- This site seems to have free homework help in the form of videos,
text pages, and a few "calculator" apps. It looks fairly well put
together, but I've no idea what their business model is, nor how
long the site will remain free.
- This site has Flash math games for kids. I've not checked the
games myself, but was given a pointer to the site by Sheryl Wright's
class at the W.B. Goodwin Community Center. (I believe that they
are in Springfield, PA, though on 2013Feb 9 their website at
www.goodwincc.org only mentions their "new location" without saying
what city or state they are in.)
- This "Interactive Math" site has lessons in mostly high school
and early college math. I have not read the lessons, but I used to
subscribe to the associated blog:
The author seems to be a competent mathematician and competent
writer, so the lessons may be of use to home schoolers and those who
need extra help in learning math at that level.
- This site, which lists web sites with various forms of on-line
help in learning fractions, was recommended to me by a student named
Samantha at the Coastal Academy in California, via her teacher
Allison Smith. I've not reviewed it carefully myself, but it looks
like a decent list of sites for fractions.
- The old columns from Muse about math by Ivars
Peterson. Jan 1999 to Oct 2006.
Tim Boester's home page. Tim writes Knossos Games
for Imagine, the magazine of the Center for Talented Youth at
Johns Hopkins University. Many (all?) of the puzzles from the
column are on the web site.
- This has a bunch of free math games implemented in Flash. I've
not tried any of them, and we're past the stage of using elementary
math games, so I've no idea if they are any good.
The goals of the Statistics Online Computational Resource (SOCR)
are to design, validate and freely disseminate knowledge. Our Resource
specifically provides portable online aids for probability and statistics
education, technology based instruction and statistical computing. SOCR
tools and resources include a repository of interactive applets,
computational and graphing tools, instructional and course materials.
What are the main SOCR Components?
The core SOCR educational and computational components include:
Distributions (interactive graphs and calculators), Experiments (virtual
computer-generated analogs of popular games and processes), Analyses
(collection of common web-accessible tools for statistical data analysis),
Games (interfaces and simulations to real-life processes), Modeler (tools
for distribution, polynomial and spectral model-fitting and simulation),
Graphs, Plots and Charts (comprehensive web-based tools for exploratory
data analysis), Additional Tools (other statistical tools and resources),
SOCR Wiki (collaborative Wiki resource), Educational Materials and Hands-on
Activities (varieties of SOCR educational materials), SOCR Statistical
Consulting and Statistical Computing Libraries.
- Free animated videos, mostly of 7th-9th grade math. Quality
unknown, as I don't have the patience to watch instructional
videos (neither does my son---reading is so much faster).
- Grades 5-12 (ages 10+) e-learning system using Flash animation.
Qaulity and price unknown.
- Subscription on-line math course that is not too expensive,
recommended on k12.ed.math by Karl Bundy.
More comments on the use of ALEKS with gifted students can be
found at http://www.geniusdenied.com/Cybersource/Record.aspx?sid=10539
We tried the 2-day free trial and decided not to bother with
ALEKS. Here are the reasons:
In short, Aleks is not a suitable substitute for a tutor
and does not make good use of computer-aided instruction.
It may be an adequate drillmaster for a child with a high boredom threshold.
- The assessement was frustrating for a kid who likes to work
at the level where he gets 90% right---it quickly got to the point
where he couldn't do the problems and stayed there.
- Once Aleks decides you know something, there is no going
back, even if it has based its assessment on only one or two questions.
- There is no way to tell Aleks that a problem is too hard
other than by getting it wrong---an unacceptable situation for a perfectionist.
- The format is incredibly boring: a problem is presented, you
type the answer, and another problem is presented.
- The problems (in the arithmetic unit) were purely numeric: no word problems, no multi-step problems, no thinking, just
drill, drill, drill.
- There are no intermediate steps to be entered in the problems---you do the
whole thing on paper and just type in the answer.
- The "tutorial" information is poorly written and does not
necessarily address the problems that a child may be facing.
I sent my critique of Aleks to their support address (they
requested feedback), and I am posting their thoughtful reply here:
Thank you for your message and for your frank comments on ALEKS.
I will respond to them by points:
We do very much appreciate your candid criticism of ALEKS. All of your
comments will be used by our development staff in our ongoing efforts to
provide the best possible tool for students' math learning.
- You are quite right about the assessment in the sense that it will
adapt to the student's level, although it actually stabilizes at a point
where the student is just as likely to answer correctly as
incorrectly--not where the student is more likely to be incorrect. The
purpose of the assessment is to determine the student's level as quickly
and accurately as possible, and this method of questioning is well
suited for achieving that purpose. We do our best to convey to students
entering the assessment that it is **not** a test, and that they should
expect questions which they may be unable to answer.
[We did give him that understanding, but the 50% right level was a
frustrating point for him to be---doing a few more questions that were
easy would have been more comfortable and gotten the assessment more
accurate, since the assessment skipped too fast over stuff he was only
partly familiar with.
I'd recommend adjusting the assessment tool so
that it tries to provide students with 80-90% correct, rather than 50%
correct. This takes more questions to do the assessment (maybe 2-3
times as many), but reduces the stress level.
- ALEKS will in fact go back if a subsequent assessment indicates the
need for review. You would need to use the system over a certain period
of time in order for this characteristic of ALEKS's functioning to
become clear. Between assessments, you can go back to an earlier topic
by using the "Review" button.
[We did not see the "review" button--that would make a big difference.
The pie charts would not let us select a topic that it thought he had
- This is an interesting point. What would you envision happening if
the student wished to tell ALEKS that a problem was too hard? Is it
just a matter of getting another topic for the time being? The student
can always click the "MyPie" icon to make another topic selection.
Otherwise, the "Review" button could be used. What different behavior
might be possible here? We are eager to handle this situation as
productively as possible.
[What would a real tutor do? Suggest taking a break, if the student
has been on for more than 30 minutes? Ask the student if he wants to
review one of the prerequisites to the problem (listing them)? Provide
a step-by-step approach to the problem? Ask some of the heuristic
questions from Polya's "How to Solve It"? Replace the question with an
easier one and work back up?]
- It is true that ALEKS is not designed in any way to be entertainment
or "edutainment." It is intended to be a core curriculum learning tool
which makes the best possible use of the time and effort provided by the
student. That being said, we are constantly thinking about ways to
improve the interface and program architecture to achieve more
engagement of the user, especially at earlier ages. In the foreseeable
future there will be a new, "early grades" version of ALEKS with a
completely different look and feel.
- There are numerous application problems and multi-step problems in
ALEKS. One needs to spend a certain amount of time working in the
program to get an accurate sense of its actual scope.
[Probably true, but the initial free trial was so negative an
experience for my son that he won't be willing to try Aleks again.]
- The content presented by ALEKS is divided into very small, specific
topics, such that the intermediary steps needed to resolve a particular
problem are actually separate items which the student has demonstrated
mastery of before arriving at the problem for which they are needed.
[Here we part company---1) the assessment overestimated some of my
son's abilities, so presented him with problems he was not ready for.
2) It is *often* better to present problems with explicit intermediate
steps, but Aleks does not seem to support this pedagogy.]
- The explanations in ALEKS are being continuously reviewed and
improved. We welcome any specific feedback on particular explanations
that our users wish to provide. The "Message" button makes it easy to
send "instant feedback" to ALEKS Corporation on explanations or any
aspect of the program.
- The thinkwell math courses, taught on CD ROM videos by
Prof. Burger have been
getting good reviews on the TAGPDQ mailing list.
The CD-ROM text runs on Windows, Mac OS 9, and Mac OS X, using the
They start with
high-school algebra and go through Calculus. The CD-ROM textbook
costs $76/course. It is not clear how "Beginning Algebra,
Intermediate Algebra, College Algebra, and Precalculus" are
related---is this a 4-course sequence or overlapping sets of material?
Thinkwell also sells CD-ROM texts for science classes, but I
have not read reviews of them yet.
- The Art of Problem Solving site is intended for gifted math
students in 6th grade through high school. They sell
books and online courses.
"Our online school emphasizes problem solving mathematics of the
type found in extracurricular programs like MATHCOUNTS for middle
schoolers and the American Mathematics Competitions (AMC) for high
The AoPS courses have gotten some good reviews on TAGPDQ, and
the text they provide on their web site seems to indicate a good
attitude toward math and math teaching.
They have now released an algebra text: "Art of Problem
Solving's Introduction to Algebra textbook is now available! This
book completes the Art of Problem Solving Introduction series of
textbooks, which offers a comprehensive curriculum for outstanding
math students in grades 6-9."
- The have fora for several different topics (their books,
various math competitions, ...). Their list of math
competitions is pretty good.
- Math challenge courses from ages 5 to 17. Looks interesting.
- Hampshire College Summer Studies in Mathematics
for mathematically talented high school students.
I don't know much about this course. I got an unsolicited e-mail
from a student who took it and thought it should be on my list.
Since it is in South Amherst, Massachusetts, 3000 miles away, it
is not likely that we will ever apply to it.
- A nicely organized set of pictures related to math (fractals,
golden ratio, ...)
- This sites has descriptions of areas of math (map-coloring,
...) that are of interest to childen, and the cartoon-like
navigation on the web site seems intended for children, but the
text seems to be written for teachers.
- Self-described: The goal of the AIMS Puzzle Corner is to
provide teachers with a variety of interesting puzzles that can be
used to create a learning environment where students engage in
doing mathematics just for the fun of it!
The monthly puzzles seem to be aimed at approximately 2nd-5th grade, but
the grade level does not seem to be a major concern.
The puzzles seem to be a feature from the AIMS Educational
Foundation magazine (see http://www.aimsedu.org
for more info.
- Puzzles by a retired math teacher. I've not checked them for level.
- A useful set of tricks for kids to learn to do mental math
more easily (many fairly obvious, like x*11 or x*101, but
useful for children just learning arithmetic).
- Multiplying two numbers in the range 5<=x<=9 on your fingers,
relying on (10-x)(10-y) = 100 - 10(x+y) +xy = 10(10 - (x+y)) +xy
- Interactive web pages to do math exercises (on-line, not worksheets).
- Contains interactive activities. The java applets seem
to misbehave on one of the machines I tried them on, which could
be very frustrating for a child. Matching game seems to be
suitable down to about 1st grade, arithmetic games seem to
start at about 3rd or 4th grade (much higher, if you expect
reasoning rather than random actions). Most games seemed
aimed at high school or college students. I like the article
on Fawcett's class:
- "All about fractions" A tutorial web site with tiny lessons
in text and simple drill games. Looks useful for practice.
- A mental math game that is supposedly good for "family
math nights". One reviewer claimed it good for 1st-8th
grades, though most teachers seem to be using it around 4th
There is a demo version on-line at
- HomePage for Brian Harvey (bh@cs.Berkeley.EDU)
- Place to get a free copy of Logo that runs on
Unix/Linux/Mac OS X, or Mac OS, or even Windows and DOS.
- A Java applet for playing with tangram pieces.
- A delphi program for solving "alphametics"---puzzles in which
10 letters stand for the 10 digits in a math problem.
- A nice program for creating tesselations and pictures with symmetries.
- A web site for searching for the name of a real number, given
its (approximate) value. (Link seems to be broken)
- The On-Line Encyclopedia of Integer Sequences tries to
identify a sequence give the first few numbers of the sequence.
- MathSmart(TM) is a dominoes-like game for teaching
single-digit addition, subtraction, multiplication, and division.
It is simple and fun for a while, but the rules are not well
thought out and there is not much room for strategy. It can
also be quite frustrating to have to wait for domino with a
usable answer to appear. This one got put back on the shelf
after the first week or two and not played again.
- Making Mathematics, a National Science Foundation-funded
project, has the goal "to provide high school students and
teachers with the materials and mentorship necessary for
engaging in a mathematical research experience."
This program attempts to pair professional mathematicians
(with some mentorship training) with either classes or
individual students. It looks like a promising way to get
students involved in math and provides a way for professional
mathematicians to do something (not too onerous) about the
dismal state of math education.
Interactive pre-algebra class and a couple of online copies of