A Tale of Two Projects: Week 1 Algebra 2 Sports Science Project

The first week of the 4th-six-weeks grading period was a short one at Cedars International Next Generation High School due to a school holiday on Monday, 1/16, and Benchmark testing on 1/17.  The 3 remaining days were still quite dense.  In this time, we launched two projects in my two main preps, Algebra 2 and Integrated Physics and Engineering (IPE).  This article describes the the first week of the Sports Science Project, an Algebra 2 project on Quadratic Functions.  The next article in this series will describe what happened in the first week of the Emerging Technologies (or NSF) project in IPE. To read about the prep that went into preparing for the launches of these two projects, you can read this blog article.  To read about later phases in this project, visit this page: A Tale of 2+ Projects.


 Repeated Disclaimer: If you don’t want to know about all the details in the PBL sausage, stop reading.  


Day 1, Algebra 2 Sports Science Project: LAUNCH!

On Wednesday, 1/18, we started the Algebra 2 class with a few activities to wrap up the NERFallistics project.  In that project students learned about polynomials and applied that knowledge while analyzing the trajectories of NERF gun pellets.  These wrap up activities were designed to give students time to reflect and revise their work.  To set the right tone and maintain the suspense for the new project a little longer, I used this for my opening agenda slide:

The band-aid is over the project icon for the project we were wrapping up, the NERFallistics  project.  The icon symbolized the work we were going to do to fix the boo-boos in our last project.  

In the NERF Report Reflection warmup, the students read over their report feedback, checked their report grades, and made plans with their NERF teammate to make revisions on the report.  In my classes, students always have 2 weeks to re-submit deliverables: after 1 week, they can earn up to a 90% on their resubmitted work; after 2 weeks, they can earn up to a 70% on resubmitted work, and after that, I no longer accept the work.  After they completed that reflection, I gave students time to complete a culminating activity from the last project that many teams did not have time to finish during our last class meeting.  In the Target Practice activity, students had to solve a regression equation the modeled the trajectories of their NERF guns to in order to hit a table and a small chair in the common room of our school.  One team succeeded in hitting the table and the chair shown below from distances of 10+ meters away.  They were exuberant to find that sometimes, Math really works!

After these wrap-up activities, we started off the six-weeks with our traditional once-a-six-weeks Class Officer Elections.  Every six weeks, my students in each period elect 3 class officers: a facilitator, a time manager, and a grade manager.  I learned how to integrate and train student leaders in my classes from my friend and mentor from Manor New Tech HS, Ms. Holly Davis.  The facilitator starts the the class each day by going over the class agenda with the class.  He or she does this while I take care of start of class logistics like taking attendance, refilling my coffee, etc.  The time manager keeps track of the time for the class and makes time announcements to alert students and teachers of the time left in class activities and in the class period.  The grade manager gathers student work on my grading days (each Friday) and follows up with students who need to submit work late because they missed some due dates.  The elections are both playful and quite serious.  Candidates give speeches to convince the class that they will be the most effective student at their desired roles.  

I let the students take their time with this process because I rely heavily on my class officers to do my job effectively.  I’m so used to effective time managers that I don’t know what time some of my classes end.  I’m just used to my timekeeper telling me when to wrap things up and move on to the next period.  My facilitator acts as my acting sub when I’m absent.  When I’m out, the facilitator leads the class through activities while the adult-sub-on-record takes attendance, hangs out, and watches.  Sometimes I get so far ahead in my prep that I forget what we’re about to do in class until my facilitator goes over it with the class.   My grade managers are amazing!  I may not have the best turn in rates on the original due dates, but my 1-week-late turn-in rate is awesome thanks to all the in-person / emailed reminders students receive from my grade managers when they forget to turn in work.


After class officer elections, we announced new teams and set up our notebooks for the next project.  

After setting up their table of contents for the new project, the students read over the design brief with their team and came up with at least 10 Knows and 10 Need-to-Knows for the project.  They divided these into Content (Algebra 2 related) items and Project (logistics, deadlines, etc) items.  The design brief communicated the project’s objectives, purpose, rough timeline and deliverables.  In the Sports Science project, students will gather and analyze 100-m dash data to create a sports science video that investigates the question: What separates everyday and world class athletes?  In addition to analyzing the Design Brief, we watched a sample ESPN Sport Science video featuring Lebron James.  This video provided a sample of their final product and showed them how motion data can be used to make a compelling argument.


Later that day, I prepared for Days 2 and 3 of the project by preparing a workshop and practice set on position-time graphs and by purchasing a 300-ft long tape measure.  My co-teacher, Mr. Fishman, had me download the Home Depot app so I could shop for my tape measure efficiently.  When you’re in the store, you can search for products and the app will give you the aisle and section of the store for the product along with a labeled map of the store.  It was so sweet.  I bought calculator batteries and a crazy long tape measure in record time using the app.


I sometimes joke with my friends that my Algebra 2 class is my Physics-2 class.  About half of the students in Algebra 2 are also taking my Integrated Physics and Engineering class.  Sometimes our projects in Algebra 2 are situated in Physics contexts because the math fits and I can’t resist because of my physics background.  This is why I found myself preparing an activity on Position-Time graphs for my Algebra 2 (not Physics) students.  I prepared the lesson because it was in my students’ need-to-knows and because I knew that students needed to be equipped with this knowledge to make sense of the data they were going to gather on their 100-m runs.  (On a side note, my students sometimes get confused by all the math they are learning in physics and all the physics they are learning in math; sometimes they write their notes in the wrong notebook and end up writing a weird location in their table of contents for an activity they placed in the wrong notebook.)


I also spent some time search for videos of world class athletes in 100-m races that we could analyze for our comparison cases.  It was really challenging to find the perfect video because many distances within the 100-m are not marked.  I settled for looking for videos with sideview camera angles and found one video that compiled sideview from several races.


[Spoiler alert] Later in Week 2 of the project I came up with a way to approximately analyze world class run data.  Usain Bolt’s stride length is well documented.  I was able to analyze his world record 100 meter run by using Coach my Video to find the times associated with each of his strides (exact time that one foot hit the ground) and used his average stride length to determine positions for those times.  Later in the project, I provided students with a data table of his world record run so they could analyze it and  compare his motion stats to their own run data.


Day 2, Algebra 2 Sports Science Project: Team Contracts / Explore Position-Time Graphs:

We started off Day 2 by completing a warm-up that was a pre-assessment on what students already knew or could deduce about position-time graphs:


I scanned their notebooks and the results were hit-or-miss.  A couple students did it perfectly, many more guessed several wrong, and a couple didn’t know where to start.  After the time manager let us know that the warm-up time was over, I told students I was going to break protocol and not go over the warm-up at this time.  I did this because we were about to go over position-time graphs and I reused the warm-up problems to make up half of the follow-up practice set to this activity.

After the warm-up, the student facilitator went over the agenda and then led a class discussion to come up with a compiled list of student Knows and Need-to-Knows.  Here are the students’ Content Knows and Need-to-Knows:


And here are their Project Knows and Need-to-Knows:

I had to play devil’s advocate a bit to get students to elaborate on their Content Knows.  They’re pretty good at specifically articulating  their Content Need-to-Knows and Project Knows and Need-to-Knows.  Over the course of the project, we will revisit and update their Knows and Need-to-Knows as students learn new things and develop more questions.

After the Knows and Need-to-Knows discussion the students set up their team contracts and shared project Google folders.  The students completed this Team Contract template and then placed their finished contract in a sheet protector and inside the Team Contract binder.  Over the course of the project they will revisit their contract and use the back side of it to document their Work Log goals and agreements.  While they prepared their contracts, I linked their Google folder to the Project Rubric Chart:


I’ve streamlined student turn-in processes such that their nearly all their work lives in 2 places: (1) in their notebook and (2) in shared project Google folders.  If their work is located in a project Google folder, I link the folder and its key contents to a rubric chart.  I use the rubric chart to give students yellow and green stamps on project work that relate to rubric items (see left column).  Having the links very close to the rubric makes it easy for me to assess project products against the rubric.  Later in the project, students refer to the rubric chart on work days to see which items they have earned full (green stamp) and partial (yellow stamp) credit.  

After they set-up their team contracts and team Google folder, we started an activity on Position-Time graphs.  I set up the workshop to be interactive. Throughout the workshop, I displayed a prompt on the board and had their teams discuss the prompt while I played Jeopardy music. While the music played, I overheard their discussions and looked at their proposed motion graphs.  After the music stopped, I called on the students with interesting insights and went over the correct answers.  We did this 10 times.  By the end of these cycles we had completed and thoroughly discussed a graphic organizer that showed the shapes for all the types of motion they would need in the project: stopped motion, constant velocity (positive and negative direction), increasing speed (positive and negative direction) and decreasing speed (positive and negative direction).

Also, while developing these workshop slides. I came up with a new trick to convey the alignment between state standards and workshop objectives.  I color-code the verbs (red) and noun / noun phrases (blue) in both the standards and the objectives to highlight the connections between the two.  I now do that in all my workshop objectives slides and in all my daily agenda slides.

After the workshop, students redid the warm-up problems and did a few more practice problems on motion graphs.  Nearly every students was able to do the warm-up perfectly on the first try after the workshop.

Later on Day 2, I did some big picture planning of the content scaffolding in the Sports Science project.  I looked at the standards again and ranked them from easiest to hardest and grouped them by similarity and developed an outline for a lesson sequence that would cover all the standards.  In broad strokes I decided we would start by learning several techniques to formulate quadratic equations (from easy to hard), then learn how to solve quadratic equations, and then learn how to solve systems of linear and quadratic equations.  


Day 3, Algebra 2 Sports Science Project: RUN, STUDENTS RUN!!!

Prior to class on Day 3, I prepped for an exciting Data Collection day by using spreadsheets to create a Track Marking conversion chart (meters to feet and inches):

I also created this visual to convey all the hats students would need to wear in order to ensure a safe, efficient time in the parking lot:


Also at the end of Day 3, I knew I needed to get student work for my grading day, so I created this visual:

This visual shows my Algebra 2 grade manager in the middle of his election speech.  He gave me permission to use that pic in visuals reminding students of deadlines.   [Spoiler Alert] My grade manager enjoyed this image so much, he had me put it up again in the IPE class where he also got elected into this role.


Data Collection day was a blast!  The whole class helped to prepare the track on the parking lot behind the school.  I put a student in charge of the tape measure and in charge of organizing the team effort to create the track.  The students were really smart.  They designed the track in a way that made data collection of a tricky data set really simple.  They used long lines to mark each 2-meter increment and they marked each line with the total distance from the starting line to that line:

It took them about a half hour to create the track.  Then I demonstrated how to properly videotape a run, by taping Mr. Ray while he ran.  This involves some back pedaling and some frantic, laughing and chasing while trying to aim the iPad camera in a way that the runner’s feet passing each increment line is captured throughout the 100-meter run.  It was really fun to watch students to gather data.  By some trick of Murphy’s law, nearly every team had a big height mismatch between their (very tall) runner and their (very short) camera-person.  However, the track design that my students came up with, made it possible to get excellent data even when the camera shorts were really dynamic due to the chasing that was occurring.  

Mental Note for Future Versions of this Project:  Everyone needs to wear running clothes and shoes because the photographers ended up running just as hard as the runner to get good footage.


Here’s a sample data set that came from a video that was really bumpy:

Even though they were unable to see some of the track markings (usually when the photographer transitioned from backpedaling to forward chasing), they still gathered enough data to see clear quadratic and linear regions.  Just the thing needed to learn how to solve systems of linear and quadratic equations!  Every team was able to get a good data set that made sense.  Data Collection day was a surprising success.  I was worried that the data would be too hard to get or too dirty to analyze, but everything worked out great.


At the end of Day 3, I did my routine Friday grading of notebooks. After I graded all the notebooks, I used conditional formatting on my Google spreadsheets grade book to create this visual.  I cropped out the student names for this post.  Red boxes represent missing work and green boxes represent turned-in work.  I emailed this visual (the version with the student names) to the grade manager along with a couple links to Google forms associated with a couple of these tasks.  My grade manager sent follow-up emails to students missing work and during the following week, he collected late notebooks from students on Tuesday when I decided to follow-up on some late work.  By Wednesday the chart was nearly all green except for one student who was out sick for several days.  Student Leadership Rocks!


Pre-Week 2 Prep:


Over the weekend, I prepped lessons that showed how to use Desmos to find linear and quadratic regression equations.  I also prepared a warmup that had students compare motion equations to linear and quadratic equations in order to relate motion quantities to the parameters in the standard forms of linear and quadratic equations.  I also finalized a Shell Science Lab Challenge grant in the hopes of getting more support to design more and higher quality STEM experiences like the ones we had in Week 1 of the Sports Science project.

CINGHS Week 2: Aug 29 – Sep 2

Week 2 School-wide Events:


During Week 2, two students led our very first school tour for visitors from the Texas Charter School association.  The students presented an overview of our school culture and logistics while guiding our visitors through a tour of our school.  They did an excellent job for their first times. This was the first of MANY MORE tours that our students will lead this year and beyond.


On Monday of Week 2, our school tried out our very first Student-Directed Learning Time (SLDT) time.  During this weekly work session, students get to make their own choices on how to best use a 2-hour block of open work time.  Students got to choose from a menu of optional and mandatory 20-minute workshops in Art, ELA, Engineering, and Math.  Also during that time, students got several opportunities to attend an info session on the Games / eSports Club.  Students not attending workshops also had time to catch up on work in any of their classes while working as individuals or with their new project teams.  It was very cool to see many students using this time wisely to further their educations.


Week 2 in 8th Grade Math:


In 8th grade Math, we launched a new project, Join the Club.  In this project, students will learn about mean, median, mode, range, and mean deviation by gathering and analyzing school-wide data on students’ club interests.  One of the project’s early activities was the Graph the Class Activity.  In this activity, we practiced analyzing the interests of one period’s levels of interests in Mondays, Sports, Arts & Crafts, and Video Games.  While completing this activity, students practiced creating bar graphs and calculating mean, median, and mode.  During a class discussion on their results, my 4th period was very excited that many of their summary results equalled 3.  They claimed this was a sign of the Illuminati.  This outburst of enthusiasm showed me how willing the students are to make connections between math and things in their own lives that they find interesting.


Week 2 in Integrated Physics & Engineering (IPE):


In IPE, we launched a new project called What’s Cooking?  In this project, students will learn about the design process, thermodynamics, electrostatics and electric circuits by inventing next generation cooking devices that are battery-powered and also powered by standard US electrical outlets.  During our project launch, our newly-elected class officers got their first opportunities to lead student-led discussions.  Our facilitators led class-wide discussions aimed at generating class-wide lists of project knows and need-to-knows.  I was impressed by how well our class officers involved ALL students in the class discussions and at the amount of Content-specific information the students included in their knows and need-to-knows.


During this week, we led our first Content workshops: Intro to Engineering Design Process and Intro to Thermodynamics.  We also started our weekly Friday tradition of ZAP time (Zeroes Are not Permitted).  During this team, students checked their notebooks to make sure they had all the activity stamps in their notebooks that went with all the graded activities for Week 2.


Week 2 in Algebra 2:


In Algebra 2, we launched an Amusement Park Logo project.   In this project, students will learn about parent functions and inverse functions by using them to create and analyze an amusement park logo.  We held our first content workshop on Parent Functions.  In this workshop, we learned the parent function names and equations.  We also practiced finding the domain, range, axes of symmetry and asymptotes of parent functions.  We also learned how to represent domain and range 3 ways: inequalities, set notation and interval notation.


Toward the end of the week, we had our very first 3-color quiz on Parent Functions.  In 3 color quizzes students use 3 colors to represent 3 different sources of info: brain only, notebook and workshop.  After students had used all 3 colors, they had a visual on what they could do on their own and with the aid of resources (notebook and/or workshop).  After this activity I asked the class if they wanted me to create more parent function practice sets.  I was surprised and impressed that most of the class requested that I create extra practice sets so they could continue to develop their understandings of parent functions.

171: Assessing Metacognition (1 of 4)





Screen Shot 2016-05-08 at 9.41.20 PM


  1. Focused Autobiographical Sketches
    • Description
      • Students write a 1 to 2 page autobiographical sketch about a past successful learning experience that may be relevant to a current course
    • Purpose
      • Can help teachers set realistic executives and objectives based on knowledge of students
      • Provides starting line info on how to assess learning
      • Build feelings of self efficacy associated with a course
    • Step-by-Step Procedure
      • Find an element of learning experiences to focus on that relates to course goals and objectives.
      • Can limit still further by limiting the life areas (personal, work, academic) and time periods autobiographical sketches can be drawn from.
      • Determine criteria that will be used to assess the sketches.  Make sure prompt will direct students to create sketches that relate to assessment criteria.
      • Design a prompt that ties to focus & assessment criteria of assignment.
      • Assign prompt to students.
    • Analysis Steps
      • Scan responses and read for stories that relate to course goals.  Try to notice stories and lessons that can be shared to give students advice on how to succeed in the course.
    • Extension Ides
      • Ask students to explain why they deemed their experiences to be successful.
      • After trust is established, ask students to write a Focused Autobiographic Sketch about lessons learned from personal failures.
      • Ask students to focus on story from the point of view of someone else involved.
    • Pros
      • Focused prompts give teachers info on students that’s more relevant to the course than general background statements.
      • Give info on range of past learning experiences and self awareness of students.
    • Cons
      • No simple guidelines for assessing the quality of this assessment.
      • Reading and analyzing sketches takes a lot of time.
    • Caveats
      • Students may need coaching on writing self-reflective prose before this assessment can yield good information.
      • Some students may balk at sharing their stories, even if done anonymously.
  2. Interest / Knowledge / Skills Checklists
    • Description
      • Students respond to checklists to communicate their interests and levels of related skills
    • Purpose
      • Inform teachers of students’ interest in course-related topics and students’ levels of related skills
      • Teachers can use data above to adjust syllabi
    • Step-by-Step Procedure
      • Divide a paper into two columns.  On one column list course topics.  On other column list related skills.
      • Come up with a simple form that will help you code students’ answers.  Examples:  use checklist with Likert scale response per item
      • Let students know why you are gathering data on their interests and skills.  Can keep surveys anonymous.
    • Analysis Steps
      • Can generate bar graphs that show average Likert responses per item.
      • If the surveys are submitted via Google form these bar charts can be created in Google spreadsheets
      • Share interesting data trends and features with students
    • Extension Ides
      • Ask students to explain why they are interested (not interested in) top (bottom) 3 topics
      • Use a graphic display to show overlap between student interests and course goals
    • Pros
      • Gives teachers access to data that helps with course planning
      • Teacher can compare students’ self perceived competencies with his or her own observations
      • Having students be explicit about their interests and skills and how they relate to the course will help them be more self-aware
    • Cons
      • Sizable front end investment to create checklists and analysis tools
      • Results may show that students’ interests do not align well with current course goals
    • Caveats
      • Students may lack interest in topics due to ignorance.  They may develop an interest when they learn more.
      • Assessments may be more a measure of self-confidence than prior learning.


Getting to know students is a key step in building positive relationships with students that can promote deeper learning.  The strategies above can help teachers harvest information on students’ habits, motivations, interests and skills.  Teachers who use this data to improve their course design are more likely to create and facilitate engaging projects for students.


Preparation Steps
  • Determine what you would like to learn about your students as learners – what information could help you design better projects and interventions?
  • Decide which format (Focused Autobiographical Sketch or Interest/Knowledge/Skills Checklists) will more readily yield the information you want.
  • Design prompts or forms that go with the selected strategy.
  • Decide how you will analyze the data gathered by the selected strategy.
Early Implementation Steps
  • Explain why you want students to complete the selected assessment.  Explain how it will inform your teaching and course design.
  • Give students time to complete the assessment – in class or out of class.
  • Analyze patterns and trends in students’ responses.
  • Share interesting stories, patterns and trends with students and explain how these connect to course goals.
Advanced Implementation Steps
  • Let students complete assessment at the start and beginning of the course to see if habits, skills, and/or interests change.
  • Try out one of the extension ideas described above.



153: Teaching Math for a Growth Mindset



Screen Shot 2016-05-09 at 6.49.00 AM


Setting Up Classroom Norms:
  • Positive Norms for Math Classes:
    1. Everyone can learn math to the highest levels.
    2. Mistakes are valuable.
    3. Questions are really important.
    4. Math is about creativity and sense making.
    5. Math is about connections and communicating.
    6. Depth is much more important than speed.
    7. Math class is about learning, not performing.
  • In small groups, lets students specify norms for things they’d like to see / hear / experience (or not) while team problem solving.  Create posters of student preferences.
  • Skills to teach:
    • Listening to each other
    • Respecting each other
    • Building on each other’s ideas
  • Communicate expectations for what math looks like when teams are actively processing such as:
    • Your group will be successful today if you are …
      • Recognizing and describing patterns
      • Justifying thinking and using multiple representations
      • Making connections between different approaches and representations
      • Using words, arrows, numbers and color coding to communicate ideas clearly
      • Explaining ideas clearly to team members and the teacher
      • Asking questions to understand the thinking of other team members
      • Asking questions that push the group to go deeper
      • Organizing a presentation so that people outside the group can understand your group’s thinking
    • I will be looking for:
      • Learning and working in the middle of the table
      • Equal air time
      • Sticking together
      • Listening to each other
      • Asking each other lots of questions
      • Following your team roles
    • You can use the checklists above to record what you’re observing while students work in teams and to provide them feedback on their teamwork.
Believe in All of Your Students
  • Have high expectations for all students and provide support and positive messaging that helps students believe & demonstrate that they can achieve your high expectations
  • Avoid early tracking
  • Avoid unspoken messages that communicate that you don’t believe is someone’s potential – like only assigning them easy work
Value Struggle and Failure
  • Assign challenging math problems that provide opportunities for struggle and learning mistakes
  • Assign low floor, high ceiling tasks
  • Communicate frequently that struggle and failure are good (failing forward)
  • Break the myth of “effortless achievement”; all achievers worked hard and failed, even geniuses
Give Growth Praise and Help
  • Growth praise and help focuses on strategies and effort, not on ability
  • When students do math problem wrong – start by validating the strategy they used to first tackle the problem before redirecting them to new strategies
  • Instead of breaking down problems for students – ask them to draw the problem and see what ideas come out of that activity
  • When students can handle a little more struggle – respond to their requests for help by saying – Do you want my brain to grow or your brain to grow?
  • Show students that math is a growth subject
Teach Math as an Open, Growth, Learning Subject
  • Closed math problems – just ask for calculations, promote a fixed mindset
  • Open up math problems so they invite students to think and grow.
    • Example of opening up math problems:
      • Closed form:  What is 1/2 divided by 1/4?
      • Open form: Make a conjecture about the answer to 1/2 divided by 1/4 and make sense of the answer by using a visual representation of the solution.
      • Closed form: Simplify (1/3)(2x+15)+8
      • Open form: Find as many ways as possible to represent (1/3)(2x+15)+8 that are equivalent.
      • Closed form:  Find the 100th case.
      • Open form: How is the pattern growing? Use your understanding of the pattern to generalize to the 100th case.
  • Ask students to discuss:
    • ways of seeing mathematics
    • ways of representing ideas
    • different pathways through problems and solutions
    • why use different methods
    • how do different methods work
  • Instead of just finding answers allow students to:
    • explore ideas
    • make connections
    • value growth and learning
    • learn standard procedures when they are ready to see the need for them and can make sense of them
Encourage Students to be Mathematicians
  • What mathematicians do and think:
    • math is creative, beautiful and aesthetic
    • propose and test ideas
    • develop working definitions for ideas based on consensus and reasoning
    • share thinking and ideas
  • Do not be afraid to call students, young mathematicians – why not? if they can be young artists and young musicians, why not young mathematicians?
Teach Mathematics as a Subject of Patterns and Connections
  • Encourage students to see themselves as pattern seekers
  • Teach traditional procedures as one of many sense making approaches to perform operations
  • Encourage students to see math as a classification and study of all possible patterns
  • Give students an active role in pattern seeking
  • Help and let students see the connections between methods
Teach Creative and Visual Mathematics
  • In expectations ask students not for speed, but for creative solutions to problems
  • Engage students by asking them to represent problems visually
  • Connect visual ideas with numerical or algebraic methods / solutions
  • Color code:
    • represent the same ideas (ex: the variable x) using the same color
    • illustrate division by using different colors for partitions (division quilt)
Encourage Intuition and Freedom of Thought
  • Encourage intuition by asking students what they think would work before showing them a method
    • give them opportunities to try their methods on problems before teaching new methods
  • Start with the hypothesis that any subject can be taught effectively in some “intellectually honest” form to a child (Bruner)
Value Depth over Speed
  • Ask questions that are open enough to bring depth into discussions
    • Closed form:  Supplementary angles add up to what number?
    • Open forms: Can two acute angles be supplementary angles?  Can two obtuse angles be supplementary angles?
    • Closed form asks for a single answer.
    • Open form provokes conjectures and discussions.
  • Ask students who finish early to extend problems in any way they wish
  • Aim for depth, not speed – engage students by allowing them to go deeper into problems
Connect Mathematics to the World Using Mathematical Modeling
  • Textbooks oven cast math in pseudo contexts (fake real world problems)
  • Use real world variables part of the time to expose students to real uses of math
  • View math as a posing questions and form math models around those questions
  • Modeling – simplification of any real world problem into a pure math form that can help solve a problem
  • Students often use modeling all the time, but are unaware of it
  • Use visual representations to represent problems (one type of modeling)
  • Use real data from newspapers, magazines, online databases, etc.
  • Make students think about how contexts constrain possible solutions
Encourage Students to Pose Questions, Reason, Justify and Be Skeptical
  • Offer students opportunities to pose questions to situations
    • Example:  Give students priced for finished bracelets and for bracelet supplies.  Then ask them discuss the situation and pose questions.
  • Give students opportunities to try out their own conjectures and use reasoning and data to prove or disprove them.
Teach with Cool Technology and Manipulatives
  • Manipulatives: Cuisenaire rods, multilink cubes, pattern blocks
  • Apps: Geometry Pad (iPad), GeoGebra, Tap Tap Blocks, and many more.  See Rich Mathematical Tasks for ideas.


Teaching mathematics in ways that promote growth mindsets enables students to perceive math as a living, engaging, relevant, and accessible subject.   Giving them access to mathematical processes other than computation, gives students a better chance to experience mathematics more fully and to relate mathematics to processes they already do – such as make conjectures, ask questions, and notice and use patterns. Creating the math culture that promotes growth mindset involves teaching students how to collaboratively problem solve, modeling and teaching more math phases (question formulation, modeling, computation, evaluating models, etc.), designing and facilitating math problems with low floors, high ceilings and authentic contexts, and integrating real world data and technology into problem solving.


Preparation Steps
  • Design and implement learning activities that promote growth mindset and collaboration norms.  Create visuals to market the ideas that emerge from these activities.
  • Research and design curriculum that includes Rich Mathematical Tasks with low floors, high ceilings, open questions, and engaging (if possible real) contexts.
  • Develop assessment tools that relate to math learning and collaboration processes.
  • Research technology tools and manipulatives that can be used to create and facilitate more rich mathematical tasks.
Early Implementation Steps
  • Implement the curriculum and tools planned above.
  • Use student feedback to adjust learning experiences as needed.
Advanced Implementation Steps
  • Identify helpful strategies that can be incorporated into routines to consistently promote a culture of growth mindset.
  • Collaborate with other math teachers and teachers in related disciplines on norms and strategies that can be used in multiple contexts to cultivate growth mindset.



146: Academic Mindsets




Screen Shot 2016-04-15 at 1.11.47 AM

Academic Mindsets:
  • Beliefs and attitudes towards learning that support academic performance
  • Simple short term interventions on mindsets have been shown to have lasting effects on student performance – may be just as important as changing the learning environment
  • Mindsets that contribute to academic performance:
    1. I belong in this academic community. (Relationships)
      • Feeling a part of part of learning community:
        • builds confidence and independence
        • feel greater sense of identify and also flexibility to support the community
        • more engagement
      • Feeling rejected by community leads to
        • feelings of incompetence and insecurity
        • lack of engagement
    2. My ability and competence grow with effort. (Growth mindset)
      • Students with growth mindsets are more likely to:
        • Use effort to build competence
        • Display academic behaviors that lead to high achievement
        • Attributing low performance to lack of effort tends toward greater efforts in the future
      • Students with fixed mindsets are more likely to:
        • Use opinions of others to discern ability
        • Less likely to be self-motivated and persistent
        • Ascribing failure to ability or conditions outside their control tends to less effort in the future
    3. I can succeed at this. (Confidence)
      • Students tend to be attracted to (repelled by) activities that make them feel competent (incompetentI
      • Feelings of self efficacy are positively related to perseverance
      • Belief in self efficacy is a prerequisite for sustained effort through challenges
    4. This work has value for me. (Relevance)
      • Being interested in topic creates intrinsic motivation for learning
      • Seeing ties to future work will make students more likely to engage in academic behaviors that lead to achievement
      • Feeling lack of relevance leads to poor academic behaviors
  • Mindsets can increase improve performance by improving perseverance.
  • Relationship between mindset and academic performance:
    • Brief treatments focused on student mindsets had lasting effects on student performance
    • Examples of treatments in experiments:
      • Watching videos to college students discussing their struggles and how their effort related to GPA growth over time (did better than students who watched video that made no mention of struggles and effort)
      • Writing letters to younger students about the malleability of ability in response to sustained effort (did better than group that wrote letters about multiple intelligences)
      • Advisory group (weekly, 25 min) that taught the malleability of intelligence
      • Writing about connection between science topics and their own lives (did better than group that just wrote summaries)
    • Caveats –
      • experiments had small sample groups
  • Are Academic Mindsets Malleable?
    • Research suggests that mindsets are malleable.  See above.
    • Racial group stigmatization creates a big challenges to feelings of belonging in specific subjects. To read why/how this effect math, read this article.
  • Role of Classroom Context in Changing Academic Mindsets:
    • Classroom conditions have major influences on all 4 mindsets that contribute to academic performance
    • Conditions that improve these attitudes include:
      • high expectations for success
      • academic challenges
      • student choice and autonomy in student work
      • clarity and relevance of learning goals
      • available of supports for learning
      • grading structure & policies
      • nature of academic tasks
      • type, usefulness and frequency of feedback on student work
      • classroom norms that create positive safe cultures
      • learning feels fun and relevant
      • reasonable expectations for learning material
    • Effects of social contexts:
      • frame what students think is possible (and not)
      • shapes sense of students’ capabilities
      • more likely to adopt the values of their social groups – can interfere with academic performance
  • School transitions:
    • Transitioning to new schools creates new challenges that can negatively impact attitudes – students are trying to:
      • reorient themselves to new academic and social demands
      • renegotiate sense of self and self efficacy
      • rebuild sense of belonging in a new community
    • Effects of growth mindset are most noticeable in transition periods because of the challenges student face in these phases
    • Effective interventions aim to:
      • normalize academic difficulty
      • bolster student sense of belonging
      • reinforce growth mindset
  • Recursive effects:
    • Good (poor) attitudes can contribute to positive (negative) feedback loops that lead to sustained success (failure)
    • Feedback loops can lead to self-validation of positive (negative) beliefs
    • Successful interventions aim to break up negative feedback loops
  • Clear Classroom Strategies for Developing Academic Mindsets:
    • Limited scope of experiments make them difficult to scale of classroom routines
    • Two approaches:
      • Change school structures to promote experiences that promote academic mindsets
      • Train students to have academic mindsets
      • 2nd approach is easier
    • Caveats:
      • Different social groups may need different interventions
      • Poor school climates may tarnish individuals’ academic mindsets
    • School Conditions that Promote Academic Mindsets:
  • Can Changing Academic Mindsets Close Achievement Gaps?
    • Mindset interventions have been shown to narrow gender and minority achievement gaps.
    • Mindset interventions can be used to combat negative effects of stereotype threat.


Helpful academic mindsets have been found to improve student perseverance and achievement.  Small scale research projects have shown that modest interventions aimed at improving academic mindsets have had long term positive impacts on students.  The small scale and out-of-standard classroom contexts of these studies make it tricky to transfer their implications to classroom practices.  A lot of research has been conducted to identify classroom conditions that promote academic mindsets.  Improving classroom conditions and explicitly scaffolding student academic mindsets can have positive, long lasting affects on their performance.  Students who can benefit most from these interventions are women, minorities, and students who have just transitioned between school.


Preparation Steps
  • Design a pre-assessment that measures presence (or absence) of 4 academic beliefs in students.
  • Analyze pre-assessment and research strategies that promote attitudes / beliefs that are student gaps.
  • Evaluate classroom practices against the list of factors that promote academic mindsets.
  • Use analysis of classroom practices to recognize what needs to be reinforced and what needs to be improved
  • Research strategies for improving classroom practices that are gaps
Early Implementation Steps
  • Implement scaffolding activities that promote mindset that are their gaps after pre-assessment analysis)
  • Gather student reflection and academic data and analyze it to determine whether or not academic beliefs and performance are improving
Advanced Implementation Steps
  • Ask students for feedback on what can be done to promote academic mindsets
  • Use list of classroom practices that promote academic mindsets to create a Likert scale questionnaire that students can use to give feedback on the presence (or absence) of key classroom conditions
  • Use feedback gathered from questionnaires to improve classroom conditions / strategies



132: Mathematics & the Path to Equity





Screen Shot 2016-05-09 at 11.12.18 AM


The Elitist Structure of Mathematics
  • Elitist views place math as subject harder than other subjects that can only be accessed by a select few.
  • Math is taught as a performance subject that weeds out people with & without the math gene
  • Some people enjoy sorting mechanism of math because they have been sorted into the side of the limited Have’s
  • Some people enjoy thinking that their math ability is due to genetic superiority
  • Sometimes math teachers feel like they are superior to teachers who teach other subjects
    • these same teachers may feel justified in failing many students because they feel like they are the guardians of math success and only stars can move to higher levels
  • Some university math departments lower grades of students who display hard work habits such as attending office hours
The Myth of the Mathematically Gifted Child
  • Even math geniuses had to work hard to be able to produce relevant work
  • “Gifted” status awarded to students who can do things quickly, not necessarily kids who work hard and are persistent
    • Myth of genetic difference can make “gifted” students intellectually brittle because they may end of devoted a lot of energy to protecting their gifted identities
  • Valuing “giftedness” over hard work may cause:
    • high achievers to hide or underemphasize the effort they exerted to achieve
    • hard workers to feel like imposters because they had to work hard to achieve
  • Elitist math views + stereotypes of who can be good at math create large equity gaps in math
    • in 2014 – 73% math doctorates were male, 94% were white or Asian
    • the more a field values giftedness, the less likely are women and minorities to enter the field
  • Rushing students to higher levels of math can dilute the depth at which they understand fundamental concepts and processes
    • could lead to students who are procedurally fast, but can’t explain rationale for procedures
Equitable Strategies
  1. Offer all students high-level content.  
  2. Work to change ideas about who can do mathematics.
  3. Encourage students to think deeply about mathematics.
    • The desire to think and understand deeply is more critical to math achievement than the ability to perform procedures quickly.
    • Include experiences that are
      • hands-on
      • project-based
      • tied to real life applications
      • allow for collaboration
  4. Teach students to work together.
    • Shared struggles make challenges less intimidating
    • Discussing math helps people make sense of it
  5. Give lots of encouragement to people who are normally left out (women and minorities).
    • Do not comfort kids by buying into their “I’m just not a math person” fixed mindsets
    • Anyone can perform poorer when they are on the under-side of a stereotype of performance
  6. Eliminate (or at least change the nature of) homework.
    • Homework spreads low income equity achievement gap because low income students have less time and less resources while completing homework
      • inequities are magnified when class starts with homework review
    • Instead of practice problems, offer reflection questions such as
      • what was the main idea learned today?
      • what is something you are struggling or have questions about?
      • how could lessons from today be applied in real life?
    • Instead of practice problems, offer inquiry problems that have students seek out examples of current concepts in their lives


Uncovering the elitist structures embedded into the structures of math curricula and the attitudes it promotes can help teachers be more aware of how to revise their practices to close equity gaps.  Equitable teaching practices have been shown to have a greater impact than minority role models.  This empowers any teacher to practice strategies that can close achievement gaps.


Preparation Steps
  • Research specific strategies related to equitable practices listed above.
  • Examine practices and attitudes critically to see if any are directly or indirectly elitist.
  • Develop strategies, visuals, and lesson plans that eliminate elitist views of math and replace them with growth mindset views of math.
Early Implementation Steps
  • Implement policies, visuals, scaffolding and assessments that combat elitist views of math and promote growth mindset views of math.
  • Teach students skills related to math achievement:
    • brainstorming
    • communicating
    • sense making
    • drawing to understand
    • reflecting
    • collaborating, etc
  • Use student feedback to fine tune policies, scaffolding and assessments
Advanced Implementation Steps
  • Assess students attitudes over time to see if their views of math and their place in it is changing over time
  • Research and implement strategies that set high expectations and also offer high levels of support to all math learners

128: The Power of Mistakes & Struggle





Screen Shot 2016-05-09 at 11.43.22 AM


Mistakes & the Brain:
  • Mistakes grown synapses.
  • Mistakes generate more brain activity than correct responses.
  • 2 brain responses to mistakes:
    1. ERN responses – increased electrical activity due to conflict between correct response and an error
    2. Pe responses – brain signal due to recognition of error
  • Brain sparks can occur even when people are unaware that mistakes were made
  • People with growth mindset show more brain activity in response to mistakes and are more likely to recognize errors
Mistakes & Life
  • More successful people make more mistakes than less successful people
  • Making mistakes is key to creative, entrepreneurial thinking
  • Successful people tend to:
    • feel comfortable being wrong
    • try wild ideas
    • are open to different experiences
    • play with ideas without judging them
    • persist through difficulties
    • willing to go against tradition
  • Practicing the attitudes above can help people learn math (or probably anything)
How Can We Change How Students View Mistakes?
  • Teach students about the positive impacts of mistakes on the brain
  • Crumble paper with mistakes, throw it against something to let out frustration.  Then open it and smooth it out and trace over crumple lines with marker to remind oneself of brain growth as result of mistake.  Then keep paper as a record of mistakes.
  • Teach and display positive brain messages.
  • Have teachers and students select and highlight “favorite mistakes”.
  • Have class discussions about mistakes.
  • Do not downgrade assignments for mistakes – upgrade assignments for mistakes.
  • Avoid over-testing and over-grading.
  • Display positive attitudes towards mistakes in group and individual settings.
  • Remind students repeatedly about brain growth that goes with mistakes and lack of brain growth that goes with correct responses
  • Teach students to appreciate & be aware of disequilibrium (Piaget) – state of disequilibrium occurs when students try to incorporate new information into existing mental maps – states of disequilibrium are uncomfortable but lead to wisdom
  • Expose students to math experiences that create disequilibrium
  • Value work with mistakes more than correct work
  • Make showing of mistakes a common occurrence in classroom and discussing how to think through the mistake


Knowing about the impact of mistakes on the brain can teach students and teachers to value mistakes more and leverage them better to grow.  Knowing strategies for creating cultures that value mistakes will help students develop growth mindsets and help them to approach mistakes creatively and constructively.


Preparation Steps
  • Research strategies for creating classroom cultures that value mistakes.  See above.
  • Develop scaffolding activities and strategies that will be used to teach & remind students of the value of mistakes.
Early Implementation Steps
  • Implement policies, strategies, and scaffolding lessons that value student mistakes such as:
    • Presenting (teachers & students) mistakes and hold classroom discussion around them
    • Crumple paper strategy (see above)
    • Creating situations that will place students in disequilibrium and funnel students towards learning targets
    • Teaching students about the relationship between brain activity and mistakes
    • Selecting favorite mistakes and why they are so helpful
    • Reflections on how new attitudes towards mistakes impact learning
    • Using grading policies that value errors
Advanced Implementation Steps
  • Create bank of problems that create disequilibrium that explore big ideas in mathematics
  • Create bank of discussion and question prompts that highlight and analyze mistakes



100: Reinforcing Effort & Providing Recognition





Screen Shot 2016-05-09 at 3.23.22 PM


What research has to say about reinforcing effort:

  • Not all students realize the impact of effort.
  • Students can change their beliefs on the importance of effort.

Classroom Practices

  • Explicit practices
    • Teachers share stories of how effort carried the day when success did not seem imminent
    • Share examples (videos) from famous people who triumphed through effort
    • Share examples of effort from famous stories
    • Students recall times when they prevailed through effort
  • Use rubrics to track effort and achievement:
  • Ask students to see correlation between effort and achievement variables
    • Ask students to reflect on what they learned about effort
    • Graph effort and achievement data
      • Achievement vs Effort
      • Achievement vs Time
      • Effort vs Time
    • Have students use graphs to notice patterns in their effort and achievement


What Research has to say about Providing Recognition:

  • Rewards do not necessarily have a negative effect on intrinsic motivation
    • Worst effect – giving praise for easy tasks can undermine achievement
  • Reward is most effective when it is contingent on reaching known performance standards
  • Abstract symbolic recognition is more effective than tangible rewards
    • Tangible awards = physical prizes, candy
    • Verbal praise is effective
    • Abstract rewards = recognition for reaching a performance standards
    • Tangible awards are still effective when tied to performance standards

Classroom practices related to Recognition:

  • Personal Best Honor Roll – students who met individual target goals made this honor roll regardless of whether or not they qualified for absolute grade-based honor roll
  • Pause, prompt and praise
    • Pause students in work
    • Prompt – have supportive conversation on how to improve work
    • Praise – After some time and evidence of improvement, congratulate student on their new found success
  • Symbolic signs of recognition
    • Stickers, stamps, ..
    • Make sure these tokens are given for meeting performance standards to create positive or no impact on intrinsic motivation


Teaching about the importance of effort relates to building growth versus fixed mindsets in students.  Showing students how their efforts tie to results by tracking rubric stores and through recognition could reinforce beliefs that tie effort to success.



Preparation Steps

  • Gather stories (articles, videos) about people who triumphed through effort
  • Gather goal setting and tracking tools such as the Effort & Achievement Rubric (see above)
  • Design lessons on the importance of effort and its connection to external results (achievements) and internal results (brain development)

Early Implementation Steps

  • Implement lessons about importance of effort – incorporate model stories, discussions, and opportunities for students to tie lessons to their own lives
  • Use Effort & Achievement Rubric and a Task chart to record effort and achievement scores daily over a period of time
  • Create summary graphs of effort and achievement shorts:  achievement vs effort, achievement vs time, effort vs time
  • Have students identify and reflect upon patterns in summary charts

Advanced Implementation Steps

  • Ask students what strategies and practices do they want to incorporate into their daily habits and routines as a result of achievement / effort tracking
  • Experiment with different ways for recognizing student effort
  • Use student feedback to identify most effective ways for recognizing student work – incorporate these into classroom routines

99: Development FIRST





Screen Shot 2016-05-09 at 3.31.13 PM


Development FIRST Steps

(David Peterson and Mary Dee Hicks)

  1. Focus on priorities:
    • What are the most important skills in your development plan?
    • Select 1-2 areas.
    • Work with focus areas for 1-2 months before moving on.
    • Figure out:
      • where are you know and where do you want to go?
      • what are you actually going to do differently?
      • what are the impacts of these changes?
  2. Implement something every day.
    • At least  5 min per day on development (micro initiative that might grow to macro impacts)
    • Seek out situations with:
      • High stakes and visibility
      • Novelty to stretch your comfort zone
      • Challenges that require you to do more than you’ve done in the past
      • Interactions that require you to work with non-subordinates
    • In these situations ask:
      • Can I take a risk each day?
      • How can I use my strengths?
      • What resources do I need?
      • What do I need to face?
  3. Reflect on your experience.
    • What have you learned from successes and mistake?
    • Write each day:
      • proudest moment
      • high light of the day
    • Look for patterns in reflections
  4. Seek feedback and support:
    • the more people you involve, the more chance of success
    • Supporters can give you
      • feedback
      • direction
      • new strategies
      • support
      • motivation
      • accountability
    • Guiding questions
      • Who are the best people to support you?
      • Who are the best people to get feedback from?
      • Can you tell them what you need and how they can help?
      • What kind of feedback is unhelpful?
      • How can you foster mentoring relationships with them?
  5. Transfer learnings into next steps:
    • Codify successes into patterns, resources, and supports needed to move forward
    • When success occurs:
      • write down success steps
      • ask others what they saw you do that was helpful
      • teach someone else how you did it
      • teach your learning to your team
      • ask others to hold you accountable to better patterns and make you aware of when you’re slipping back into old habits


There are so many skills teachers can acquire to become better educators.  With so many options out there, it’s sometimes hard to choose and stick to a development plan that will lead to substantial change and success in any one area.  Following the steps above can help teachers and students achieve goals that relate to tricky change efforts.


Preparation Steps
  • For teacher development plans:
    • Do an inventory of the teaching strategies and skills you would like to master to become a better teacher
    • Prioritize your inventory – seek out 1-2 focus areas
    • Brainstorm how you can take small risks each day to learn something new about your focus areas
    • Recruit people who can offer support, advice and feedback
  • For student development plans
    • Help students use learning targets to identify 1-2 focus areas
    • Research and develop scaffolding strategies, tools and activities that students can implement every day to become more skilled focus areas
    • Have students assume appropriate roles in development plans – thought partners, observers, feedback partners – train students how to perform roles well
Early Implementation Steps
  • For teacher development plans:
    • Keep record of risk tried each day and related learnings
    • Supplement notes with advice, feedback and observations from support team
  • For student development plans:
    • Have students record what they tried and what they learned from it.
    • Have student supplement their reflections with advice and observations from their support teams.
Advanced Implementation Steps
  • For teacher and student development plans:
    • Look for patterns in successes in journal entries
    • Identify the most effective strategies
    • Solidify the HOW in the effective strategies by teaching them to another team member
    • Identify new patterns you’d like to convert into routines
    • Recruit an accountability team that will let you know when you are sticking to new routines and when you’re slipping back into old habits



98: Coaching Conversations





Screen Shot 2016-05-09 at 3.36.58 PM


  1. Hear the problem or issue fully.
    • Ask questions to determine what happened, when it happened, why it happened.
    • Reflect back content and emotions without giving advice.
  2. Get more details.
    • Ask more questions to find out:
      • duration of problem?
      • what’s been tried already?
      • who’s been affected?
      • what does everyone think the problem is?
      • anything work at all (even part time)?
    • Reflect back content and emotions without giving advice.
  3. Honor their ideas for a solution.
    • Ask questions to help him, her or them describe their possible next steps
      • What should be done next?
      • Who might benefit?
      • How long will next step(s) take?
      • What resources do you need?
      • How will you know if it’s working?
      • What are the merits of various solutions?
  4. Ask if they want your advice.
    • If not, confirm what they will next.
    • If they really need but don’t want it, offer it.
  5. Give your advice and make a plan.
    • Don’t just give the answer – create a mentoring moment
    • Think aloud (making thinking visible).
    • Explain considerations for choice
    • Explain why you selected choice
    • Explain what was considered and ruled out and why
    • If one exists, explain impact of a similar experience you’ve had and what you would’ve done better now that you know more
    • Explain what things they did not consider in their choice – unintended consequences, impact on stakeholders, resources needed, time needed, skills needed, etc.
  6. Plan
    • Decide on a next step
    • Decide when they will check back with you
    • Decide how they will know if next step is working


Coaching conversations are a critical tool in managing teams during PBL projects.  Teams will sometimes reach an impasse and will need the assistance of a facilitator to think through a problem.  Observing the steps above will help teachers guide students through the process of analyzing, brainstorming, evaluating, and planning possible solutions to their team problems.


Preparation Steps
  • Prior to needing to facilitate these conversations, offer up the Coaching Conversation as one of a selection of extra support tools that teams can use when they are feeling stuck or overwhelmed.
  • Teach students what are the purpose and format of Coaching conversations.
  • Observe teams to identify if any teams might need a coaching conversation.
Early Implementation Steps
  • If a team requests (or is perceived to be in need of) a coaching conversations, facilitate one using the steps listed in the WHAT section.
  • After the conversations have students reflect and provide feedback on how the session went.
  • Set up a plan to implement and evaluate next steps.
  • Check in on teams to see if their next steps worked.
Advanced Implementation Steps
  • Teach students how to have coaching conversations with their team mates.  While scaffolding this skill provide: a checklist of steps, modeling of steps, and practice role play opportunities.
  • After observing the steps being modeled or role played, ask students to brainstorm situations that may require coaching conversations.
  • To help students be more effective listeners during coaching conversations, look at ideas in here and here.