Games
Puzzles
Tools
Manipulatives
Wednesday, July 28, 2010
Tuesday, July 27, 2010
Interactive (dynamic) geometry software, free online
There are many options here. I think it makes sense to download one or more of the free software packages and see how they "play," then look at the demo version of Geometer's Sketchpad for comparison and decide whether or not it's worth the investment for your family. Personally, I am quite smitten with Sketchpad and highly recommend it.
C.a.R.
Cinderella
DG Dynamic Geometry (for PC only)
GeoGebra
Geometer's Sketchpad
The free demo version available online is
If you are a teacher or homeschooling parent, it seems that you could download the demo and use it for 60 days to decide whether you wish to purchase the software. The student edition is available for $39.95. If your child's school has a site license, you can get the student edition for $29.95. Here's the link:
There is a vast array of videos, lessons, and many other resources online for GSP. Here are a few:
Dynamic Manipulation and Mathematical Learning - The Geometer's Sketchpad Resource Center
Monday, July 26, 2010
Dynamic Geometry Follow-Up
Just to show what you can do with dynamic geometry software, here are some illustrations using the free software, Cinderella.
The task is to draw any quadrilateral, ABCD; locate the midpoints of the sides; connect the midpoints of the sides consecutively to obtain quadrilateral EFGH. Drag free points and make a conjecture about EFGH.
Here are three pictures of what happens when you move what is free to move. First, the diagram at the start:
Next is a picture showing what happens when the original quadrilateral is dragged to make it convex:
Finally a shot of what happens when the dragging makes ABCD into something we wouldn't even call a quadrilateral:
What appears to be true about EFGH in all three illustrations? How could you prove it?
Thursday, July 22, 2010
Aunty Math for math challenges
The DuPage Children's Museum sponsors a web page with math challenges for K-5 children. The whole web site is worth exploring!
Tuesday, July 20, 2010
Mathematics sites by category
Algebra including functions, graphing, trig
Arithmetic/Number/Infinity
Problem Solving
Newton's Window Math Challenges Getting Started
Number Theory
Discrete Math: Combinatorics, Graph Theory
Fractals
History of Math
Geometry and spatial visualization including symmetry, tessellations, topology, knots, origami
Probability/Statistics
Applications/Connections including art, music, sciences, etc.
Multi-category, miscellaneous
A Disney classic in three parts:
Monday, July 5, 2010
upcoming workshop
I'll be doing a workshop for parents of students in the Leapfrog program at the Center for Talent Development, Palatine location, on Friday, July 30, 2010, 10:00-11:30 a.m. The focus is technology, so I will be sharing ideas and examples about ways to use the internet with gifted children, grades pre-K - 3. For more information, contact the Center for Talent Development at Northwestern University.
Wednesday, May 12, 2010
Excellent Math Resources for Families
Family's Guide:Fostering Your Child's Success in School Mathematics
offers suggestions to help parents and guardians become involved in their child's mathematics learning. In particular, see pages 6-12. 
The textbook publisher, Houghton Mifflin, offers a Parents' Place on their website with links to some excellent resources for families. Try their Pre-K page and navigate from there.
offers suggestions to help parents and guardians become involved in their child's mathematics learning. In particular, see pages 6-12. The textbook publisher, Houghton Mifflin, offers a Parents' Place on their website with links to some excellent resources for families. Try their Pre-K page and navigate from there.
Thursday, April 22, 2010
Turtle Geometry
I just stumbled across Bill Kendrick's WEB TURTLE - A Java-Free drawing program on the web!
In my early days of computing, with my trusty Apple II+, I had a LOGO software package that I loved. This is very similar to what I remember, with the advantage that it is free! Do take a look and explore the examples and commands.
Here's what the turtle drew in response to the set of commands I gave:
In my early days of computing, with my trusty Apple II+, I had a LOGO software package that I loved. This is very similar to what I remember, with the advantage that it is free! Do take a look and explore the examples and commands.
Here's what the turtle drew in response to the set of commands I gave:
If you are interested in more on turtle geometry, try this:
Sunday, April 11, 2010
Summer 2010 opportunities for mathemically gifted students
Summer Program Catalogs, Johns Hopkins Center for Talented Youth
SWIM 2010 Women in Mathematics Summer Workshop, Princeton
Partial Home Schooling
One of the issues that frequently comes up in discussions with parents who call or attend my presentations at CTD is home schooling. I "partially home schooled" one of my gifted students when he was in sixth grade and wanted to learn plane geometry. His school recognized that his needs in math were not being met at school, so he was permitted to leave during the school day to come to my home for math. (This was about five years ago, so I don't remember whether we did this once or twice a week, but it was never more than twice a week.) He was able to get his other subjects at school and maintain a full complement of after-school activities. Of course, when he got to the high school, they made him jump through hoops in order NOT to have to repeat the course, but that's another story. The bottom line was that he did not take geometry in high school.
In the elementary grades, teachers and schools tend to be more willing to acknowledge that a student's needs are beyond them, and to let parents take their child out of school for part of the weekly schedule, either to homeschool the student themselves or to hire someone (like me) to mentor their child in mathematics. There is typically less flexibility on the part of the schools in grades 6-12, where many schools take the position that offering algebra in grade 8 (or, rarely, in grade 7) solves the "problem." In my opinion, it usually does NOT.
In the elementary grades, teachers and schools tend to be more willing to acknowledge that a student's needs are beyond them, and to let parents take their child out of school for part of the weekly schedule, either to homeschool the student themselves or to hire someone (like me) to mentor their child in mathematics. There is typically less flexibility on the part of the schools in grades 6-12, where many schools take the position that offering algebra in grade 8 (or, rarely, in grade 7) solves the "problem." In my opinion, it usually does NOT.
For a fuller explanation of partial home schooling, check out this article by Deborah Ruf:
I think this is a viable option for children who are particularly gifted in one subject matter area. The children can get what they need in math, for example, from someone with the expertise to provide appropriately challenging content without sacrificing all the social advantages to staying in school for most of the day. The cons include extra driving and the expense, which usually must be handled by the parents.
Saturday, April 10, 2010
Competitions
Participating in math competitions can be a terrific experience for gifted students. Many mathematically gifted students have been accelerated in math; a student with a couple of years of high school math can be a huge asset to a middle school math team, even if he/she has never been in a math class with any of his/her teammates. It adds a social element to doing math (some of the problem solving is done by teams rather by individuals), and, for some gifted students who are not also gifted athletes, this may be the only opportunity to be on a TEAM.
An excellent author for appropriate books is George Lenchner
.
. Note that there are books with Problem of the Week formats (NOT math workbooks!).
This is a good one:
The handbooks from past years
can be useful for preparing to compete, and contain some interesting problems.
can be useful for preparing to compete, and contain some interesting problems. There are many resources for problems from past ARML contests
:
: There are books containing problems from past exams
.
. This is the "big time!" So, naturally, there are a host of available resources for students
competing at the very highest levels. Here are links to a sample of international math olympiad
problem books.
2001
competing at the very highest levels. Here are links to a sample of international math olympiad problem books.2001
2002
2003
2005
Multiyear problem sets:
I think two of the best books for high school competition prep, and for deeper understanding of mathematical topics than high school classes typically provide are these:
The Art of Problem Solving Volume 1
and
The Art of Problem Solving Voume 2.
The Art of Problem Solving Volume 1
and
The Art of Problem Solving Voume 2.
Saturday, March 27, 2010
An excellent book...
Adding It Up: Helping Children Learn Mathematics
offers insights on how children Pre-K through grade 8 learn mathematics. The whole book is excellent, but, in particular, I like the discussion of what mathematics understandings children develop BEFORE entering a school program (starts on page 157). You can also read the book online, free.
offers insights on how children Pre-K through grade 8 learn mathematics. The whole book is excellent, but, in particular, I like the discussion of what mathematics understandings children develop BEFORE entering a school program (starts on page 157). You can also read the book online, free.
Amazing Geoboards!
The geoboard is pretty much my favorite manipulative--there is so much mathematics that can be addressed using this simple tool.
My newest student is a gifted 6-year-old and the first manipulative I introduced him to was the geoboard. He had used one before, but I assured him we would be doing activities with it unlike any he had done at school.
By the end of the first hour, he was happily finding the areas of squares on the geoboard, and NOT just squares of size 1, 4, 9, and 16!
(There are FOUR other squares whose areas are whole numbers. Give it a try. Email me with your results.)
During the second hour we collected data about the areas of shapes classified by the number of boundary pegs and the number of interior pegs. Over time, we'll work our way to Pick's Formula. (A mathematical discussion is presented in Chapter 2 of Strange Curves, Counting Rabbits, & Other Mathematical Explorations
.)
By the end of the third hour my student had discovered a tessellation,
but was more interested in creating more of his own designs.
My newest student is a gifted 6-year-old and the first manipulative I introduced him to was the geoboard. He had used one before, but I assured him we would be doing activities with it unlike any he had done at school.
By the end of the first hour, he was happily finding the areas of squares on the geoboard, and NOT just squares of size 1, 4, 9, and 16!
(There are FOUR other squares whose areas are whole numbers. Give it a try. Email me with your results.)
During the second hour we collected data about the areas of shapes classified by the number of boundary pegs and the number of interior pegs. Over time, we'll work our way to Pick's Formula. (A mathematical discussion is presented in Chapter 2 of Strange Curves, Counting Rabbits, & Other Mathematical Explorations
.)By the end of the third hour my student had discovered a tessellation,
Tuesday, February 16, 2010
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