Friday, December 13, 2013

Googling "rails video tutorials" aka Learning Rails

I took CS 106A at Stanford, and "Mehran Sahami change my life!" as I'm sure he has done for many Stanford-crafted software developers.

So I have decided to learn enough Ruby on Rails to finish a rubric-based assessment tool that a friend was building. I will reflect here and will be updating this post regularly.

I tried on my own* - to little avail. So I took CS 142 Web Development at Stanford, and learned that higher level CS courses at Stanford have a DIY feel. A bit tricky when you are a grad student with few friends in the class. So I became an office hours inhabitant and made some friends, the TAs were accessible and made the class very manageable.

<!-- To be continued -->

*Preliminary Musings
I'll be starting with some reading of has been fun. was a bit glitchy... but taught some syntactical rules.

I wanted to check the usual MOOC suspects and iTunesU for a short listing, but figured someone's blog contains this search. So I gBlog-searched, "best ways to learn ruby on rails"

I then read:

suggested codeschool

Started to watch nettuts+

Talked to a web-developer who wrote the code I am attempting to add to, she said:

1) Google MVC framework - first chapter or two of book or something similar (conceptual)
understand js, html, css. Make sure its Rails 3.2 and ruby 1.9

2) Think of an action that a user can perform. And can you trace it through the code?

3) Get everything working from my machine. Installing ruby, installing rails, requisite gems,

Once comfortable use (rails s) to localhost and test changes to the code.

I might use free video tutorials at  ShowMeDo

There are responses in a forum thread on stackoverflow and that led to stackoverflow's learning threads

Pretty sure I can youtube it for free.
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Tuesday, December 10, 2013

Design Behind Wuzzit Trouble

A medium as interactive as a tablet should be doing a lot more than spoon-feeding worksheet problems to children.

Game Design

Innertube Games is breaking the mold. They have a super team of individuals developing learning experiences to serve as grounding metaphors for mathematical ideas. They bypass the traditional education system to address the quantitative skills gap directly. Their product, Wuzzit Trouble (2013), is a prime example of this. I demonstrate the design below.

The game can easily be learned through play, but if you’re curious and press the ? key you’ll see the instructions screen.

Your world is a numbered gear with modulus 65. You have the ability to scale given integers with small gears that turn the large gear. You can scale to the left or to the right. By playing this game, a learner can develop a schema for integers and integer modular arithmetic.

The game levels are like lessons planned by an experienced math instructor. They provide an adequate challenge, give immediate feedback, and encourage mistakes.

You may be thinking, "So I just turn these little gears and they move the big gear to free the cute creature called a Wuzzit? Easy enough, what’s the catch Rushton?"

First check out the list of advisors. No catch.

Learning Design

B. F. Skinner wrote, "A machine that teaches by arranging contingencies of reinforcement is a teaching machine.”[1] (p. 110) Many of the game features in Wuzzit Trouble are similar to those found in popular mobile games, like Angry Birds (stars for achievement, high scores, cute creatures expressing emotions...) Our children become increasingly persistent at tackling the obstacle presented by the game to earn the next reward. We demonstrate a behavioral reaction not so different from Skinner's dog jumping to the sound of a clicker.

James Paul Gee wrote, "Good games operate at the outer and growing edge of a player's competence, remaining challenging, but do-able" [2] (p. 2). This sounds like a condition for the state Csikszentmihalyi dubbed "Flow". I was completely absorbed by this game, and feel like it satisfied many of Gee's video game learning principles. The complete discussion of these principles is in his 2003 book, What Video Games Have to Teach Us about Learning and Literacy [3]. This work was heavily referenced in Keith Devlin's 2011 book, Mathematics Education for a New Era: Video Games as a Medium for Learning [4] where Devlin applies Gee's ideas to mathematics education, through a mathematicians lens. 
For more immediate content:
There is a useful post/interview of Keith Devlin by Jordan Shapiro.
There is a useful post/interview of James Paul Gee by Henry Jenkins.  
James Paul Gee has a short series of youtube clips on this topic.

People love video games. Most readers would probably agree with Gee arguing that all video games are teachers. They are designed to teach the user how to play the game better. The trick lies in making the mechanics of the game near enough to the underlying principle being taught so that transfer of the mental models can occur. Wuzzit Trouble is fun to play and the progression is smooth. In order to get to the later levels, the game designers will have taught a course to you in the form of a game. The fundamental mechanics of a well designed game will transfer to other structures in the world. You will be able to solve systems of linear equations in 4 variables on a mod65 ring, feel accomplished for it, and see number patterns and structures in your mathematics classes as a result of your fun.

Keep 'em coming Innertube Games! Thank you for your considerable contribution to our society.

This is an extraordinary game. Get it for your children.

Peace and Blessings,


Enhancement - I Wish...

The highest scores were reserved for the least number of moves. (3 stars and all bonus items in 6 moves should not be the same as 3 stars and all bonus items in 5 moves )

There were more levels.

When you overshoot a position it counts against you. (right now the excess is ignored)

There were a way for me to tell the story of the game and identify features of the game, in my own reflective journal. (interact with the progress metrics somehow)

There were multiplayer options to promote collaboration and/or competition.

Appendix - Wuzzit Trouble is "Standards-Based"

I will identify the “standards” that are being taught for the first 5 levels to serve as examples to support this claim, and I encourage the reader to play the rest of the levels to verify the veracity of this claim.

Integer addition, subtraction and multiplication are a subset of the Number & Operations in Base Ten Domain: and the fact that there is negative scaling to turn the wheel counterclockwise provides a foundation for the Number System Domain that starts in grade 6:

In addition to content standards, the game helps to reinforce some of the Standards of Mathematical Practice. It is a process of discovering new properties of numbers in order to beat the progressive levels. It involves persistence, precision, repeated reasoning, and developing an awareness of the underlying mathematical structure.

Level 1-1 – Positive integer addition
The student will demonstrate the ability to tap and turn the small gear clockwise.

Level 1-2 – Positive integer multiplication and addition
The student will demonstrate th\e ability…
(2 stars) to tap and turn the small gear in multiple moves
(3 stars) to tap and turn the small gear a scalar multiple of turns.

Level 1-3 – Positive integer multiplication and addition
The student will demonstrate the ability…
(2 stars) to tap and turn the small gear in multiple moves
(3 stars) to tap and turn the small gear a scalar multiple of turns.
CCSS.Math.Practice.MP7: Look for and make use of structure.
The student will be introduced to repeated intervals

Level 1-4 – Negative integer multiplication and addition
The student will demonstrate the ability…
(2 stars) to tap and turn the small gear in multiple moves
(3 stars) to tap and turn the small gear a negative scalar multiple of turns.

Level 1-5 – Negative integer multiplication and addition
The student will demonstrate the ability…
(2 stars) to tap and turn the small gear in multiple moves
(3 stars) to tap and turn the small gear a negative scalar multiple of turns.
CCSS.Math.Practice.MP7: Look for and make use of structure.
The student will again see a repeated interval in the negative direction


[1] Skinner, B. F. (1986). Programmed Instruction Revisited. The Phi Delta Kappan, 68(2), 103-110.

[2] Gee, J. P. (2003). What video games have to teach us about learning and literacy. Computers in Entertainment 1, 1,             pp 20-24. DOI=

[3] Gee, J. P. What Video Games Have to Teach Us about Learning and Literacy. New York: Palgrave Macmillan, 2003.           Print.

[4] Devlin, K. Mathematics Education for a New Era: Video Games as a Medium for Learning. Natick, 
Massachussetts: A        K Peters, Ltd., 2011. Print.

Sunday, November 24, 2013

Interaction Design: 4 Approaches to Balancing Whole Number Expressions

Mathematical Model:
A scale measures equality between two weights, represented by mathematical expressions. By adding opposites that sum to zero, expressions can be simplified. The balance responds to the relative weights in the virtual manipulative.

Problem Statement:
What is the best user experience that stays true to the mathematics, and is engaging to interact with?

1) MathPlayground ( offers a solution to the problem of Solving Whole Number Linear Equations (Fig. 1).
Fig. 1 Mathplayground's Algebra Equations Practice Mode
I like:
·      Realistic Functionality - balance responds to inequality
·      There is exactness to the equality of the symbols on each side
·      There is a symbolic representation of the equation
·      Tiles are in a convenient place to grab

I wish:           
·      You could scale the number of tiles you were adding/subtracting, and could have more than 20 tiles on a side
·      The game had multiple representations
o   Table
o   Graph
o   Abstract symbolic
·      That other representations could be chosen to work with and automatically updated when a move was made 
·      That the manipulatives were made into fun items that were less abstract
·      That tutorial mode was not the default user first experience, it is much more restrictive than the practice version of the manipulative. 

2) Utah State University's NLVM ( has Algebra Balance Scales (and a Negative Integer version in Fig. 2)

Fig. 2 NLVM's Algebra Balance Scales - Negatives

I like:
·      Realistic functionality - balance responds to inequality
·      Exactness of symbols - equivalent on each side
·      Symbolic representation of the equation
·      Symbolic manipulation of the equation
·      Tiles are in a convenient place to grab, and they drop easily

I wish:           
·      Other forms of manipulation other than symbolic (The objects were still moveable after being placed on the scale)
·      You could scale the number of tiles you were adding/subtracting, and were able to have more than 10 of a given object on a side
·      The game had multiple representations
o   Table
o   Graph
o   Abstract symbolic
·      That other representations could be chosen to work with and automatically updated when a move was made 
·      That the manipulatives were made into fun items that were less abstract

3) DragonBox Algebra ( has a gamified approach to teaching the procedures for solving linear equations. (Fig 3)

Fig. 3 DragonBox's Algebra Equations Progression

I like:
·      The graphics are great and the functionality is intuitive
·      The symbols and operations are consistent
·      The way anti-objects are implemented, and the scaffolding pictures are slowly removed
·      The gamification elements make it an addicting experience
·      That a child will learn all of the procedures for solving linear equations without thinking they are doing math

I wish:  

·      There was a relation to the real world, like the balancing of weight
·      There was a conceptual underpinning to things like dividing every term by a value
·      The game had multiple representations
o   Table
o   Graph
o   Abstract symbolic
·      That other representations could be chosen to work with and automatically updated when a move was made 

4)  Curtis Wang designed a Whole Number Linear Equation lesson that can be extended as a game concept. (Fig. 4)

Fig. 4 Curtis Wang's Solving Whole Number Linear Equation Lesson
I like:
·      The graphics and friendly design
·      The animations in the original version (
·      That this could be more fun to play than the abstracted form

I wish:           

·      There was exactness to the symbols on each side
·      There wasn’t a change in the moment of inertia when placing objects
·      There were anti-objects like helium balloons to remove weight with

·      We could incorporate scaling (Whole number multiplication/Division)

Neighborhood Boundary Project

I tried to use some Buck Institute Project-Based Learning materials and methods for a few days with Algebra Project Cohort students.  If you are not familiar with their free DIY guide, I recommend it.
Fig. 1

This came after we spent a good deal of time with students on the idea that when "solving" a linear inequality in one variable, we were putting an equals sign in place of the inequality symbol in order to identify the boundary points (Fig 1). After finding the boundary points we were then able to find the solution set by testing left/right of the boundary point on the number line.

The Neighborhood Boundary Project was an attempt to extend the idea for two variables.


The original hook involved overlaying multiple definitions of our neighborhood (zip codes, city council districts, community member-made street line drawing) and asking who was right?

Who decides the neighborhood boundary lines?

Fig. 2 Neighborhood Boundary deck. See the .key for the actual animation

Fig. 3 Eagle Rock product

The idea was to teach a geometric interpretation of linear inequalities as boundary lines with a shaded region above/below the boundary line in the y-direction or left/right of the boundary line in the x-direction.

Students had to define their own system of linear inequalities such that the overlapping solution areas would generate the community they were assigned to.
Fig. 4 Highland Park product

Learning Outcomes

Students did a good job of explaining why they chose particular inequality symbols to get the correct shading. However, not all students were able to produce the symbolic representations of the boundary lines, which is the major skill on standardized tests. Therefore, in future iterations it would be important to provide an opportunity for students to practice and repeat this skill in a way that does not detract from the engagement of the project.


We did not put together a composite graph due to time constraints, even though the students were all using the same coordinate system.

I would have loved to have students argue about the boundary lines that were defining adjacent regions. We alluded to gerrymandering of district lines, and this could have made that idea more relevant.

There need to be other ways to get students reflecting on their abstract symbolic inequalities.

Grab the files and adapt as you please. Let me know how it goes.

Wednesday, July 31, 2013

Standards-Based and Rubric-Based Grading


I would be using JumpRope if I were teaching this semester. I would save so much time not having to do purposeless record-keeping. I'm a fan. Try it.

This is definitely in the correct direction when it comes to a Growth Mindset replacing a Fixed Mindset. We should be focusing student attention away from scores/numbers and toward goals/mastery. A 67% doesn't tell me what I need to improve. Feedback needs to be self-explanatory and timely.

Example for teachers:
Do you truly believe every one of our students can achieve mastery?

I do. I believe there is a distribution of the amount of support and intervention required to get every child to mathematical literacy. We aren't successfully serving our youth yet. I argue that our progress in defining the appropriate interventions is muddled by assessment practices that damage curiosity and confidence in our youth. New assessment practices will help put an end to the shaming our defamatory culture brings to the people.
Enjoy Work.

Image: Nigel Holmes / Graph Content: Carol Dweck / Blog Source: QED Foundation

Tuesday, May 14, 2013


It was to my great amusement when a student of mine told me how his sleeping in class would increase his productivity. 
 I am a fan of ASAPScience.

Saturday, April 13, 2013

Resources: Assessing Mathematical Proficiency for Common Core

What questions do you have about this?

I had the honor of attending Critical Issues in Mathematics Education (CIME) at the Mathematical Sciences Research Institute on April 3-5. There was an impressive gathering of mathematicians, educators, education researchers, and other interested parties. We worked collaboratively to build mathematical tasks, and felt unguided and uncertain of our products. It is critically important that tasks are implemented, iterated, reshaped, and adapted to the needs of the particular students. While we don't all have time to go write tasks, we do have the time to meet with our departments and create realistic goals for ourselves. I recommend for anyone who isn't already incorporating weekly or monthly common group tasks in their classrooms, to do so. Once there is momentum in the direction of this change, it will become increasingly easier to implement these ideas. I hope to quickly share some of the resources I was introduced to.

CIME 2013 Resources for Item Writers

  • A livebinder with a collection of great resources (some of which are repeated):

  • PARCC sample items

  • Smarter Balance Sample Items

  • New York City Common Core math task exemplars developed by “Common Core Fellows”

  • New York State Common Core Sample Assessment Questions

  • The Mathematics Assessment Project
"The team uses its well-established engineering research [PDF,100K] methods involving: input from prior research; design skills to produce draft materials; iterative systematic development through trials in US classrooms, with revision informed by structured feedback data from the observer teams."

  • Illustrative Mathematics, 700+ tasks aligned to the CCSSM intended for a variety of purposes:

  • The Shell Centre:

  • East Side Community High School Math Portfolio

There is a clandestine implementation of the Common Core State Standards for Mathematics in LAUSD. Everybody expects there to be a mastermind pulling the strings, but in the end, it is our collective effort and effective collaboration that will eventually result in changing the way we teach.

A large district like ours seems very much like a game of telephone, and the messages get morphed as they are passed from vessel to vessel. Luckily, we all have the freedom to access materials at their source. Unfortunately, many parties use this freedom as an opportunity to spread ideas/practices, and this creates the added job of data filtration and discovery.

For all skeptics of the Common Core, be mindful of the research and work that has been put toward these efforts. As for the image above, I emailed the Shell Center requesting the research paper it is in. I could not find it on their publications site.

Enjoy work.