Wednesday, December 27, 2017

Communicating Mathematically

One of my favorite activities I do in PBL 101 trainings for BIE is the ideal graduate.  The activity involves participants writing the knowledge, skills and dispositions students would have when they graduate. I add a twist to the activity by having people to think about one student that they love and one student they wish were absent. They must think of traits that both students would possess at graduation.

When I first did this activity for myself, it wasn't hard to come up with a list of items. What was difficult was narrowing my list down to something I could realistically work on students achieving in one school year. My list is 10 traits that have changed slightly over the years.

Although the list hasn't changed much, my strategies and classroom protocols change frequently. I think about what I do that prevents and support my ideal graduate. This is a very humbling experience because I have to admit what is not supporting my goal. For example, I have long wanted students to be a self-manager. A long classroom practice was keeping students materials in a bin in the room. I did it because they often would not keep up with items. However, this past summer I realized I was not giving them even an opportunity to self-manage. This year I have a bin but is only for students who feel they can't keep up with the notebook. I encourage students to keep the items and I periodically check to make sure they have them. So far, I have about 30 students out of about a 130 who use the bins.

Another trait I have made some major changes to this year is communication. I am modeling proper mathematical communication more and using a basic rubric more consistently to support my expectations. The rubric follows the same format at the concept rubric to help students understand. The rubric includes students written and oral communication of mathematical concepts. You can get a copy of one of my rubrics for a concept and communication by clicking here.
My changes are a great compliment to some of my past practices that support the building of students communication. One of my practices is a common one to classes--Ask 3 before me. I have a huge poster on my door that I reference a lot during the beginning of the school year and after winter break. I have discovered it is really important to call students on if they asked people before asking me. I often will go to the people they ask and see what they said. Rather than just letting the students say they didn't know. I challenge them to say what they do know and work with the students to improve their collaboration. 

Another strategy I use is one day dedicated to students only working with each other to solve a problem or a set of problems. This day is embedded in my 2-1 cycle. Students get at least 2 days to understand a concept before an assessment will be taken. Sometimes these assessments are placed in the gradebook. Every time the assessments are used for students to reflect on their learning progress. Typically, students are allowed to work together on the first assessment. I spend this time observing or reviewing other classes work. Below is a video I captured during one of the days students could work with each other. Notice the discussion occuring between the students.

How do you help students communicate mathematically? What is your ideal graduate?

Saturday, September 16, 2017

Whirlwind of Strategies to Build the Culture

The last three weeks were crazy. In addition to so many things occurring in the school, there was a slight hiccup with me being out to complete trainings in Boston and Tulsa. My goal of posting once a week had to be put on hold. I am going to try to summarize some of the greatest aspects of the last three weeks that involve building a culture that is ripe for PBL. Build the Culture is an essential element for teachers to implement PBL. BIE defines it as teachers explicitly and implicitly promote student independence and growth, open-ended inquiry, team spirit and attention to quality. In this post, I talk about strategies I used to promote independence and growth and team spirit.

Promoting Student Independence and Growth

Setting and Monitoring Expectations 
In order for students to be independent, they must be a part of setting the classroom routines and rituals. One way of doing this is having them set how we work together. As a part of the syllabus project, students created norms for me and for each other. They were able to submit their own suggestions for norms. I compiled the list and students voted for five. The top five voted norms were placed on a poster (see the list of norms below).

Although I haven't done a great job of it for the last few weeks, I try to recognize students who are following the norms and update the norms periodically. Before I was out of the classroom for a few days, I talked to students about the norms, specifically number 1 and 4. I explained how this is an expectation that is even higher when I am out of the building. It is important that they respect the substitute and our room. They need to speak politely and clean up their space. I had a student from each class period text me a picture of the classroom at the end of the class period. If the classroom was clean and there was no bad report from the substitute, they would receive candy. A small reward for following the norms. When I returned from my second time of being out of the classroom, I was happy to see these post it notes from the substitute. We had a lot of substitutes at the beginning of the month, it is easy for students to not follow the norms when a few of their classes were substitutes.

Ask 3 Before Me & Help Desk
Students are not used to leaning on themselves and each other to understand concepts. Ask 3 before me is a great strategy to help students to start to lean on each other rather than the teacher. For almost 7 weeks, I worked on students asking each other and modeling proper ways to help. Students also had the benefit of identified SMEs to get help. Some students had a hard time with this rule. One mentioned openly that he doesn't like getting help from students. While rubbing his back, I told him how I understand how he feels but the rule still applies. He needs to see the greatness in his fellow classmates.

After students learned how to lean on each other, I started to create another form of support that involved me. This helps me fulfill one of the norms they created for me. It is called the help desk. After students have received their first round of feedback, I have one to two class period where they continue to practice but can come to the help desk to get one on one help from me. Thankfully the implementation of the other supports, I don't have hardly any students who need the help desk.
Help desk is a section of the room where students get help.

Team Spirit

It is so important for students to feel connected to each other so that they help each other learn. In addition to doing team builder activities several times for the first few weeks of school, I try to do a team builder a week. Two of the team builders students did in the last few weeks is to choose a team name and symbol. Various competitions and tasks will be supported by their team name and symbol. It is a small way to help connect them together.
Example of Team Names and Symbols

How do you build culture in your classroom?


I have always had a hard time accepting compliments. It is not that I don't appreciate it. Sometimes it makes me feel uncomfortable. I feel like everyone's eyes are on me and I fight to find words to say. Other times I can't identify with what they see. I see all my faults rather than my strengths.

However, I love giving people compliments and telling them how much I appreciate them. I try to give a compliment or say thank you to everyone I encounter. Last year, people shared how I have impacted their life as 40th birthday gift. It was very humbling and made me realize I need to take in the compliments as well as the criticism.  As a start, I would like to share two great compliments I received last month.

I almost fell out of my chair when I read through my emails on August 9th. The state director of elementary mathematics and coordinator of the Presidential Award for Excellence in Mathematics and Science Teaching shared with me that I was one of 3 state finalist (see email below). Although I may not be chosen at the national level, I am honored to be recognized for my teaching at the state level.
Email confirming my selection for PAEMST

Teacher of the Month
Marquee displaying James Womack and I as teacher of the month
At the beginning of September, I was informed by my principal that I was selected by my peers to be the teacher of the month along with another co-worker. I thought it was going to be just a simple recognition in the school newsletter. I was blown away when I saw my name on the school marquee. Although we do not need to put everyone's names up in lights, it is important to appreciate people. I realized this month that I can't stop appreciating people and it does feel good to be appreciated.

How do you show colleagues and students you appreciate them?

Sunday, August 27, 2017

Roles that Reflect the World & Maintains the Classroom

When I first started teaching, I wanted to model the working world I had worked in for over 10 years. I was always told that school helps prepare you to be a productive citizen and have a career. I thought what better way to run my classroom similar to the career world. It was in the first two years of teaching that I created Logic Inc (Click here for how I did it). It is a fictional consulting company that helps their clients solve their most pressing problems using mathematical concepts. I explain on the first day of school that they are apart of this company which will build their resume and open up opportunities for employment. This is very enticing for my high school students who want to make money.
This is the company logo.

Consistent Classroom Roles

One of the components of the company is roles that will remain constant all school year. These are roles the students get to have input on the qualifications and are allowed to interview to be in the positions. My current constant roles are manager, SME and class reporter. A manager oversees 3 to 5 students for the duration of a unit or a project. They are responsible for helping students who were absent be caught up, facilitate activities, encourage collaboration among the team and reporting the health of the team to the CEO (the teacher). A SME is a subject matter expert who helps students to understand a concept during work time. As seen in the picture below, SMEs float around the room helping any student with problems. A class reporter is responsible for summarizing what occurred in the classroom that day.

Qualifications for the Roles

There are basic requirements I have for each role. A manager must have a desire or shown leadership abilities. A SME must have demonstrated understanding of the concept in which they are helping students. A class reporter must know how to type and be organized. 

However, students get to add at least two additional qualifications they want in a person for each role. This is completed during the syllabus project completed within the first 3 weeks of school. During the project, students are told about the roles. They ask questions about the details of each role. The answers and their past experience shapes their suggestion for what qualifications the person should have. They submit their personal thoughts individually and then work as a team to create a final proposal of qualifications. Below are three students suggestion for this school year's qualifications. 

Selecting & Supporting Students for the Roles

After the classes vote for the qualifications, students apply and interview for the positions. The application process is simply asking them during an opening activity all the positions they want to be considered. They have the option to not apply for a position at all. During an extended class work time day, I interview students for the various positions. Here are the interview questions I am using this year when interviewing the students. It is based upon my own requirements and the requested qualifications of the students. I plan on interviewing students every 9 weeks because sometimes a student doesn't want to apply at one point in time and changes their mind later. There are times that I appoint a student without them applying. 

Supporting the students is something I am still working on and invite suggestions. For this year, I am going to meet with the managers on a weekly basis. They will fill out a quick form to update me on their team by Thursday and I will discuss with them changes we need to make on Friday. During my weekly discussions with them, I will share quick tips to develop them and troubleshoot any issues. The meeting will be from 5 to 10 minutes as a group. I will have a meeting with all SMEs right before they are required to help people on classwork days. I will share with them questioning techniques and coach them during the day they are helping. Class reporter will review my postings in Edmodo to guide them on how to summarize and report to the class. I will provide suggestions for the first few days of their work and then I will monitor on a weekly basis.

Friday, August 25, 2017

Getting To Know Each Other

I hate team builders, energizers, ice breakers or whatever you want to call games you play to get to know or connect with people. You wouldn't know I hate them if you ever play one with me. The competitive side of me takes over and I am immediately in it to win it. Sometimes it is not even a contest but I make it one.

Even though I hate it, I have not found a more powerful way for me to get to know my students and for them to get to know each other. I have found it to be an effective tool for building community even for those who would rather not "play". This year, I have made a commitment to do them more often than just the beginning of the year or when things seem off. My goal is to do one at least once a week after the syllabus project ends. I also complete other routines or tasks to get to know my students. In this post, I share how I use team builders to set the culture of the class, some of my favorite team builders, how I will use team builders to develop soft skills and ways I get to know my students.

Setting the Culture

To help set the culture of my class, I have students participate in what I call a lite version of PBL. I call it lite because it doesn't have all of the 8 essential elements of PBL. However, it has some of the key elements that can be easily done outside of a PBL and it helps to build the culture for when students complete a PBL. In the syllabus project, students are working to answer the driving question--"How can we create a fair and engaging learning environment?". While answering this question, we complete almost daily team builders.

Students are finding their seats through a class challenge

Starting with the first day of school, students get into their assigned seat by completing a challenge. The first student to class is the only person who can give the directions that are already written on the board. Everyone else has to be silent. This is usually a stretch for this student because the first student to class is typically a shy student. They have to sit in the correct order within a specified time frame. They do this challenge every day for 5 to 7 days depending on what day of the week school begins and how many schedule changes have to occur. Some examples of ways they have to sit include alphabetical order, height, number of pets or number of extracurricular activities. I take pictures the entire time so that I can see who are the leaders and followers and other personality traits.

Favorite Team Builders

My wonderful friend Myla Lee shared a great site of team builders with me a few years ago. It is I have been sharing this site with everyone I meet. One of the ones I have used on the site is Two Truths and a Lie.

I am in love with Kagan. In addition to having great collaboration structures for learning, they have great team builders. I have used a few activities out of their teambuilding book. I have used blind sequencing, match mine and team interview. I also love their team builder cube and silly sports and goofy games flip chart. The picture below is students playing "Magic 11" found on page 21 of the flip chart. Students move their fist in the air and a leader counts--one, two, three, eleven. On the count of eleven, students make a fist or show 1 to 5 fingers. They count and if they make 11 they win. If they don't, they try again but they can never tell people what number to use.

Developing Soft Skills 

We always say we want students to be better communicators or critical thinkers or creative. However, none of these things just happen. We have to intentionally teach and assess it for students to develop it. I use team builders to teach various skills that I have as a goal for students. To teach a soft skill, I have students complete a team builder that brings out one of the skills I want students to develop. While they complete the team builder, I walk around collecting evidence of the outcomes I want students to have in regards to the skill. During the debrief, I point out the observations as well as lead a discussion with the students. For assessment, I walk around with a clipboard that has the seating chart and mailing labels with the learning scale. I observe a group and write the assessment of each student on the seating chart. I then write it on a mailing label and gives it to each student.

Other Ways to Learn About Students

I have every student complete an index card sharing details about themselves. I place all of the cards on a ring so that I can refer to them throughout the year and update them as I find out new information. Below are the details of what students write on the card. The front is basically their contact information and any important information they want me to know. Sometimes students have shared that their parents are getting a divorce or they have lost a family member recently.

A colleague shared with me a great form for students to fill out at the beginning of school as well. In addition to filling in the information. You can allow students to be creative and color in parts of the intro about themselves.

What do you do to get to know your students?

Tuesday, August 22, 2017

Need Your Input

I can't believe it has been 12 years since I started teaching and working to implement PBL in my classroom. Time really does pass by fast when you are having fun. I am excited to finally take enough things off my plate where I can share my classroom on a regular basis.

It seems like yesterday when Suzie Boss and Jane Krauss convinced me to blog about my experience. I shared how I wish I could be a bird on the outside of a window looking in on a PBL classroom. A few moments later I agreed to blog about my first collaborative PBL. I really enjoyed sharing how I worked with my 9th grade academy team to implement the food project.

I want to share again but include items that people really need. I am thinking of sharing videos of my classroom as well as materials. Please write in the comments below what you would like to see from my classroom. I am going to also use this to help edit a book I am writing with Chris Fancher this fall.

Thanks so much. I can't wait to post more details based upon your feedback this week.

Wednesday, March 15, 2017

Collaboration Dynamics

When you think of a math classroom, you probably think of a teacher explaining how to do a problem in the front of the room. You may also think of students doing about 20 of the same problems. Rarely do you think of students discussing problem solving strategies in small groups or wrestling with a concept as an entire class.

However, students talking is the heart of doing PBL in a math classroom. It is a research based practice proven to increase mathematical competence. National Council of Teachers Mathematics explained the necessary elements for mathematical learning in their Principals to Action publication. One of the necessary elements for effective teaching is discourse. "Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments."

It is easy to say students need to have discourse but it is sometimes hard to make it happen. Here are some strategies I have found indispensable to facilitate discourse.

This is a commonly used strategy and great way to get students started on working collaboratively. I typically start with students thinking about the answer to a success starter (a question at the beginning of class that gets them started with the day rather than review). They then talk it out with a partner even if it is just details about where they got stuck and how they may need help. I don't let them say I don't know. The share is them sharing what the other person said.

Rally Coach
A love a lot of Kagan strategies but this one is a favorite. Here are the steps for the cooperative learning strategy:

  1. Pair Shoulder Partners. Determine who is A and who is B.
  2. Present a problem for which there is only one correct answer.
  3. Partner A solves the problem while Partner B coaches, checks the accuracy of the answer and praises.
  4. If the answer is incorrect, Partner B coaches Partner A to the correct answer.
  5. Present a new one-answer-only problem. 
  6. Partner B solves the problem while Partner B coaches, checks the accuracy of the answer and praises. 
  7. Repeat from step 1. 
Some of the twists I make to the process is students are given the problems that have a similar format like the one on this worksheet. I like using it because the answer is the same for the same number problem. I have the students use a colored pencil for accountability purposes. They must write a synopsis of what they said to coach the student using the colored pencil.

Question Formulation Technique (QFT)
This is a great strategy for having students develop their inquiry muscles. Students work individually and small groups to generate questions for them to explore within a unit. Students generate the questions from viewing a prompt (an image or words) that requires following four simple rules. The rules are ask as many questions as you can, do not judge or discuss questions, change any statements into questions and write down every question exactly as stated. Students go through a refining process and use the questions to make sense of the unit. You can find out more details on the technique at

Paideia Seminar
Many people are familiar with the socratic seminar. Paideia is similar in that students do have a discussion however it includes more than just a discussion. It is a complete process for reading, writing, speaking and listening. It is one of my students favorite activity in my class. They are always asking me when are we going to do a seminar. I use Paideia seminars to help my students discuss deeply as a class and to deepen their conceptual understanding. Students have a pre-reading which is typically a difficult math problem, a portion of a reading or an examination of a student's math work. Students then move into the discussion which includes them setting goals for the seminar and evaluating themselves at the end of the discussion. The discussion is guided by my questions. Students complete the circle of the seminar with a response to a writing prompt. Get more information about Paideia seminar from their website.

I would love to hear about some of your strategies for having students collaborate. Respond by commenting below.

Saturday, February 6, 2016

5, 4, 3, 2, 1....And We Are Off!

Scott Haselwood has issued me a challenge.  He knows I can't back down from a challenge. Below are my answers to his five questions. I hope you will join the challenge too.
What has been your ONE big struggle during this school year?
1. Saying yes to good things but not to the best things.
Share TWO accomplishments that you are proud of from this school year?
1. I am really glad that we did not have students who didn't have a teacher in the math department.
2. I am proud that we are having more fun together as a faculty. We have events each month and more and more people are joining the festivities.
What are THREE things you wish to accomplish before the end of the school year?
1. Finish a book that I am writing with Chris Fancher on Project-Based Learning in the math classroom.
2. More than 90% of my students pass the Geometry EOI test.
3. Precalculus students finish their first book on making math concepts simplier.
Give FOUR reasons why you remain in education in today’s rough culture.
1. Teaching is what God has called me to do. I can't miss my calling because it gets rough.
2. As Rita Pierson said, every kid needs a champion.
3. I absolutely love it.
4.  The kids, the kids, the kids.
Which FIVE people do you hope will take the challenge of answering these questions.
Rafanz Davis - She is a guru at tech and math.
Myla Lee - One of the best elementary teachers I know.
Jonathan Atchley - Every time I interact with him on twitter or edcamps, he fills me up.
Kelli Anglley - Can't stop retweeting your comments.
Sarah Hagan - I love her dedication to her students. Drumright is lucky to have her.
Read some other responses:
Teach From Here
For the Love

Monday, December 21, 2015

Great Ideas for 2nd Semester

Every 3rd Monday of the month, I host a math webinar for secondary math teachers in Oklahoma. It is a joint partnership by Oklahoma Council of Teachers of Mathematics and OK Math Teachers. Today, the webinar focused on great ideas for second semester. The ideas were focused on classroom routines, assessment and learning strategies. During the webinar, I shared some of my classroom resources. This post is an expansion of that discussion as well as links to many of the resources.

Classroom Routines
Our routines say a lot about what we believe as a teacher. In the summer, I always take time to think about my beliefs and what I want my students to accomplish. I then think about what I am doing or not doing to help achieve my goal. During holiday break, I think about how well I am doing towards my goals. I use this time to make adjustments and set a plan to change course 2nd semester. In the webinar, I shared some of my routines that support my educational philosophy and student goals.

Collective Wisdom: One of my goals for my students is for them to know how to self-manage. This means they must be given the opportunity to decide how to manage. For the last couple of years, I have implemented an activity called collective wisdom. I explain to students that I only have one rule for the class--Don't be a problem (I got this from Love and Logic). Although it is a simple rule, what constitutes a problem must be decided between us. The students then write on a 3 x 5 card a problem for them. I take the top 5 to 6 problems and students complete the collective wisdom protocol using the following form:
  • On the form, write one of the problems at the top and tape it on the wall. Example problem is classmate is disruptive during class. Repeat this for all of the problems making sure there is distance between each paper.
  • Students number off  based upon the number of posters. 
  • Students go and stand next to their assigned poster. 
  • Teacher gives each group a different colored marker
  • For 2 minutes, students write possible causes and solutions for the the given problem.
  • At the end of time, students rotate clockwise to the next poster adding possible causes and solutions for 3 or 4 minutes.
  • Students rotate until they are back at their poster. They star the best cause and solution and share it with the class.
  • The star will now be how the class will handle the given challenge. Copies will be made of all posters and placed in the class folders.
Contracts: In addition to being able to self-manage, I want students to know how to work with anyone. One of the ways I help students to work with people is for them to create a contract with their group members. Here is an example of a completed contract and here is a link to the contract form:
Tracking Progress: One of my greatest educational philosophies is that I must help my students be 21st century literate. According to Alvin Toffler this is the ability to learn, unlearn and relearn. A foundation to be able to acquire this skill is the ability to know how you are doing towards a learning goal as well as how to change course on your learning journey. I teach my students how to track and analyze their progress. Here is a picture and link to the form I use:

This is a power packed topic. I have spent over 5 years just studying the topic. I shared two resources to think about as you go into 2nd semester. The first resource was a technique I learned through the book Max Teaching with Reading and Writing: Classroom Activities for Helping Students Learn New Subject Matter While Acquiring Literacy Skills. It is called Math Translation. Here is a link to an example created by Tulsa Public Schools. 

The second resource was rubrics. The use of rubrics has changed my classroom. It enables me to have a different conversation with my students. Rather than talking about points and what can I do for extra credit. We talk about demonstration of learning based upon the rubric. Here is a link to one of my rubrics. 

Learning Strategies
The webinar ended with learning strategies. I did a brief discussion of number talks and complex tasks. I referred to webinars for both of the topics.  The link for the number talks webinar is The link for complex tasks is

Wednesday, September 18, 2013

Conceptual Understanding and Procedural Fluency

I know I am supposed to share my first few years of PBL. I have it all in my head. I just got distracted with school. Things are starting to be "normal" for me so I am going to try and write weekly. Key word is try :). I want to share something that happened in class this week. It is not PBL but a key aspect of helping all kids learn math deeply which is the heart of PBL.

In my Algebra II classes, we started the systems of equations unit on Monday. I always start a unit with a small pre-assessment. It is never more than four multiple-choice or written response questions and it is basically skills students need to be successful during the unit. See this link if you want to know the pre-assessment questions. Well, the pre-assessment let me know that most kids didn't have the necessary background and I would have to do some reteaching as we learn how to solve a system of equations. 

We started with the simplest way to solve--graphing. We reviewed how to convert an equation into slope-intercept form so that they could graph the equations. The example I used was 2x + 4y = 36 and 10y - 5x = 0. I knew from the pre-test that some students knew how to convert from standard form to slope-intercept form so I just asked for volunteers on how to convert the two equations. This gave me the opportunity to see how students approached converting the equation. For the first equation, some students wanted to divide by four for each term. Although this is a perfectly acceptable first step, I asked for another way just to make sure I didn't throw off students by putting fractions in early. 

In each class, various students helped me follow the typical process of subtracting/adding the term with the x variable, then dividing by the number with the y variable at the end. With each step, I reminded students of the desired result (isolating the variable of y) and why we are doing each step. We then completed the last step of placing the equations in the graphing calculator to determine the solution. I send them off to work time like normal and this is where the class becomes interesting. 

I completely expected to help students with using the graphing calculator. We have only had them a week. However, I was shocked by the number of students who were still lost with converting the equation. At the end of the day, I discovered the root of the problem was students lacked the fundamental understanding of equations. They had practiced such a specific algorithm they didn't know what to do if it came in a different form. For instance, the first problem in the book was 2y - 3x = 7 and 5x = 4y - 12. A few didn't know where to begin while others were doing the typical process. As I helped student after student, everyone wanted to subtract 5x as for he second equation.   

Just like other teachers, I thought about what to do the next day. The plan calls for me to move on to substitution. They have a test on Thursday that includes them solving by graphing and substitution. The students don't have a conceptual or even a solid procedural fluency of equations. 

What would you do? How do you help students who have misinformation while staying on track with learning new information?