Monday, July 26, 2021

Robert Parris Moses' Algebra Project saved my life

It is with a heavy heart and steadfast spirit that I take this moment to honor one of my greatest heroes, Bob Moses. He was the kind of organizer who listened the most and spoke the least; and what he said was heard and heeded. He will be missed but never forgotten. He put his life on the line for the liberation and fair treatment of "We the people". His determination and commitment to the movement was awe-inspiring. We will keep on pushing in the spirit of Ella Davis, Bob Moses and the Student Non-violent Coordinating Committee through the We the People Alliance: Math Literacy for All and the countless realities Bob has shaped.

Bob was relatively unknown to me in 2009, when I was blessed to teach an Algebra Project cohort class under his mentorship and guidance for four years. I was twenty-six, four years into my teaching career, and losing my mind as I fought for attention in classrooms full of disinterested teens. I learned about community, culture and a history of injustice from and with my students as a result of that transformative professional learning experience. I witnessed both my and my students' skepticism dissolve over those years as our hope and joy of mathematics grew within our learning community.

That hope and joy still lives in me, and I thank you for it Bob. The legacy you leave is unmistakable and our work continues.

Mr. Rushton
Math/Morals Teacher

Friday, December 18, 2020

Book Club: High School Mathematics Lessons to Explore, Understand and Respond to Social Injustice

Hi team,

We* are currently reading High School Mathematics Lessons to Explore, Understand and Respond to Social Injustice (Berry, Conway, Lawler and Staley 2020).

We divided ourselves into two breakout groups by content area: (1) Algebra & Functions, (2) Statistics & Probability. Each group is choosing a lesson to analyze in more detail.

The book emphasizes, Content Matters, Context Matters, When Matters, and How Matters.

I appreciate that Critical Mathematics Education has been included alongside Standards-Based Mathematics Instruction (SBMI), Complex Instruction (CI) and Culturally Responsive Pedagogy (CRP).

Any teachers planning to do this kind of work must attend to power dynamics and status differences in their class. Expect contributions from each and every student. Leverage students' cultural funds of knowledge. Pursue generative themes that come from dialogues with students. These skills are difficult to obtain. The authors have provided a great primer for folks seeking educational equity and social justice.

The stats+prob group chose to analyze, "Do Postal Codes Predict Test Scores?" (pp. 182-187)

I did the lesson for myself below.

1) Access

What do you notice?

- I notice that CA no longer releases SAT averages - scores are from 2016
- Average scores range from roughly 800 to 1300 (low: 746, high:1374)
- Lower income seems to score lower in L.A., Houston and Boston.

What do you wonder?

- I wonder how the size relates to the number of students for the school.
- What these data tell us?
- What can we do about it?
- How do we measure what we value rather than value what we measure?

2) Explore

What data do I want to analyze?

I am interested in which correlation is stronger: scores ~ income or scores ~ adult education. I am interested in building a model with all of the available features and seeing which describes the majority of the variability in test scores.

Create a table of data points (by hand?!)

Collecting values by hand seems ridiculous given modern tech. I'd prefer to access to the database entries that are being visualized - I'll accept that data challenge soon. 

But for the sake of this task - by hand - I'm game. I zoomed into Northeast Los Angeles, where I taught. 
I collected data from the schools in and around this region to make the following table,

School Avg SAT CensusTract % Unemploy % College % 2-parents % Private Sch Median Income
Benjamin Franklin 991 1835.10 .07 .26 .68 .04 64000
Academia Avance 889 1838.10 .08 .25 .49 .03 33000
Eagle Rock 1046 1816 .14 .43 .66 .06 69000
Los Angeles International 923 2013.02 .1 .58 .91 .34 66000
Los Angeles Leadership 888 1993 .11 .38 .72 .07 53000
Renaissane Arts 1083 1871.02 .08 .34 .8 .03 51000
Alliance Tennenbaum 920 1871.02 .08 .34 .8 .03 51000
PUC ECALS 930 1871.02 .08 .34 .8 .03 51000
Sotomayor 851 1871.02 .08 .34 .8 .03 51000
Alliance Leichtman-Levine 985 1864.01 .1 .13 .51 .05 32000
Lincoln 998 1992.02 .11 .24 .59 .09 47000
Wilson 911 2014.02 .08 .19 .7 .11 55000
Alliance Stern 973 2017 .14 .28 .59 .13 58000
Alliance Smidt 873 1997 .08 .3 .53 .04 32000
South Pasadena 1253 4807.04 .09 .61 .7 .04 77000
Blair 1037 4640 .06 .79 .88 .68 107000
John Muir 945 4609 .08 .25 .44 .05 69000
Aveson Global 1060 4603.02 .07 .33 .74 .21 83000
La Canada 1307 4607 .05 .74 .91 .25 184000
Glendale 1099 3021.04 .12 .4 .79 0 54000
Hoover 1149 3012.05 .08 .55 .94 .17 86000

Appropriate Units

A nice conversation can be had around independent and dependent variables. The question I decided to ask is, "Can we predict average SAT scores with census tract data?" Given that question, the Range of possible outputs will be 400 to 1600 for SAT scores, and the Domain will be from 0 to 1 for percentages and 0 to +inf for income. 

Graph the Data

I did some plots using SAT scores as the independent and dependent variable. I restricted SAT scores and income to 600 -1400 and 20k - 200k respectively to better display the data.

- Is there a correlation?
It seems like schools in lower income areas have lower scores. By looking at the deviation from the mean in both data sets, we can see how correlated the variability is.

- Correlation coefficient r
I measured the correlation coefficient between Avg SAT and each of five census tract variables (% unemployed, % college, % 2-parent, median income, % private) using =CORREL(Y, X) in sheets. 

Correlation coefficients between Avg SAT, % unemployed, % college, % 2-parent, median income, % private
% Unemploy % College % 2-parents % Private Sch Median Income
Avg SAT -0.15960 0.60929 0.39436 0.19450 0.72320
% Unemploy -0.28184 -0.29719 -0.31252 -0.43266
% College 0.71028 0.68975 0.76143
% 2-parents 0.46960 0.53873
% Private Sch 0.54839

From these data (n=21) income and college education are most correlated with SAT scores, so those are the plots I am including here.

3) Summarize

With a class, this is where we have a gallery walk of everyone's graphs and discuss similarities and differences. We should come to some conclusions about correlation coefficients. The fact that they lie between -1 and 1 and the closer to either of those extremes the more linearly correlated the points are.

From the graphs, it looks like SAT vs Education is more linear than SAT vs Income. So that is interesting, and worth investigating. Why is the r 15-20% higher for the income data compared to the college data? (.72 versus .61). What happens when we remove that one outlier (La Canada)?

Another interesting point is Blair, with the highest adult education but an average SAT score. Looking into it further, they also have 6 times the average % private school for schools in the area! 

Our stats group brought up how important a conversation around correlation is not causation is to have here. Using real-world data that highlight social injustices will raise a lot of important issues in the class and it is critical that we as teachers are prepared to field student questions and honor their perspectives.

A student could takeaway from this lesson that "poorer kids are dumber than richer kids" - even though that isn't our intention at all. They might go spreading rumors to their parents and other teachers that they learned this fact in math class.

The fact is that quality education is not a constitutional right in this country and we don't know how to measure what we value. Rich kids may be "better prepared for college as measured by the SAT on average" but what about collaboration, communication, and creative problem solving skills? How about respect, responsibility and integrity?

Don't let the system fool you. You are not a test score.

Enjoy work.

* Algebra Project Los Angeles (APLA) is a regional branch of the We the People Alliance: Math Literacy for All. A network of educators, researchers, organizers, parents, students and policy-makers committed to quality education as a constitutional right - particularly relating to math literacy for all.

National Laboratory for Education Transformation (NLET) is largely a volunteer based nonprofit where extraordinary individuals and organizations work together to try to understand and unite the pieces of the education, training and personal learning puzzle that are necessary to truly change student success, college completion and access to well-paying jobs.

Wednesday, October 28, 2020

Teacher Streamers

A question I get a lot in conversations these days is, "What impact has covid had on teaching?"

Teachers are scrambling to create a "synchronous" online experience to simulate their former classrooms and are being asked to teach both in-person and online in hybrid models. One thing is certain, teachers have been forced to stream some of their content.

This is a roundup of Teacher-Streamers I've encountered to inspire educators looking to become streamers. Please link to other model streamers in the comments. This is a new skillset that millions of teachers and professors across the globe are having to pickup on the fly. Let's share what others figure out, so we all can improve.


Grant Sanderson is a Stanford math grad who started his online teaching career at Khanacademy and has since become a famous Youtuber with a large following and incredible Linear Algebra playlist. He recently did 10 live lessons and showed the world a modern rendition of the old lecture format. Check out his setup with Open Broadcaster Software (OBS)

Coding Train 

Dan Shiffman is an NYU CS professor who has been teaching online for roughly 5 years. His codingchallenges are a powerful way to learn to code and he has an impressive collection of community contributions. He made a video of how he streams

Michael Wesch 

The KSU prof who has been experimenting with and trailblazing online teaching for over a decade. He discusses OBS and his Fall teaching plans for the coming school year here. He has tips on setting up online classes more generally in a few shorter videos in this playlist

Matt Solomone 

A math professor at Bridgewater State Univ who teaches on Twitch? I am intrigued.  Here is his rig


Josh Starmer is a UNC Chapel Hill professor who has been uploading statistics concepts "Clearly Explained" to youtube for the past 5 years. BAM. 

David Robinson 

@drob is a former R instructor from Data Camp. He is a tidyverse expert who livestreams an hour a week analyzing a dataset he has never seen before. For practical coding skills like statistical programming in R, it doesn't get more instructional than a livestream practitioner IMO. 

"Dr. Chuck" Severance 

Python for Everybody (PY4E) has been a labor of love and a gift to the world in the spirit of open source under the guise of a MOOC. Chuck is a champion of learner privacy and has stayed at the forefront of online learning management tools since the dawn of the internet. 

Walter Lewin

Forever tainted by harassment allegations, Walter Lewin is one of the original teacher streamers who posted his lectures online and they were amazing. The internet has come so far since 1999, and the possibilities for interactions between learners has increased tremendously.

I think Lewin's legacy demonstrates an important point about the future of teacher-streamers. It is not enough to be incredible at explaining a concept and bringing it to life, in order to be a great teacher-streamer, you need to be an incredible human being too.

Thursday, July 30, 2020

[talk] The Art of Coaching, NCTM Boston 2019

I delivered a 30-min burst session at NCTM Boston last summer, The Art of Coaching. 

Initial script: This talk is about voices. Voices in education that have challenged my thinking and guided my beliefs. As coaches we often discuss actions. The look-fors in our instructional practice guides and teacher competency frameworks... We discuss beliefs. The mindsets and attitudes that people bring to the work. We don’t often discuss ways of being. These are voices that make my heart sing, and perhaps - some of what I share in these 30 minutes will resonate with you too.

 Here are the slides.

Thursday, July 23, 2020

[activity] Stick and String

Mysteries of Trigonometry, Jerzy Kocik

"trigonometry is the theory of a stick with a chord attached"

Wrote Jersy Kocik in his book, The Mysteries of Trigonometry (2005), along with a brilliant activity for teaching trig ratios, the stick and string.

Here is a handout and some files that support this activity.

I submitted this activity for a Rosenthal Prize, and here is my response to their implementation question,

Imagine that another teacher were trying to implement your activity in their classroom. If they had to start from scratch, what materials would they need? How much time would it take to prepare? What would be the cost (at market value) of all materials involved?*

This activity will likely take two 60-min periods or one 90-min block. It may take up to 2 hours to plan the first time around, but is relatively straightforward after that. Plan for groups of three. Each group should have a stick, string, protractor, 8.5x11 paper, scissors and markers. Ideally the sticks are as straight as possible, have no markings and are a range of sizes. If you can manage to have each individual build their own stick&string it might be worthwhile. One way to do that would be to ask each student to bring their own unmarked stick about 20 inches long and a string that is a bit longer. Whether you tell kids to bring materials or not, you’ll need your own supply. I find that shorter than 12 inches is crowded to mark (and less accurate) and longer than 40 inches is cumbersome to work with. I bought various lengths of (½”) dowels from home depot with a mean length of around 24 inches.

For a class of 30 with ten groups of three plan to buy:

- 4x72” dowel rods at $2.57 each and cut them at the store into 16”-40” lengths ($10-15 per class).
- A ball of twine or any inelastic string will do ($3-5).
- A class set of protractors ($10).
- A class set of markers ($20).
- A class set of scissors ($10).
- A ream of 8.5x11 paper ($3).

This activity would cost about $(50 + 12c) where c is the number of classes if you had none of these materials. I personally like doing it with branches because they feel like wands, and that cuts the cost to about $50 for the first time and less than $10 for each subsequent time. The class will benefit to have at least one computer to compile the data and graph the result, but it is not required.

Tuesday, February 18, 2020

Play Cribbage, Make 15s

I recommend this game to develop number sense using ten frames and have fun. Players find patterns and make 15 via addition. There is some beginning combinatorics when scoring 3 and 4 of a kind. (if I have three 2s, how many pairs do I have? What if I have four 2s?)

Rules for 2 players described below. (Rules for 3 players)

Cut to deal, low card is dealer. Face cards are 10, ace is 1.

The Players
    are dealt 4 cards each.

Pegging occurs.

Each player keeps 2 cards and puts 2 cards in the Crib.

Hands are scored and pegged. Scoring.

The Crib is scored and pegged.

Roles switch and repeat until someone pegs to finish.

#mathchat #elemmathchat #playmath

(image credit:

Monday, July 29, 2019

Making Tens Matters; Play Shut the Box

Math Toys and Games for Young Learners

In this post I highlight toys, games and habits to develop young mathematicians.

Age 0-3

The concepts of cardinality (numbers have quantity) and ordinality (numbers have order) are not obvious. It is one thing to learn a string of words "one, two, three, four..." and another to understand that each of those words represents a quantity, or that the order of those quantities carries meaning. These concepts are reinforced through multiple representations of number and quantity. Have fun. Learn from mistakes. Don't punish children's partial understandings. Build upon them.


Count physical objects with your kids
    Ask "How Many?"
           "How do you know?"
           "How else do you know?"
Play with patterns
    Ask "What comes next?"
           "What else could come next?"

Physical Toys

Be careful of choking hazards.
Check out Frebel's Gifts as a progression of mathy toys to orient a child for future mathematics.

Digital Toys


Age 3-7

Making tens is silly; why wouldn't a young child to rebel against such a mundane task? Memorizing a 12x12 table of numbers is worse yet. Many games reinforce these foundational math facts without the pain of forced repetition.


Ask "How many?" "How far?" "How long?" "How much?"
       "What units?"
       "How do you know?"
       "How else do you know?"
       "What comes next?" 
       "What else could come next?"

Physical Toys

  • Shut the box
  • Board games (Sorry, Candyland, Monopoly, Careers, Katan)
  • Card games
  • Dominos
  • Backgammon
  • Chess
  • Go
  • Cribbage

Digital Toys

Number Sense
  • Dragonbox Numbers
  • Motion Math Zoom
  • Motion Math HD
  • Dragonbox Big Numbers
  • Wuzzit Trouble
Visual Spatial
  • .projekt

Age 8-12

Fractions are daunting. All of the symbols and numbers have new rules that are easily confused. Abstraction seems so irrelevant. How is the letter x going to help me in the real world? The symbol barrier can be overcome when learners are given time to mathematize a concrete experience and use symbols to represent mathematical features of their lived experience. Games like Slice Fractions and Dragonbox Algebra demonstrate this idea.


Cook together. Weigh and measure objects. Cut things in halves, thirds, quarters... Fold clothes together. Demonstrate that math is all around us, don't pressure children into seeing math as right and wrong; and the rules and symbols will come with time.

Digital Toys

  • Slice Fractions
  • Amplify Fractions
  • Refraction
Proportional Reasoning
  • Ratio Rancher
  • Dragonbox Algebra
  • Game over Gopher

In a previous post I discussed resources for high math achievers. That may be relevant for you.

For Teachers

What apps, websites, software programs, etc. do you use with students (or have them use independently) to improve their math skills? Why do you use these tools? What are their strengths and weaknesses?


  • Google – search in class with students to teach searching strategies
  • Wolfram Alpha – use to demonstrate function behavior
  • Wikipedia – search in class and discuss how to validate claims and track sources

Skill Practice

  • Open Middle - open questions provide more practice and engagement
  • Kahoot - gamified knowledge quizzes
  • Motion Math HD - Fractions
  • Motion Math Hungry Fish – Adding positive/negative Integers
  • Motion Math Zoom – Number Line and Place Value
  • Sumdog – basic skills + some metrics to demonstrate gains
  • ST Math – spatial reasoning
  • Khanacademy – Knowledge Graph with Demonstration and Practice
  • IXL - vast range of topics

Conceptual Understanding

  • Desmos - engaging classroom activities to promote mathematical discourse
  • - engaging critical thinking tasks, sequenced into courses
  • Geometer’s Sketchpad/Geogebra - visualize/simulate mathematics
  • NLVM - virtual manipulatives
  • Shodor - interactive activities

Top 3-4 concepts/skills that hold students back

Algebraic expressions: Integers, Fractions, Order of Operations

Functions: Multiple Representations, Relational Reasoning, Inverse Functions

Proportional Reasoning: Scale Factors, Ratios, Percentage

Statistical Reasoning: Randomness, Normal Distribution, Conditional Probability

For more product reviews and tips for raising kids in our digital world, check out Common Sense Media.

This post is just a scratch at the surface. Reach out or follow-up in the comments with more resources to share with parents and teachers.