!

2. When I sat in daytime (45 min) planning with teams, I looked for opportunities to come into their classes to support and model. If I heard them talk about not knowing how to approach something, after I gave an example, I followed my spill with "I can come in and model or co-teach"! This statement probably won me the MOST time invited into classrooms.

3. Sitting in PLCs discussing data were prime opportunities to invite myself into classrooms! Once a teacher inevitably asked, "how can I reteach this?..." I found my window of opportunity and put them on my schedule!

4. While observing in classrooms, rather than standing at the back taking notes, I sat with kids and helped them. I engaged in the classroom learning as if I was a student. This way when the teacher stopped me later and asked what I thought...I found a way to ask if they needed me to support them with anything- another window to slide into classrooms!

5. After each co-teach and modeled lessons, I made it a priority to follow up with the teacher and consistently ask, "Let me know if you need me to come in and help!"

6. Offering to stay after school with them to help them look up resources and flush out their lesson plans!

These practices, along with building relationships with teachers: eating lunch with them (although I'm an introvert and prefer time to myself or was busy and had other things to do), and chatting with them after school while they planned all conspired to build trust and before long I was invited to classes (rather than inviting myself).

So yes, there are 99 problems in Instructional Coaching, but getting into classrooms and working WITH teachers, should NOT be one of them! It should be a front burner priority. It is how we impact learning and make footprints in best practices. The desire to "BE IN THE CLASSROOM" should never die out. It should be the motivating factor for Instructional Coaches and Administrators alike. If we ever lose the hunch and drive to be in a classroom (after we've taken a different role than teacher) then we've forgotten why education is important. Now, while I personally don't believe climbing the "corporate" ladder should be a mindset for Educators, I do understand (and don't "shade" people for trying to financially improve - we all know Educators are the catfish of salaries). But there's so much more reward in the touching of lives, that I feel our focus should be pursuing what we are passionate about and gifted in. It should be about impacting more teachers and students with best pedagogical practices with the intent to stay as close to the classroom as possible.

As a District Math Program Coordinator, not much has changed. Going from serving 20-24 teachers to now 32 campuses (roughly 800 teachers), the mindset has to be the same. My plate is not only full, it looks like a buffet overflowing with food. But I make it my purpose to set aside a day a week to be on campuses, showing my face in classes, highlighting the wonderful things our dedicated teachers do everyday and looking for open doors to be in PLCs, planning and/or classrooms by invitation. I still get that tingly feeling when a teacher sees me in their class, and invites me to join in the lesson. No greater joy than working with kids and gathering authentic data to not only continue my growth as a lead learner but to make ripples in the lives of Educators and students alike! 

"I got 99 problems (things to do) ...

...but being in classrooms AIN'T one of them!"

Hyped over Hyperdocs!

So one of our District Goals this year was to provide Review Resources to our teachers so they could focus more on having collaborative discussions around their data and creating their instructional lessons to align to the standards. So as I fumbled over the first few modalities I would use to send this MASS REVIEW resource out to teachers, I stumbled across this amazing website!

It gives samples of Hyperdocs (a google doc on steroids with hyperlinks to various resources) created by teachers for various subjects. I grew particularly fond of this one Hyperdoc Game board template and began to play around with it.

6 months later, I have a compilation of various Benchmark & STAAR review Hyperdocs created for teacher clickable ease!

Check them out!

Kindergarten Benchmark Review

1st Grade Benchmark Review

2nd Grade Benchmark Review

3rd Grade Benchmark Review

4th Grade Benchmark Review

5th Grade Benchmark Review

3rd Grade STAAR Review

4th Grade STAAR Review 

5th Grade STAAR Review

Facts or Fractions?

                VS                 
Lately I've had this re-occurring question pop up and not far behind has been it's coupled demand...

Question:
"Shouldn't students have a good grasp on multiplication facts before they manipulate with fractions?"

Demand:
"We need to put Multiplication/Division unit before the Fraction unit in the Scope and Sequence. It makes sense that students need to master their facts before they work with fractions!"

I beg to differ and here's why:

3.3F (Equivalent Fractions) TEXAS standard says students are to...

"Represent equivalent fractions with denominators of 2, 3, 4, 6 and 8 using a variety of objects and pictorial models, including number lines."

If we isolate the content (equivalent fractions) from the WHAT or skills students are to do (represent) we get a very concrete and representational approach to instruction.

The CRA (concrete-representational-abstract) process is evident in the progression from 3rd to 4th grade.

Check out the verb difference...

3.3F - Represent...

4.3C - Determine...if two given fractions are equivalent using a variety of methods.

Do you see the progression? Third grade is the place to develop "Fraction Sense" (conceptual and visual foundation of breaking fractions in half) through the lens of the concrete and representational lens. Fourth grade is the place to make connections and build on their fraction sense by using abstract methods to find equivalent fractions. 

So perhaps we use 3rd grade as a training ground for exploring with manipulatives and creating visual mental pictures of how to break fractions in half; leaving students with an ability to find methods that make "fraction sense" when they get to 4th!

I do resolve that Multiplication should precede Fractions but so that students have a longer "school year" to master their facts, NOT for the purpose of using the knowledge to master fraction equivalencies.

Here's a quick video to clarify!

Instructional Nourishment

What was the last meal you had? What all did it consist of?
Better yet, can you give an account for the last three meals you've had (breakfast, lunch and dinner)?

I'm hoping your breakfast was full of protein, oats and fruit! Typically, lunch might not be as wholesome. Perhaps some seafood, salad, maybe a sandwich and chips with some veggies on the side. And for dinner...lets say you make a nice thick piece of beef or chicken with a starch like scalloped potatoes, a green leaf like a salad or spinach and some bread. Okay so you thoughtfully attempted to balance your meal with doses of the proper nutrients and minerals to give your body the nourishment it requires to help you function. Let's even go so far to say you're a health nut and you enjoy preparing very balanced, high in (insert nutrient here) with just the right number of calories to help you with your personal weight goals.

What you don't do is fill your refrigerator and pantry with vitamins and mineral supplements with the intention of tossing a Vitamin C pill into a hot skillet and cooking it sunny side up. Nor do you empty a half bottle of Fish oil capsules in between two slices of bread to get your dosage of meat for lunch. And you certainly don't place an arrangement of various sizes and colors of supplemental vitamin pills into the sectionals of your dinner plate, pull out a fork and knife and dig in!

How silly, right!? Because supplements are meant to take up for where the planned, well-balanced meals might fall short in terms of nutrients. They're the back up plan when your Plan A happens to be missing some critical components. And even in their use, they're not intended to be consumed continuously in place of food, unless you're physically unable to intake the foods that contain those essential nutrients.

Teachers, a guaranteed viable curriculum is the critical component in Tier 1 or Initial instruction for students. A guaranteed viable curriculum is comprised of a healthy knowledge (depth and breadth) of the standards and content you are tasked with facilitating learning around. It involves a healthy balance of backwards design in planning out lesson approaches (rigorous formative assessments), low floor, high ceiling tasks that engage and hook students and peak their interests, hands-on math tasks that encourage exploration and evoke questions while promoting visual stimulation. It's a class full of peer to peer discourse and movement, students testing their theories and learning from their mistakes. It's students receiving small group support or one-on-one conferencing to adjust their goals. It's students eagerly anticipating the stations their teacher has so diligently prepared so they can independently or collectively explore their own ideals about math. When a teacher takes this type of approach to their initial instruction, they are providing a well-balanced instructional meal to their students.

The textbooks are simply a supplement. They serve the purpose of supporting the well-balanced healthy instruction that occurs initially, in the areas where the student didn't get enough of the nutrients from the initial lesson. They are created to take up the slack, just like a supplemental vitamin. Now, if you're the novice teacher and more specifically, you're dealing with little to no supports from a district or infrastructure, the textbook might account for a larger percentage of your initial instruction meal for a while. But nothing a few trips to a local professional development won't cure. Investing in PD can knock the crutch of depending on the textbook "to teach" from under you and get you to walking the right path soon enough. But the general idea here is that as we (teachers) move from the keeper of the knowledge to the facilitator of the knowledge/guide in helping students find the information; our job is to prepare the well balanced meal in such a way that we can guide students to the correct information and guide their uncovering of the appropriate learning. We do this rather than shove textbooks in front of them (like pills down someone's throat). After all we can't call ourselves educators when textbooks and worksheets eat up our instructional minutes anymore than we can fill our dinner plates with Omega-3 and potassium pills and say we had a hot meal for dinner.

Let's nourish our students by showing them we are willing to plan out instructional meals that will make them want to feast at the table of learning and leave the supplements on the shelves.

25 simple steps to solving Word Problems

I'm surprised you even clicked on this blog, after reading a title like that. Seriously though, who wants to learn (or has time, let alone mental capacity to absorb) 25 whole steps (which is NOT simple, by the way) to solve word problems?

But this is the type of absurd pressure we place on our students in Elementary schools in efforts to cram comprehension down their throats, get them to pass their annual accountability assessments, or convince them that they have some false level of mastery. You know what i'm talking about. All of the colorful, cute posters that we spend endless minutes dressing up and hanging confidently on our walls for students to reference when we leave them to solve word problems in isolation! Let me jog your memory...

Any of these look familiar to you!? I can honestly say I used that last one (RUBIES) one year, after seeing it at a local conference. I was duped into believing that my students who had 1-2 years of gaps, were struggling in ELA and read on levels lower than their current grade would be able to take a few doses of this poster medicine and magically make growth or passing grades in math.

Think about the title of this blog and how silly that sounded...that's just how silly that RUBIES acronym proved to be to my students. Some of them came from other districts where they had been exposed to (through drill and kill) various other Acronym posters forced upon them and here I was saying, "Forget that smut and learn this NEW-TRIED-AND-TRUE method!" At that rate and under those conditions, by the time a 3rd grader exited elementary, they could have easily been exposed to 25 "simple" steps to solving word problems!

I tutor this 5th grader (weekly) who attends school in a different district than the one I currently work in. This student has been the sad victim of several teachers who were inexperienced and/or had crumbled under the pressures of being a teacher, leading to their quitting in the middle of the school year. After weeks of re-teaching concepts from a conceptual and representational standpoint, I tested the waters with introducing him to abstract learning through the lens of word problems. I had him read (and re-read) the word problem and tell me what he thought was going on in the problem.

I had him talk me through the meaning of each sentence and then I asked the question that caused me to fall out of my chair:

"What do you think the problem is asking you to do? How do you know?"

To which he replied, "I think we are dividing because it says 'which'." 

*crickets...blank stare*

I could have screamed! Why did he think "which" meant to divide? Perhaps it had something to do with those posters? After some brief investigating, I uncovered that his teacher had taught him the following:

"Which" means divide

"How much" means to add

"How many" means to subtract

...and so on. 

I stopped him and mentally scolded that teacher. I was up against a much bigger giant than just closing his years of math concept gaps, and firming up his ability to comprehend word problems...now I also had to break his bad habits and train him in new ones. 

This is an example of the gaps we can create and the ultimate fate of giving students cute-sy short cuts and fast food feaux learning tricks rather than helping them understand how to think through a problem. 

John Van de Walle (as if I could write a blog without quoting my Mathematical boyfriend) says its profitable for students to draw pictures, act out and model (with objects) word problems as early as Kindergarten so they (in true slow cooker form) grow up into a deeper, more solid foundation of how to think through and solve word problems. The TEKS even make provisions in their explicit wording that yearly building on students' developmental abilities should suffice in regard to word problems. 

Model the action of joining and separating... 

(K.3A)

Solve Word problems using objects and drawings...

(K.3B)

Explain the strategies used to solve problems...using spoken words, concrete and pictorial models... 

(K.3C)

Use objects and pictorial models to solve word problems involving joining, separating and comparing... 

(1.3B)

Represent word problems involving addition and subtraction...using concrete and pictorial models... 

(1.5D)

Explain strategies used to solve problems...using spoken words, objects, pictorial models... 

(1.3E)

Represent and solve addition and subtraction word problems... 

(2.7C)

Not to mention the explicit use of strip diagrams in 3rd-5th for multi-step problem modeling. 

Let's commit (for the NEW YEAR) to cut the tricks out of our lesson plans and get down to supporting student thinking. This means that among the other numerous hats we wear, we must also be reading teachers! Guided Math and Math Workshop are great vehicles through which we can foster such conversations with students. We have that small teacher to student ratio (uninterrupted time) to have a two-way conversation with students about thinking through each sentence of a word problem, providing them manipulatives and scratch paper to model and draw out their thinking. I can guarantee this method is NOT simple. But for my class of 22 (full of students with severe gaps and low reading levels) this proved successful as I watched my students gain confidence and make significant steps in growth. 

If you have ideas of innovative and non-cliche methods that have worked in YOUR classroom, drop your ideas, videos and/or pictures in the comments. Or follow me on Twitter @kloneal2 and leave me a comment!