I just finished working with a large group of teachers in Montpelier. They were inquisitive and eager. In the exit slips, several participants asked for more information about using questions to teach. This post is a response to these requests for more.

I tell everyone who will listen that the two most important elements of effective math instruction are:

*The learner must do the work*.

And

*What the students have to say to each other is more important than what you have to say to them.*

My goal in telling teachers this is to get them to have students make personal meaning of important concepts. It doesn’t really matter whether what you’re telling students makes sense to *you*. It only matters if *they* can make sense of what they’re doing. For this reason effective educators make questioning the most important teaching tool in their arsenal. It’s the “good question” that points students in the direction of discovering a key concept – “doing the work.”

I’ve seen good teachers find these questions (seemingly) effortlessly. When watching Sandi Stanhope (ALN Operations Manager and Facilitator) work with students on subtraction, for example, I have often heard her ask an important question that leads to deeper understanding. For example, in solving the expression:

402-174

Sandi will ask, “Where can I find 174 *in* 402?”

It’s a fabulous question. Not only does it point a student in the direction of taking 402 apart into 174 and *something else*. This question gets a student right into the essential part-part-whole nature of additive reasoning. With one question the student is drawn into thinking about an expression as both addition *and *subtraction *without anyone telling them*. This is the deep nature of “The learner does the work.” This good question presents the learner with an opportunity to construct important understanding on her own.

Good questions are powerful and sometimes subtle (more on that later). Sometimes, though, questions can be simple but the *timing* of them is critical. Anyone who has ever watched Karen Reinhardt (ALN Facilitator) do a number talk will know that her favorite question is:

“How do you know?”

Someone will say, for example,

“I knew four 25s make 100.”

Karen will ask, “How do you know?”

The nature of this question – and using it at that moment – asks the student to go deeper. Often students “just know things.” By asking, “How do you know?” after making, what appears to be an obvious, assertion, Karen is asking the student to think about the concept at a deeper level, to think about *how* he knows this is true. She is asking this because she knows that there is a potential connection between money and this statement. She wants the student to be conscious of this connection, too.

In both cases these skillful teachers are making use of their deep knowledge of the mathematics they’re teaching, and using that to make a little trail of crumbs to the important concept. They *never tell students, “Here’s what you should know”*, but rather, ask a question that will help students make their own leap to a new understanding.

So, what does one do when students *don’t* make a leap, even after a good question? Sometimes even the best question is not enough to lead a student to understanding. My advice is: Ask a smaller question.

Recently, for example, I was working with a student who was trying to learn to do some mental math. She was a relative stranger to doing math in her head, so she was having difficulty with most parts of the process. I was using the equation:

15 x 12

I like this equation because it makes use of 10s, 2s, and 5s – all of which are important for developing multiplication strategies. She looked at the equation and just shrugged.

“I don’t know. I can do it with paper.”

“Ok,” I said. “Do you know what 10 x 5 is?” This is a smaller question.

“50”, she said.

“What about 10 x 2?” I asked.

“20”.

”Does that give you any ideas?” I was trying to leave her room to make a leap to decomposing, but she wasn’t able to make a connection.

“I don’t know what 10 x 12 is.” She said.

“How would that help you?” I asked.

“I could do 10 x 12 and then 5 x 12.”

I then asked her a series of smaller questions, trying to leave a trail of crumbs for her to follow conceptually. We wrote on some paper we were sharing.

“What’s 3x 10? 4 x 10? 8 x 10? 10 x 10? What do you notice about what happens when you multiply by 10?”

She looked at her answers on the paper and thought about it. Her face lit up and she said, “You add a zero at the end when you multiply by 10.” She was right… and she was wrong. I tried to head this off by reframing her statement:

“I think I see what you’re saying. You end up with a zero in the ones place when you multiply whole numbers by 10?”

“What?” She said.

“Are you actually *adding* anything? What happens when you add zero?”

She thought about this and then said, “Oh, right. OK. You’re *putting *a zero in the ones place when you make something 10 times bigger.”

I thought, OK, I can work with that.

Now I asked her, “So what’s 12 x 10?” She looked confused again so I helped her remember her own advice: “What did you tell me happens when you multiply by 10?”

“You put a zero in the one’s place because… wait, is it 120?”

“Yes!” I said. “Why?”

“Because when you multiply by 10, you put a zero in the ones place!”

This is an emerging understanding – I still want her to understand what happens multiplicatively when multiplying by 10 – but focusing on smaller questions allowed her access that she didn’t have when we began.

When a student is stuck, and I’m looking for smaller questions, I think about:

What is a concept the student would have to understand to do what she needs to do?

How could I ask a simpler question (or problem) to give her the chance to figure this out?

If I were thinking of the current problem as the *end* of a series of problems (a “goal” problem) what would previous versions look like?

Would using smaller numbers help?

Would using a simpler situation help?

Is there another piece of her work I could have her look at that might yield some insights.

As most ALN Interventionists can tell you, the first few attempts at smaller questions seem difficult. But, once you get the hang of them, the practice of asking a smaller question to encourage making a developmental leap will be second nature.

Blog: Practice Notes RSS Read more posts]]>*This week we hear from Paige Benedict about Conscious Discipline – an approach to managing challenging behaviors with integrity and respect. Since we hear quite a bit about the prevalence of these behaviors, we thought this was an important topic to explore in math teaching and learning.*

*Children with emotional challenges often have difficulty with math. There are many theories as to why this is so. Perhaps the most commonly accepted ones have to do with difficulty focusing. Approaches to managing behavioral/emotional challenges are often structured as reward systems. While this type of behaviorism is not absent from CD, the premise is to respect the humanity of the students being served, something I find is completely in line with the mission of teaching All Learners. - John Tapper*

A question on the mind of many educators right about now is, “What can I do about all the disruptive behaviors in my classroom?” I don’t have a magic wand with the answer. But through a professional development opportunity I was given this past summer, I have found a way to help get through the daily challenges with students. *Conscious Discipline* (CD) is a multidisciplinary, self-regulation program that integrates social-emotional learning, school culture and discipline. Created by Dr. Becky Bailey, Conscious Discipline is a tool that has been created for teachers and parents to facilitate changing THEIR beliefs and the way that THEY teach. To have an impact on our students, CD demands that we *commit to changing ourselves first*. Conscious Discipline has forced me to focus more on my core values and what I want to share with my students. Conscious Discipline has taught empathy to my students and has helped them through some really difficult situations.

Conscious Discipline is based on seven principles:

*https://consciousdiscipline.com/methodology/seven-skills/*

As an alternative classroom teacher, I work with students of different ages, grade levels, and skill levels. The area in which my students struggle with, maybe more than any other subject area, is math. When a student is already having a difficult time managing the world around them, expecting them to sit down and complete a math task is a challenge. Sometimes putting a worksheet down in front of them leads to screaming, ripping up the work, and storming off. Since many teachers have similar experiences, some strategies for dealing with these situations are helpful.

Conscious Discipline is based on a brain state model that *connects our internal states to our behavior*. Instead of trying to control the environment in our classrooms, we learn to control our own emotions and how we respond to stressful and unexpected situations. Every mistake is a teachable moment. Every time a conflict occurs, or a child acts out in the classroom, there is a skill missing. It is our job to use that moment to replace the missing skill with something new, something positive.

Conscious Discipline addresses these missing skills by supporting students to build trusting and safe relationships in classrooms. The school family is created through routines, rituals, and structures. Consistent routines create a safe environment for students to learn. Students know what is expected of them, what to expect in their classroom. They understand how to navigate their school day.

A common technique used in Conscious Discipline, is called, a Safe Place. The Safe Place is an area in the classroom reserved for students to go when they are feeling sad, mad, or frustrated. Along with the Safe Space, students are also taught skills they can use to help calm down before having a conversation with and adult and make a plan for moving forward.

The Safe Place has helped in many situations, but it doesn’t work for all of them. Just the other day I had a student who was given a math assignment that was supposed to be a review of content she had been covering in her 3rd grade classroom. She has been having a difficult time and hadn’t been in her classroom the last couple of weeks. As soon as the math assignment for the day was put down on the table in front of her, she exploded. She started acting out and saying things she didn’t truly mean.

After giving her some space, I had a conversation with her. I started by saying what I noticed when I handed her the math work, “I noticed that when I handed you your math work you got really angry and mad.”

Describing through noticing is a great way to achieve eye contact and begin making a connection with the student. She agreed with me, and I had her attention. “This math work is really hard for you. That must be really frustrating.” She nodded.

“Were you hoping to work on something different today?” Acknowledgment through empathy teaches emotional regulation. She nodded again.

“I wonder if we started by reviewing your work from yesterday, and then, after, I could help you with the new math work. Maybe you would feel less frustrated?” She nodded and smiled at me.

This student was triggered by seeing math work she couldn’t do. She knew it was too hard for her. Instead of getting in a power struggle with her, I chose to help her identify and name the real problem. The real problem was that the math was too hard for her and that was frustrating. I was able to help her relax and shift to an executive brain state. In the end, it was a win-win situation. She was able to express her real feelings and we accomplished some math work, together. I try to remind myself that whatever is about to happen will happen, but that it is happening in front of me and not to me. It is my job to support the student who is having a hard time and not to take it personally.

I use Conscious Discipline because it is powerful! When a student or adult is absent, or having a difficult time in our classroom, my students stop what they are doing, and wish them well. They take a moment out of their day to place that person in their heart and send them a well wish. This may seem silly, like a complete waste of time, but it makes a big difference.

When choosing to implement Conscious Discipline into your classroom, be prepared for it to start with you. The anchor charts and tools are fantastic, but you have to be willing to make the change first! Once you take the leap, I would suggest starting with rituals and routines in your morning meetings. It is important to create expectations and form a connection with students, building your school family. The next piece I would add would be the Safe Place. You may already have a place like this in your classroom, but by shifting the language and making it a common place within each classroom in the school, students understand the appropriate times to access it. For more information about Conscious Discipline and to how to use it in your classroom or school, you can visit www.consciousdiscipline.com.

Wishing You Well,

Paige Benedict, St. Albans City School

Blog: Practice Notes RSS]]>*Practice Notes has been on vacation over the holidays. We return with a piece from Essex Westford School District on a topic that has come up numerous times in ALN meetings and workshops:*

How can I use Bridges for Differentiation? Here is the learning from one district who has taken that question on.

*Using Work Places in Bridges to Differentiate and Support All Learners*

Betsy Allen, Essex Westford School District Math Coach

Essex Elementary School adopted the Bridges Program this school year. Previously we constructed our lessons guided by our curriculum Frameworks. Teachers made individual choices for lessons and grade level teams worked together on assessments and best practices. Some teachers also used stations or math menus. As we completed units we moved on to the next content focus. I wondered how could we could use this new program to address the varying needs of our students within the classroom or within the grade level, without adding more to the workload of our colleagues. Erica Moy, our math interventionist, works with K-2 classes to address some of our Tier 2 student needs. She and I are involved with the All Learners Network and wanted to find a way to bring this philosophy of focus and research to our teachers without overwhelming them.

We began by making connections to the Common Core and to Bridges. *Achieve the Core* (https://achievethecore.org/) has created a document that identifies the Major, Supporting, and Additional Clusters of standards for each grade. Bridges uses that information to guide teachers in attending to the major focus areas of their grade level. Erica and I analyzed the High Leverage Concepts with those documents as a way to support the HLC work of the All Learners Network (see the document below). Our goal was to help teachers answer the question:** “How do we ensure all students have the essential math skills to be successful in the next grade? What are those essential skills?”** This was our link for introducing the All Learners Network High Leverage Concepts with our Bridges program in a school wide workshop. We were able to show that a focus on the High Leverage Concepts was supported by both national standards and our current curriculum.

After sharing the Alignment document we asked grade level teams to identify a specific essential skill that some students are struggling with. They used data from Bridges Checkpoints, unit assessments, classroom observations, and High Leverage Assessments (kindergarten only had this data) to identify students for intervention instruction.

The next step was getting down to the real work of finding and organizing resources for reteaching. Teams worked together to create a menu of games and lessons along with a formative assessment to progress monitor students.

Teams were given an template to record their plans, like the ones above.

The idea of differentiation using menu, or *Work Places*, fits well with the Bridges program. Some teachers pulled their intervention group first while the rest of class proceeded to work places; some teachers squeezed in intervention at other times during the day; some teachers worked together to share students across classrooms; and some students received services from special educators or Erica, our interventionist. We are trying to “catch” struggling students and support them with intention.* *We know the power of “With Math I Can Do Anything!” And that **all** students need the opportunities to succeed.

**Alignment Document**

Sorry for the delay in getting another post up. Thanksgiving and all.

Our webmaster (Natasha) has added a couple of buttons to the site that will allow you to have the blogs pushed to you. Let me know how this works.

Past posts have focused on the practical side (Thank you Erin, Ashley, and Sandi). For this post, I’d like to tell a story about a woman with whom I worked for a couple of years and remind us why we do the work we do. I tell my college students that they’re learning to do a job that can change the world every day. And, it’s true.

I was doing some research at a literacy lab in Hartford when one of the teachers approached me. We had been holding focus groups for our study and she had been a participant.

“You’re the math guy, right?”

“Well,” I said, “I’m *a* math guy. What can I do for you?”

She told me about her wife who had terrible problems with math. She had been trying to get into nursing school but kept failing the basic math exam. She asked me if I could work with her. After finding out a little bit about her, I agreed to meet her.

I didn’t expect my meeting with Marcie to amount to much. Up to that point, most of the adults I’d worked with were overwhelmed by math would give up pretty quickly. They didn’t seem to like the element of learning math where you had to get stuck – and then make the intuitive leap to deeper understanding. When faced with something that feels unsafe, the automatic response from the brain is to prepare for flight or fight. This is an evolutional adaptation. The mind can’t attend to critical thinking when it’s in a survival state. When you’re scared, it’s hard to do math. (Much more on this in a future post)

Marcie was (and still is) one of the fiercest people I know. She just wanted to know if it were possible to really learn math, if everyone could really do it. I told her that, aside from a couple of students I’d worked with who were nonverbal and had severe physical limitations, I’d never come across anyone who *couldn’t* learn math. I’d worked with some students who weren’t particularly interested in learning it, but even they were competent. That was all she needed.

***

Marcie came from one of those families that every teacher deals with from time to time. Her father was in jail a good part of her childhood and her mother had problems with substance abuse. At the age of 12, Marcie took charge of her two toddler sisters. She made sure they were fed, as safe as a girl her age could make them. She made sure they felt some sense of parental love. When I met her, the girls were teenagers and about to move in with her and her wife. This should tell you much about her as a person. She is fierce and fiercely loyal.

She took on this absurdly difficult job into the sixth grade with the usual work a middle school student must do. Not surprisingly, her school work suffered, particularly her work on math. She had way more important things to do than what she did in school. She prioritized. Unfortunately, this is when she started getting unhelpful comments about her native ability from her teachers. That trend continued throughout high school. In the end, Marcie came to believe that she was stupid (her words) when it came to math.

***

As you read this, I’m sure you can think of 20 kids who believe the same thing about themselves and math. Sometimes the message comes at very young ages. There are obvious ways children get the message that they are incapable, tracking, for example. And, there are subtle ways they come to understand that there’s something wrong with them, like when we use the term, “low kids”. Even the term I use so much, “struggling learners” has a message to it. We are trying to communicate that we want to support some students to be more successful but, sometimes, we show a bias that is deeper than we realize. This is why I always ask teachers, “Do you believe that EVERY child can learn math?” This is a different question than, “Do you WISH every child could learn math?” Working with Marcie challenged me to think hard about what I really believed.

I worked with Marcie for two years. I never pushed her. We took things at her pace. Some weeks she was overwhelmed by her life and seemed to take two steps backward. We recalibrated, returned to previous concepts and strategies, and began again. Some weeks she was sharp, and her intellect showed. I tried not to have too many expectations about her work on any given week. We were in this work for *understanding*, and that often means patience and steadiness. During that time, I grew very fond of her, of her incredible persistence, and of her clever mind. It’s the thing we all do with our students. I’ve often wondered how that positive regard translates to support learning.

She eventually took the exam and was passed into a more advanced class for nursing than “basic math”. She did well in that class. I spoke with the woman at the community college who tested her. Her score on algebra and geometry was almost perfect. The arithmetic part of the test, material which brought back strong memories of inadequacy for Marcie, was harder. The tester told me she frequently stopped and closed her eyes before continuing. I told her this was her way of dealing with the anxiety. We had worked out ways for her to identify her anxiety when it arose and to calm herself down, so she could access to her own cognitive resources. In these moments she was upshifting from her brain’s survival state to its executive state.

Marcie, it should be obvious, had a big impact on my teaching. She made me a believer that *all* students can learn. She taught me what it means to listen to a learner, to be patient for understanding, and to encourage persistence with an absolute faith in her ability.

John Tapper

Winooski, VT

Blog: Practice Notes RSS]]>One of the reasons I joined the All Learner’s Network is the High Leverage Concepts. There is so much power in the HLC’s. There is power in their focus. There is power in pushing students to deep understandings of each concept. As a math interventionist at my school, the High Leverage Concepts are the guide-map for all our math intervention. We determine what intervention instruction students receive based on their understanding of the HLC’s. Number talk strings are chosen based on a students’ understanding of the HLC’s. Goals are written with the HLC’s in mind. Essentially, the HLC’s drive every aspect of math intervention at our school. As a result, I spent most of last year building up resources, tools, instructional strategies, and manipulatives that help students better develop their own understanding of each High Leverage Concept. My intervention instruction was more targeted, more focused, and the tools and manipulatives students were using were producing lots of growth in understanding.

By the end of last year, my intervention instruction was at a whole new level just by staying focused. However, there were still some big obstacles I was facing in each of my intervention groups. I was still plagued with some heavy questions for my most struggling learners. What can I do to increase student engagement in math class, especially for the students who believe they are not good at math? How can I create math experiences for students that better connect to real life, especially for students who believe the math we’re doing doesn’t matter? How can I help students leave behind problematic labels or beliefs about their own potential in math class?

I stepped into my summer job still pondering these questions. In restaurant work, there is always down time in between meals when the employees are just filling the time with prep work. As I completed prep task after prep task at Folino’s over the summer, I would create pizza-related math problems related to each High Leverage Concept. It was my math dork way of getting through the boring work of food prep, but it was also the seed for the idea to create math field trips at Folino’s.

The more restaurant industry math problems I made up in my head, the more I realized that problem-solving in a real world context is one way to try to address some of those questions that plagued me last school year. I believe that the excitement of being surrounded by the restaurant while problem-solving and the opportunity to be immersed in the actual real life context of each problem will create an even higher level of engagement and effort in math problem-solving than we may see in our classrooms. I think stepping out of our classrooms and into the real world is a way for some students to step out of the labels they live in inside our school walls. I believe that a math field trip to Folino’s could be a mini math experience for some of our students that helps shift the belief they have about their own ability to problem solve and make sense of the math.

I created a set of 4-6 pizza math problems related to each High Leverage Concept at the grade levels K-5. In addition, there is a series of problems related to the Folino’s pizza dough recipe for grades 6-8 that also all connect back to the HLC’s around proportional. Below is a link to the info on booking a field trip! If you go to Folino’s with your class, please let me know how it goes!!!!

LINK TO MATH FIELD TRIPS AT FOLINO’S INFORMATION FOR BOOKING TRIPS

Pre And Post Field Trip Activities

Erin Oliver

Math Specialist at Grand Isle School

**FOLINO’S MATH CHALLENGE PROBLEMS**

**FIRST GRADE**

Tyler just folded 85 boxes. How many stacks of 10 boxes can he build with the boxes that he folded?

A birthday party orders 5 juice boxes, 9 cokes, and 4 sunkists. How many total drinks does Amanda need to charge them for?

At the beginning of the night, we only have enough shrimp left for 20 more of the firecracker shrimp pizza. Erin sells 3 shrimp pizzas for a take out order and 5 more for customers in the restaurant. How many shrimp pizzas do we have left to sell?

There are 33 seats still available in the restaurant at 6 o’clock on Friday night. At 6:30, Tyler seats a group of 10 people. How many seats are available in the restaurant now?

Bobby folds 42 boxes in one hour. Seth folds 49 boxes in one hour. How many more boxes did Seth fold than Bobby?

**SECOND GRADE**

Erin knows that the restaurant needs 35 salads prepped and in the salad line before the dinner rush. There are already 7 done. How many more does Erin have to prep?

There are 4 reservations for 5 o’clock. Bobby needs to reserve 8 seats for a birthday party. He needs to reserve 9 seats for a work party. He also needs to reserve 6 seats for a family. How many total seats does he need to reserve?

405 is the record number of pizzas sold in one day at Folino’s. Seth told the team that they had sold 256 pizzas so far that day. How many more pizzas would they need to sell to **beat **the record?

Jesse, Alex, and Julio are making a big pizza order. A school wants 40 pizzas for a celebration. They want 10 pepperoni, 12 cheese, and 9 buffalo chicken. The rest will be sausage. How many sausage pizzas do they need to make for the school?

For Saturday, Seth figures out that we need to have 368 large dough containers ready to cook. There are already 54 dough containers in the front and another 139 in the back cooler. How many more dough containers does Seth need for the night?

Last weekend was super busy for the team. On Friday, the team sold 329 pizzas. On Saturday, they sold 285 pizzas. How many did they sell in total for the two days?

**THIRD GRADE**

Maeve is refilling small ranch containers before the dinner rush. She figures out she needs to fill 30 more containers. Draw three different arrays that she could arrange her containers into to make the task easier. Write a multiplication equation that matches each drawing.

Charlotte is folding more large pizza boxes to get ready for the dinner rush. She needs to fold enough boxes to make five stacks of fifteen. How many pizza boxes does she need to fold in total?

The special pizza tonight is an eggplant parm. Seth wants to know how many more special pizzas can we make before we run out of the eggplant slices. There are 75 eggplant slices left, and we put 8 slices of eggplant on each special pizza. How many more pizzas can we make before we run out?

Buddy needs to buy enough menus to leave three on every table. Inside the restaurant there are 11 tables. Outside on the patio, there are 8 more tables. How many menus does Buddy need to buy for the restaurant?

Seth needs to transfer 160 dough containers to the Folino’s in Shelburne. Each transfer bin holds 40 dough containers. How many transfer bins should Seth bring with him?

A family of 6 comes to the restaurant. They order 3 large pizzas. There are 8 slices of pizza on each large. How many slices does each family member get to eat?

**FOURTH GRADE**

Amanda is folding boxes. She has four packs of unfolded boxes. Each pack comes with 50 unfolded boxes. How many stacks of 15 boxes can Emily fold and build? Will she have leftover boxes?

Six friends went to Folino’s for a birthday party. They decided to order 5 large pizzas. They ordered a pepperoni and a margherita pizza for 16 dollars each. They ordered a buffalo chicken pizza and an BK special for 18 dollars each. They ordered a frankenstein pizza for 19 dollars. They decide to split their total bill between all 6 of them. How much does each person have to pay?

Bobby is looking for someone to come clean pizza stains off the carpet at the restaurant. He knows that the carpet area is 22 feet by 35 feet. The carpet cleaner he finds charges based on the size of the carpet. He told Bobby he calculates the price by dividing the area of the carpet in half and charging that amount in dollars. How much will he charge Bobby to clean the carpet?

A family of 5 comes to the restaurant. They order 3 large pizzas. There are 8 slices of pizza on each large. How many slices does each family member get to eat? Will there be leftover slices if everyone eats the same amount?

Seth needs to transfer 250 dough containers to the Folino’s in Shelburne. Each transfer bin holds 40 dough containers. How many transfer bins should Seth bring with him?

Our dough recipe makes 1 batch of dough which is enough for 155 large pizzas. We are expecting to sell over 300 large pizzas this Friday night. We already have 54 large dough containers in the walk-in cooler. How many more large pizza doughs do we need? Should he make 1 more batch of dough or 2 more batches of dough?

**FIFTH GRADE**

The recipe for our scallops calls for ¼ cup of lemon juice for every batch. Mama has 3 cups of lemon juice left. How many batches of scallops can she make with the lemon juice she has?

Our water jugs hold 5 gallons of water, but Erin only fills it up to the 2 ½ gallon mark to make it easier to carry. By late lunch, ⅔ of a gallon are already gone. How many gallons of water are left in the jug before Erin will need to refill it?

A family of five orders 3 large pizzas: a buffalo chicken pizza, a veggie pizza, and a cheese pizza. Each pizza is cut into 8 slices. The mom ate ½ of the veggie pizza slices. The dad ate ¼ of the buffalo chicken slices and a ¼ of the cheese slices. Each of the three children ate ⅛ of the slices on each pizza. How many slices are left of each of their pizzas?

Tyler walks to work at Folino’s every day. He walks ⅚ of a mile to get to the restaurant in the morning. On the way home, he takes a shortcut and walks ⅘ of a mile home. How many miles total does he walk he day?

**MIDDLE SCHOOL (6th-8th)**

The middle school Folino’s math challenge problems are set up differently than the elementary grades. The middle schoolers will be given the real Folino’s pizza dough recipe and will be faced with four different problem-solving stations related to the dough recipe that are based on the real-life math that happens with the dough recipe every day!

Dough recipe problem 1- Students will be given the cost of all the ingredients for one batch of dough and the amount of dough containers one batch produces. They will use this recipe to calculate the unit cost of one dough container.

Dough recipe problem 2- ** **Students will use the original recipe and figure out the amount of ingredients needed for ½ of a batch, ⅓ of a batch, a double batch, and a triple batch.

Dough recipe problem 3- Students will figure out how much dough to make for the next morning based on formulas that the restaurant uses to calculate this every day.

Dough recipe problem 4- Students are given the ratio of the diameter of an unstretched large dough ball to the diameter of stretched large pizza dough. Students use this ratio to figure out how much you could stretch other size dough balls. They are also given the formula to figure out area of a circle to compare the square inches of pizza for each size as well.

Follow Blog: Practice Notes RSS]]>The *Problem Introduction Protocol* was a joint effort among all the coaches at the first All Learners convening. We were searching for a way to provide access to problems being used during Main Lesson. Often, students who had trouble would raise their hands almost immediately to declare, “I don’t get it.” We observed that there was something fundamentally amiss when a student couldn’t even begin a problem. As a result, we created an approach for introducing problems that, we thought, would provide an opportunity for everyone to take a stab at the problem. The original version was launched more than a year ago. After gathering some (admittedly thin) data from practitioners, we’ve come up with the version below.

The Ongoing Cohort of ALN is going to be testing this protocol this fall. We’ll report on the results in December. In the meantime, if any educators use what we describe in the blog below, please let us know what your experience was. You can start a conversation or add to an existing one here: https://alllearnersnetwork.com/community/

• Read the problem chorally.

• Ask, “What are we trying to figure out?”

• Ask, “What would an answer to that look like?”

• Brainstorm strategies

We do this to accommodate students who might have difficulty with reading and those whose first language is not English. Older kids fuss a bit about reading chorally, but I make them do it anyway. It’s important that students get a chance to hear a clear reading of the problem.

In the first few iterations of this approach we had the teacher read the problem to students before the choral reading. I wouldn’t discourage this, particularly in one-on-one settings. In general, though, people reported that this was overkill.

** **

Step 2 involves determining what kind of answer we’re looking for. Many teachers write a statement on the board to summarize student thinking. Some teachers have students write a statement on the paper where they’re going to solve. Some (teachers of younger children) will write it on the board and ask students to copy it onto their papers.

Whether you write it or not, students should all be able to articulate what the goal of the problem or task is.

This step was a contribution from our Maryland colleagues. It’s really helpful. We don’t use this step exactly as written. In other words, we don’t ask students this question. Instead, we ask about two elements of the problem:

What units will the answer have?

What’s a ballpark estimate for the answer?

The estimate is usually the result of a teacher question about extreme (and unreasonable) answers. Teachers will ask questions like, “Could it be 1? Could it be 100?” By eliminating unreasonable answers we’re helping kids narrow their thinking a bit.

So when you’re done with this step, kids should know what the units for the answer will be and what a reasonable solution might look like.

When I introduce this to teachers I have the habit of saying, “This piece should come with a Surgeon General’s Warning: Do Not Narrow the List of Strategies”. As students suggest strategies (addition, making a list, drawing a picture, multiplication, etc.) teachers simply respond by saying, “We might be able to use that strategy.”

An example of what doesn’t work is when teachers say that one strategy is the “right” one: “Yes, this is a division problem.” We want to leave the possibility open for children to use whatever makes the most sense to them, even if (right now) it’s not the most efficient approach.

One added piece to the brainstorming that seems to work well is to record the strategies on the board. As students are getting started they can refer to these.

This is a step that we originally included, and one that is recommended by several texts on supporting struggling learners. While we want children to get the important information from the problem, the practice of highlighting or underlining numbers or important facts often translates into students pulling numbers out of the problem and doing some (often inappropriate) arithmetic. The result is a “How Old is the Shepherd?” outcome. For this reason we don’t use this step in the protocol. It doesn’t mean, of course, that you can’t. But if you have students find important information, be sure they have a strategy that makes sense to them and makes sense mathematically.

The Problem Introduction Protocol, then, facilitates reading of the problem, focuses on what the answer is trying to find, gives a decent estimate for a solution, and provides a variety of strategies for getting started. So far it has provided greater access for students to get started with problem solving. As always, we’re interested in your experience with this technique. Please let us know how it worked for you.

*John Tapper*

The *30 minutes of Math Intervention* is the time when our math interventionist pulls a small group of students (a mixed group from four different classes). Our Special Educator also pulls a small group of students (also a mixed group from four classes). I work to support a group of students from my own class at this time. I choose to use Math Menu for intervention.

For my Math Menu at this point in the school year, students are able to move fluidly through multiplication fact practice, math games, skill practice and an exit ticket/formative assessment/journal based on the current content in my first instruction. Students have 30 minutes and (right now) can choose which activities they need/want to work on. I am still in Phase I of Math Menu implementation[*]. In the next few weeks I hope to be more deliberate in preparing math menu options that are specific to certain students and their needs.

I choose to use Math Menu during my intervention block because it is an opportunity for me to support students in their learning based on where they are at NOW. The separate intervention block encourages teachers to follow a Tier 2 intervention plan where students are receiving instruction based on an informed decision by the teacher. Currently, I use the information gained from my CRA on multiplicative reasoning- the high leverage skill listed under third grade on The Map to determine who will have “Teacher Time” as part of their Math Menu.

My focus for this group is on modeling multiplication using equal groups. I also re-teach/pre-teach to some students during this time based on information gained from their Exit Tickets in first instruction. Math Menu works well for my intervention block because students feel empowered with choice. In the few weeks that we’ve been doing Math Menu so far, I’ve observed that all students are engaged, they work the whole time, they work quietly and they say that they really enjoy it. I like that I’m able to focus on instruction when meeting with my group because the management of the rest of the class is fluid.

I find that students make good choices for themselves, but are also willing to complete the “Must Do’s” when I ask because they know they will also get choice in their next activity. I asked my students what they think about Math Menu and these are their responses:

*“I like the different activities and I like specifically math games.”*

*“I like that you get to pick your own choice. One thing we do want is even more choices that are some easy and some hard.”*

*“I think math menu is one of the best parts of the day because you get to be free and do math games and stuff.”*

Having a designated intervention time outside of first instruction has allowed me the flexibility to ease into using Math Menu in my class. My goal is to move to a more fluid math block that includes Math Menu over the course of the whole math lesson. I enjoy Number Talk and Math Message as a whole class because of the dialogue, but I’m thinking I can start Math Menu BEFORE snack so that it is also part of my first instruction. That way all students have Math Menu time, because in our current format, students who are pulled for small groups are not necessarily getting a Math Menu on a regular basis.

[*] For more information on the continuum supporting menu development, please see the *Developing Menu *link at: https://alllearnersnetwork.com/math-coaching-tools

*Ashley Marlow*

*Grade 3 Teacher*

*Colchester, VT*

]]>

We were hoping to attract 100 “math people” to Killington last Friday. In all, 228 people attending the Math for All conference. It was an outstanding turnout to support the important work of helping *every* student to be successful with essential mathematics. There were many helpful suggestions for future work. Most people had an overwhelming positive experience:

*“I thoroughly enjoyed the whole day from beginning to end. It is always nice to get together with colleagues from other schools / districts. On a side note: Lunch was fabulous, too.” *

*“I was very engaged in all sessions and learned a lot. I was honestly pleasantly surprised by how much I took away from this!”*

*“I look forward to working with the All Learners Network! Excellent conference. A huge thank you to the AOE for funding the event.”*

Here are some things I think we learned from the conference:

· We might need to do a session in the Northern and the Southern Vermont.

While we had a great turnout from the southern part of the state. We had far fewer from up north. This meant our recruiting was much better south of Rutland.

· We need to do something (in a workshop) around Main Lesson.

There was an abundance of information around Menu and Launch (through Number Talks) but less about how to design inclusive experiences during the Main Lesson. This is something we’ll consider in the future.

· People appreciate information from the leadership perspective.

We knew there would be a few leaders who would want to know more about the “bigger picture”. Responses to workshops from Linda Keating, Jill Cohen, and I lead us to believe that we need to pay attention to keeping leaders engaged productively.

· There is passion and commitment to serve all learners in Vermont.

One of the big take-aways for me was how eager participants were to access more knowledge and resources to augment their ability to guide and support students to be successful. The energy participants brought to the conference was amazing. I think this will help us learn much more in the coming year.

It was a wonderful day of conversations – and just the beginning. Please check on this blog regularly as we’re committed to putting up new information here regularly.

We’ll let everyone know when we’ve booked a date for the Specialized Instruction day in November. This will be a series of workshops designed specifically for Special Educators and interventionists. We’ll look at Clinical Interviews, Collaborative Study, Inclusive Practices for Main Lesson, Push-in During Menu and Addressing Specific Learning Challenges like working memory and attention deficit. Please let your SpEd folks and interventionists know that it’s coming and keep checking the website!

John Tapper

Winooski, VT

Follow Blog: Practice Notes RSS]]>Teachers participating in our All Learners Convening in early June had the opportunity to review and suggest edits to the High Leverage Assessments (HLAs). I facilitated the discussions around the HLAs for Kindergarten, First Grade and Second Grade. Our group included teachers from Maine and Vermont who communicated their experiences with the HLAs and the student outcomes. These teachers had used the HLAs with multiple students in a variety of classrooms and had a lot to share. The discussions were dynamic and focused on creating or refining tasks that targeted students’ understanding of the important identified concepts on the MAP (our continuum of math understanding). We didn’t just talk about the assessments. At the center of all our conversations, we talked about how young children develop their mathematical thinking and how to support all of them.

It was really hard to bring closure to our conversations because there was always one more “what about…?”, so we created a “next steps” list. One of the next steps was linked to our thinking about pre-requisites skills and knowledge needed to be successful in kindergarten. MJ Mitiguy (Georgia Elementary & Middle School, VT) and I agreed to investigate what that might look like in Pre-K. The question we wanted to address was “What would we want Pre-K children to know and be able to do before they entered Kindergarten?”

We met on September 7th and brought lots of resources to support our work. Research done by Douglas Clements, Julie Sarama, & Kathy Richards around preschool number sense was very helpful. We also used our years of experience with other assessments to identify critical concepts being developed in Pre-K. Two essential understandings became quite clear- subitizing and counting. (I bet that’s no surprise to those of you who teach Pre-K children.)

Subitizing and Counting are at the foundation of all mathematics. After creating the High Leverage Concepts for Pre-K, we then created a High Leverage Assessment (an interview) to pilot this year with interested pre-school teachers and their students.

This is an opportunity for us to actually employ the ALP Rapid Cycle of Inquiry that John wrote about in the previous blog post (Sept. 4, 2018). We’re hoping that Pre-K teachers will use these suggestions and resources and let us know the results. Anyone interested? We hope so. The materials and resources will be shared on this site along with the other HLAs. Please keep us posted.

Sandi Stanhope

Swanton, VT

Follow Blog: Practice Notes RSS]]>And, beside all the tools and support materials we’ve posted online, there is also this blog – *Practice Notes. *The intention with these publications is to bring new understandings to the whole network about teaching experiments, district initiatives, new tools, and new resources. *Practice Notes* will be a resource to support the ALP Rapid Cycle of Inquiry – our practice of trying out new instructional techniques or resources and reporting back to the group.

As we report this fall, you should stayed tuned for pieces from Network members on:

The new Middle School HLCs and assessments

Templates for a 30-minute intervention block

The use of the Rekenrek as an alternative intervention model to 10 frames

Techniques for choosing low-floor-high-ceiling tasks for Main Lesson

Supporting students with challenges for inclusion in the Main Lesson

Menu for Middle School

Using HLAs for Clinical Interviews

Getting teachers onboard with differentiation

For the first post, I want to articulate the critical elements of All Learners. For people new to our work, this will help (I think). For those of you who’ve been onboard for a while, this may add some clarification. We’ve included a version of these elements on the website.

The All Learners Project began life as an attempt to walk the talk of, “All students can learn.” Coaches in the Franklin West Supervisory Union did all the groundbreaking work on this idea in the spring of 2016. The idea was further fleshed out through work with the Worcester County Schools in Worcester, Maryland and the Mount Desert Island School District in Maine. (Why these places? It’s a long story. The short version is that I was working with these folks and the leaders in these districts were people with vision and skill. They made it happen)

Within the first year, we saw very positive results – some measurable, some more qualitative. As a rapid cycle of inquiry is part of our essential elements, we learned a great deal (and continue to learn) about how to support our students in increasingly effective ways. As math leaders and teachers began to see the results a *hope* that all kids could learn math became a *belief* that they could. When faced with a difficult challenge – such as including a student who was three years behind the class in a Main Lesson – our motto became, “all means all.” One of my favorite Special educators said of our effort, “Just because we don’t know how to do it now, doesn’t mean it can’t be done. We’ll figure it out.”

The All Learner Project relies on the following components to do its work:

High Leverage Concepts (What matters most, the most effect for the effort)

All Learners Lesson Structure (inclusion AND differentiation)

A Systems Approach that Starts with Math Leaders (and relies on professional learning communities)

A Rapid Cycle of Inquiry (We “try things out” and reflect on their effectiveness)

Formative Assessment (Understanding student thinking leads to good instruction)

**1.** **High Leverage Concepts**

*High Leverage Concepts (HLC) are key mathematical understandings that students will need to be successful in the following year of school. For example, all students need to demonstrate understanding of the HLC in first grade – adding and subtracting numbers to 120 – to be successful in second grade where they will be adding and subtracting numbers within 1,000. HLCs are the focus of most/all remedial efforts at a particular grade level.*

**2. All Learners Lesson Structure**

*The All Learners Project makes use of a workshop-style approach to lessons in order to leverage both inclusion and differentiation for student learning. Instruction in the All Learners Project is focused on the use of conceptual models to facilitate individual student understanding. Multiple ways to solve (and understand) problems are encouraged. The elements of the All Learners Lessons include:*

*Launch (often a Number Talk or short problem)*

*Main Lesson (focused on heterogeneous problem solving and student discourse)*

*Menu (a differentiated part of the lesson used for remediation and the presentation of “just right” practice and reflection)*

*Closure (a time for sharing, reflection, and formative assessment)*

**3. The Use of Instructional Leaders to Facilitate Instructional Growth**

*Instructional coaches and teacher-leaders are the key participants in the All Learners Project. Through tools made available in ALP instructional leaders support teachers to develop their pedagogical skill, interpret and use assessment data, and support learners who struggle with math. *

**4. A Rapid Cycle of Inquiry**

*The instructional leaders who have participated in the All Learners Project are concerned primarily with what works. That is, they are focused on instructional practices that support all learners to demonstrate understanding of High Leverage Concepts before the end of the year. ALP coaches are constantly trying new practices, revising instruments (like the High Leverage Assessment), learning and revising techniques (like clinical interviews). As teachers and coaches in the field find success, their results are reported throughout the ALP network so others can validate or revise these new practices. *

**5. Formative Assessment Informs Instruction**

*The All Learners Project is focused on the success of *every* child. We believe that children can only be successful at mathematics if they construct their own understanding from experience. Since each learner has unique qualities, a big focus of our work is on understanding how students think in order to provide them with the kinds of experiences that will deepen their conceptual understanding or make it more efficient. We use Formative Probes, Clinical Interviews, Collaborative Studies – specific coaching tools to help teachers and leaders get good information on student understanding and plan accordingly.*

I hope you’ve found this introduction to the All Learners Project helpful, or at least informative. We’re happy that you found your way here and hope that we can engage you in our rich conversation as we find ways to help *every* student be successful with mathematics.

John Tapper

Winooski, Vermont

Follow Blog: Practice Notes RSS]]>