Friday, March 15, 2019

Measuring Tape Radians Activity #piday

1) Give each group a 5-foot measuring tape roll.

2) Have them roll it around 4-5 fingers. The roll should measure more than 7 inches, otherwise re-wrap it larger. Then tighten it down to a little more than 6.25 inches (estimate 6.28").

3) How big is the radius of this rolled measuring tape?

4) Take predictions.

5) Measure from the outside toward the center of the roll.

6) Have students write reflections about how many radii fit around the circumference. Will this amount change for different sized circles?

Let me know how it goes in the comments!

Thursday, September 13, 2018

CMP@CPP: Task Design

I recently presented for the California Mathematics Project at Cal Poly Pomona and am sharing my talk and reflections here in hopes that someone can benefit and/or share their own thoughts and resources with me.

Stated goals

    Build trust
    Do math together
    Share strategies and resources

Here is a trimmed down video of the session along with the slides:

Overall Reflection

I felt more trust by the end of my session and feel that I was able to get many voices heard and shared during my talk. The introductory math task felt like a positive experience for everyone. Teachers shared their strategies and approaches in their small groups as well as during whole group discussions. I would like to get teachers to really visualize themselves in their actual classrooms, and plan lesson ideas around activities they intend to use with their students. This has proven difficult to do. Suggestions toward this goal are coveted.

Moment to celebrate

I was happy that I remembered to discuss the idea of taking estimates (albeit after the fact). I am not sure if making this mistake of ordering helped or hurt uptake to the idea of taking estimates before attempting a problem. I was proud that I was able to pull out of a single participants solution strategy to ask for another approach.

Missed opportunity

I intended to have multiple groups share-out after a period of small group work, and only had one group share. Then I shared my own approach. I think I made this adjustment because folks hadn't really gone down the path I intended. In retrospect, I should have shared a summary of my own approach before the group work so that the teachers had a clearer idea of what was expected of them. The conversations were too general and un-focused. Many teachers didn't talk about their lesson or unit planning at all, and the time felt less productive than it could have been. I also think that my circulating, listening, and probing was not where I want it to be in terms of active listening and pulling the nuggets from multiple groups in a short time.

What surprised me?

I was surprised at how quickly we used up the time and how little of my talk we got through. I plan to break it up into a few parts and try to deliver a more focused session on open questions later this year. My goals are the same, but my main evidence for success will be teachers leaving the session with problems they actually use in their classrooms, that have a fresh new feel thanks to our session.

Monday, August 6, 2018

Do the Math

What do folks mean when they say, "do the math"?

How about, "I'm not a math person"?

For what, by and large, do folks (randomly sampled from the entire population of English speakers who know the word
math) mean by math?

In a recent survey of LAUSD elementary teachers, most agreed with the statement "Some students have a natural talent for mathematics and others do not." There is a camp of math educators who disagree with this statement, but it seems they are in the minority. Is it possible that the primary confound in this conundrum is differing definitions of math?

To me, doing math means much more than the arithmetic that comes once a solution strategy has been followed to its natural end. Once a complex problem becomes a simple computation, the math is done, and the computers have homework.

I recently presented for the California Mathematics Project at Cal Poly Pomona and had this to say,

What are some things that the computer can't do that I am going to continuously do with my students to get them to reimagine what math is?
Over the course of two hours, I tried to make the point to a group of primary teachers that math is not about getting correct answers, rather it is about discovering patterns, the structure of solution strategies and critiquing each others reasoning.

Watching the entire video and writing this post, I realized some unstated goals:

    Demonstrate how math is a creative process
    Create dissonance around what it means to "Do the math"
    Create dissonance around what it means to be or not to be a "Math person"

If you or someone you know has a similar goal for their students, parents, or teachers; what are some strategies or suggestions you have to create such experiences for folk? I'd love to discuss ways to measure progress toward these goals in the comments.

This post is mainly a recapitulation of Lockhart's Lament and a resounding "hear hear" to Conrad Wolfram's 2010 TED, Teaching Kids Real Math.

SALVIATI: If everyone were exposed to mathematics in its natural state, with all the challenging fun and surprises that that entails, I think we would see a dramatic change both in the attitude of students toward mathematics, and in our conception of what it means to be “good at math.” We are losing so many potentially gifted mathematicians— creative, intelligent people who rightly reject what appears to be a meaningless and sterile subject. They are simply too smart to waste their time on such piffle.

Yet even though we have read and watched these ideas, think to yourself the next time you say or hear someone use the phrase "do the math" or "I'm not a math person": has anything changed... yet?

Written for Sam Shah's Virtual Conference of Mathematical Flavors

Monday, January 22, 2018

Learn Data Science 2018

I am building a portfolio on a new blog to apply to Data jobs in 2018. 

from letustweak
I would like to use Data Science to support teachers, students, and learning in the information age.

    I combed through resources and am sharing highlights.

What is Data Science?

As described in a recent DataCamp podcast with David Robinson,
Data Transformation - how can I clean this and reshape it?
Statistical inference - how can I separate signal from noise?
Prediction - I've got some inputs, how can I predict the outputs? (a classifier)
Visualization - how can I better understand this? (making graphs)
Communication - how can I share the results?

Where I am learning it?

I am reading help pages, documentation, github repos, and stackoverflow to analyze open data sets. 

I did EliteDataScience's 7 day email introduction and feel confident about learning all of their Machine Learning steps through projects, online resources, and Kaggle's courses + competitions.


- All courses with Dr. Chuck Severance at Python for Everybody.
- Practical Deep Learning for Coders with Jeremy Howard at
- Exercises on Project Euler


- Exercises on codeacademy, hackerrank, and leetcode.


- Tidyverse (Hadley Whickam's R for Data Science)
- Rachel Tatman's Data Science in R Kaggle course


freeCodeCamp has a beta site offering 6 modules
- Blocks contain examples

More Resources

- DataCamp has some great tutorials in R, python, SQL, and others.
- Andrew Ng's Machine Learning Coursera course (old Octave back when it was free).
- Version Control with Git Udacity course
- MITx Introduction to Probability: The Science of Uncertainty
- TypingClub is not a crime

Online curricula

David Venturi's DIY Masters (He did some blog updates in 2017)


I joined the Coursera Data Science community.
I attended various free Data Science meetups in SF at Galvanize and Metis.
I am stalking many Data Scientist blogposts and podcasts to keep up with trends and learn proper etiquette.
Looking for an in-person group of DIY Data Scientists who want to meet up and hack on data sets together.

Stretch Goals

- Kirill Eremenko's Data Science A-Z Udemy course
- Udacity Data Analyst Nanodegree

- crush

Hit me up if you are DIY Data Science learning also.

Friday, September 22, 2017

The Algebra Project Keeps on Pushin'

>>>> Alliance Website <<<<

In my discussions with teachers I often drop a line like,  "The Algebra Project saved my life" or "The Algebra Project changed me irrevocably".  And folks ask me how they can learn more or get involved. 

There is a small website and a few books {Radical Equations, QECR, Educating for Insurgency}, but educators are left asking, where is the curriculum? the pedagogy? What is this “approach” that they espouse?

The Algebra Project has been working on Math Literacy as a vehicle to organize social change for the past 35 years. Join the "We the People" Alliance. (Edit 5/23/18, added link to website above)

It isn’t a textbook series, although there are curricular modules: Tripline, Road Coloring, Flagway, Winding Games… 

It isn’t a set of instructional activities, although there are design principles: share a common experience, 3 Ps (produce, present, and peer review mathematical reasoning), a mathematization process... 

It doesn’t claim to be a magic bullet. The Algebra Project understands that what works in one context will not necessarily work elsewhere. We have a wealth of knowledge and experience that can support math literacy efforts in your area, and we need math literacy workers across the nation to join forces.

Our shared goal is to amplify student and teacher voices from underserved contexts.

Watch the Student Voice video:
Watch the Teacher Voice video:
Watch the Community Voice video:
The Algebra Project is a bottom-up community organizing effort to prepare students performing in the bottom quartile of math achievement to take college math for college credit upon completion of high school. We use math literacy as an organizing tool.

There was an NSF-funded convening focused on the question: 
What roles and structures are needed for a mini-backbone organization in order to scale a "bottom up" model of social change into an organized, full scale collective impact model?
There currently is an NSF INCLUDES grant to establish a national network focused on building an Alliance around students in the bottom quartile of achievement in the lower grades being able to do college math for college credit post-treatment:
The proposed work will comprise the design of effective learning opportunities; building and supporting a cadre of teachers who can effectively work with students learning under the proposed approach; using technologies to enhance teaching and learning; and utilizing evaluation and research to drive continuous improvement. 
In speaking with Bob Moses and Ben Moynihan directly over the past few months I have uncovered some tacit goals:
1) Institutionalize the teacher voice
2) The issue of the materials
  • What to teach?
  • How to teach it?
  • How to assess what’s been taught and learned?
Wondering if any of this strikes a chord with you or if there are ways you'd like to be included further. Next steps would likely involve getting on a conference call, in-person meeting, or workshop/conference in the coming weeks/months. 
Upcoming opportunities:
1) Join the "We the People" alliance facebook group:
2) Park City Math Institute (PCMI) in summer 2018 Dates: July 1 - 21, 2018;
3) Critical Issues at MSRI

Please reach out in the comments, join the Facebook group, and share widely.

A former educator and colleague of mine, Marcus Hung, with Room 212 Photography produced the four videos embedded in this post that highlight The Algebra Project's current "We The People" Alliance work.

Tuesday, August 23, 2016

If we want smaller class sizes, we need more teachers.

The shortage is real.


Some may point to this graph and say that the slowed rate of retirees will make up for the teacher shortage... I was on of those people. I was wrong.

The argument presented by the Learning Policy Institute [PDF] at the beginning of this year should convince anyone with the time to read it that the teacher shortage is in fact real, and not going away soon. Evidence was presented at the start of the year. [VIDEOS]

In the current climate, we are forced to hire unqualified teachers.

and here I am...

still collecting unemployment and not returning to the classroom...

searching for the elusive alternative model that will incarcerate less and employ more...

Perhaps I need to get back in there to support teachers - but I am not willing to give up on the possibility for external communities of support yet.

Saturday, June 6, 2015

Teaching with Problems at a Cafe

This is a story to support my belief when it comes to learning math. 

  1. I believe that students need to have basic math facts stored in long-term memory. 
  2. I believe students need to use these math facts to support logical arguments for mathematical conjectures.

I overheard two young girls (ending grades 4 and 2) practicing addition and multiplication facts in a cafe today. The older, Kate, asked her younger sister, Sara, "What is ten thousand plus one hundred?" to which Sara replied "Eleven thousand?"

Kate: No.
Sara: Eleven hundred?... eleven...
Kate: No, ten thousand one hundred.

Kate: How about 23 times 18?
Sara: uuummm, thirty- no forty one.
Kate: Times! silly
Sara: oh, hmm...

I felt compelled to save Sara from questions that were a bit beyond her apprehension, while challenging Kate with something more than just declarative knowledge. Since their mother was present, it might be an opportunity to model effective differentiation of a problem space to involve both of her children. I happened to be reading a book on "Teaching with Problems" and wondered how they would fare with one of Lampert's problems of the day. The focus of Lampert's teaching is to have students "reason from assumptions to their implied conclusions". I knew I could ask a question involving 2-digit addition and subtraction (a skill they both could perform), that would still be challenging for Kate to figure out.

I wrote the same question on two sheets of paper and gave the girls pencils to experiment with.
I. Problem of the day
I expected the girls only to attempt part a of the problem, but I included part b because I was curious how someone would go about using hundreds with such a problem format. This is something Lampert alludes to in her book but doesn't go into detail on. The girls did not end up making their own assumptions about what could fit in the boxes, but operated under an assumption that single positive digits would occupy each box.

The girls started by finding one correct subtraction problem, each declaring: "I found one!"

I asked them to share what they found,
Kate: 46 - 23 = 23
Sara: 33 - 10 = 23

At this point a friend of Sara's named Jane (also ending grade 2) joined her in solving the problem. I explained to their mother that the girls were now practicing their subtraction facts without being asked to do a worksheet, because they were necessary experiments to find a pattern that would lead to conjectures to count all of the subtraction pairs they could find.

Both solution paths started as lists of all subtraction pairs involving tens {33-10, 43-20, ... 93-70}:
II. Kate's initial experiments
III. Sara & Jane's initial experiments
The girls were satisfied that they had found multiple solutions to the problem, but I reminded them that the question wasn't to solve the subtraction problems, but to figure out how many there were. I also wondered if we could make an estimate of how many there were, without listing them all. As the girls began to lose interest in the problem, I realized they would need more guidance to come up with estimates. Kate's mother encouraged her children by saying, "I am curious to know how many there are! Aren't you curious?"

I pointed out to Kate that some of her solutions had too many digits, and she crossed out 103-80 and 113-90. She drew a bold line to indicate the maximum for subtracting by tens. I asked her if she had found all of the subtractions ending with the digit 0 and she said, "yes", although at this point she had not considered 23-00 (top left of fig IV. added to fig II).

I guided her with a plan that might help us come up with an estimate. If we had found all of the subtractions ending with the digit 0, could we do that for all of the ending digits? For example, I pointed out that she had found one subtraction ending with the digit 3, her first attempt which was 46-23 = 23. This spurred her on to find all subtractions ending with the digit 3.
IV. Kate's further experiments
With further guidance from me and her mother, Kate came to an initial estimate of 80 combinations. She had discovered 26-03 and realized 23-00 would also work, so she was making a conjecture that there were 8 possible combinations for each digit, and 10 total digits. I left Kate to work with her mother on the final details of her approach and checked on Sara & Jane.

I asked, "How many combinations do you think there are?", and Sara replied "We found 14!"
V. Sara & Jane's further experiments
Given the level of support Kate needed to make an estimate of 80 using the final digit approach and her higher level of mathematical ability, I was glad that there was the beginning of a different pattern on this paper. Namely, {23-0, 24-1, ... 29-6}. I pointed out that we could continue with this pattern, but when we repeated 33-10, Sara noticed and was like "uh oh! we already are counting this one!"
VI. Sara & Jane's new pattern
I started listing all of the subtractions in order without writing them to suggest that we would repeat all of the subtractions by ten she had listed earlier with this new pattern. I wondered out loud when this pattern would end and I asked, "what is the biggest 2 digit number that we can subtract from?" and Sara replied "99". I told her to leave space for all of the other pairs, so she wrote it very small in the bottom corner.

After all of this, I had lost Sara a bit and she was still guessing her estimate: "88?" I could see that having two different approaches on the same list was interfering with her ability to see the new pattern I was trying to extend. But she continued thinking about the problem, and before I left the shop she suggested to me, "My estimate is 76, because there will be 76 subtractions." I noted that she wasn't counting 23-0, and she revised her thinking and said "77!"

VIII. Sara & Jane's response
VII. Kate's response
Overall, I feel like I did too much leading in this exercise, and it uncovers some of the pitfalls that a teacher will encounter using open-ended problems. However, given the time constraint of meeting in a cafe, and the design constraint of not knowing the girls' prior knowledge; I was pleased that both girls had come to believe in their guesses, had consensus in their results, and had used different approaches.

More importantly, the discourse between the sisters shifted from Kate demonstrating her prowess in mathematics by asking her sister declarative questions that were beyond Sara's level of understanding, to an exploration in which both girls were engaged in productive struggle. There is no clear "winner" in a situation where two girls come to the same answer through different solution paths, both require help, and both make small contributions throughout the exploration.

We need to equip our students with a strong foundation of math facts, but let us not forget to ask questions that require them to use this knowledge to produce new knowledge.

I recently read Magdalene Lampert's excellent analysis of teaching in, Teaching Problems and the Problems of Teaching. Without which this experience would not exist, so thanks for that effort.