Resources To Accelerate High Algebra Achievement

I ran into an LDT alumnus named Dan Gilbert on Saturday who helped facilitate Stanford's GSE Energizer, and he asked me a great question, 

'My son is high achieving in algebra, what resources do you recommend for him?'

Depending on the learner, there are a plethora of options out there. So a more specific request or richer context might produce better resources. However, I will do my best here to answer the general question,

What resources are available for a high algebra achiever to accelerate their growth in understanding?

This is relevant to parents and educators alike. This is a draft list, and I would love your feedback on it as well as additions you might suggest in the comments.

1. POW (Problems of the Day/Week/Month #Problemoftheweek)

GOOD for motivated learners who want a challenge.
BAD for reluctant learners who would rather do something else.

  

Find problem banks
    https://www.nctm.org/pows/ (NCTM)
    http://mathforum.org/library/problems/ (List)
    http://www.moems.org/zinger.htm (Middle School)

    http://pleacher.com/handley/probweek/ (teacher archive)
    http://mathcounts.org/resources/problem-of-the-week
    http://krazydad.com/ (If you like Sudoku/Ken-ken...)
    http://www.math.purdue.edu/pow/ (Universities have higher difficulty)

I really liked the NCTM Calendar problems when I was ~7th grade. Unfortunately, they require NCTM membership to access. I also think that my math club in high school, involvement in tournaments, and acadeca helped to support my mathematical development. Below I list two of the current social options to support learning (Communities and Competitions) as well as two newer supports (Practice Engines and Games).

2. Communities (Clubs, Makerspaces, MOOCs, social media...)             

GOOD for social learners whose experience a supportive environment.
BAD when the learner and community have different goals or there is insufficient support.

Find communities
    School clubs (Academic decathlon, math, robotics,
    cryptography...)
    Hacker spaces
    Makerspaces
    Afterschool programs
    Reddit, youtube or other forums
    MOOCS (coursera, novoed, edx, udacity, udemy,
    iTunesU, MIT OCW...)
    Robotics clubs
    Coding clubs or programs
    Math Circles - http://www.mathcircles.org/
    Cyber Patriots - https://www.uscyberpatriot.org/
    MESA - http://mesa.ucop.edu/

3. Competitions (AMC, Mathcounts, University competitions...)

GOOD for motivated and competitive learners who want to push their limits.
BAD for social learners who dislike competition or underachievers who need more support.

Find competitions
    http://en.wikipedia.org/wiki/List_of_mathematics_competitions
    http://www.artofproblemsolving.com/Wiki/index.php/List_of_United_States_middle_school_mathematics_competitions (Or high school if you'd like)
Look at past exams to determine difficulty
    http://www.artofproblemsolving.com/Wiki/index.php/AMC_Problems_and_Solutions
    http://mathcounts.org/past-competitions
    http://www.moems.org/sample.htm
    https://sumo.stanford.edu/smt/
    http://www.imo-official.org/problems.aspx

I participated in the AHSME and a few local university competitions while in high school and enjoyed being part of a team in many of the school competitions. The next categories are things I wish existed when I was a kid, and areas where innovation is creating opportunity.

4. Practice Engines (Khan, IXL, Alcumus...)

GOOD for tracking and individualization of procedural skill practice.
BAD for conceptual understanding and higher order thinking skills.

Find Practice engines

    http://www.artofproblemsolving.com/liz/Alcumus/index.php (Art of Problem Solving is a much larger effort addressing the overall question)

    https://www.khanacademy.org has mastery missions and can be quite fun

    http://www.sumdog.com/ (Gamified practice elementary skills)
    https://www.sokikom.com/ (Gamified practice elementary skills)
    IXL, ALEKS, EnableMath, Pearson MyLab are paid products (Tons of these...)

I really hope Duolingo make a move into the math problem space, because what they did for language learning is admirable and perhaps applicable.

5. Virtual Games

GOOD if the game is well designed (intrinsic integration) and aligns with learner goals.
BAD if the game is poorly designed (Extrinsic integration) or doesn't align with goals.

 

Find Games
FREE
http://www.wuzzit-trouble.com/ (My favorite)
http://www.mathsgames.com/fraction-games_refraction.html (Fraction operations)
https://www.mathbreakers.com/

PAY
http://www.dragonboxapp.com/
http://motionmathgames.com/parents/
http://www.greenglobs.net/

Find Simulations and Interactives
https://teacher.desmos.com/
http://nlvm.usu.edu/en/nav/vlibrary.html
http://illuminations.nctm.org/Games-Puzzles.aspx


As you can imagine, this only scratches the surface. My hope is that I have uncovered some nuggets to get you started. For each broader category you can follow-up with your own search (google, blogstalking, twitter, forumcrawling...) and find an infinitude of cognitive overload. If you come across something great, please share it!

Thank you for your work.

Peace be with you,
Evan