Gas station without pumps

2013 August 8

Hard Math for Elementary School

Filed under: Uncategorized — gasstationwithoutpumps @ 20:34
Tags: , , , , ,

Hard Math for Elementary School by Glenn Ellison: (ISBN 9781489507174) looks like a book I could have used with my son about 8 years ago (too bad it was just published a couple of months ago).

The premise is simple: it is a math enrichment textbook, intended to take the topics of elementary school math deeper for gifted students.

The presentation is good, but the students will have to be reading at the 4th grade level as well as doing math at that level to get much out of the book.  This is not a flashy book with lots of illustrations and stories—it is just cool math, presented as cool math.

Disclaimer: I don’t have a copy of the book, and I haven’t read much of it. I used Amazon’s “Look Inside” feature to look at the table of contents and a couple of pages, and saw such gems as calculation tricks for computing some squares (like 552=3025) quickly.  (The trick is based on (x+y)(x-y)=x^2-y^2, but the author wisely avoids algebraic notation.)

Reviews from people who have looked at it in more detail can be found at and

Glenn also has a book for middle school students: Hard Math for Middle School

2012 October 13

When is a line graph not a line graph?

Filed under: Uncategorized — gasstationwithoutpumps @ 21:39
Tags: , , ,

I recently discovered that elementary school teachers have taken to calling histograms “line plots”, and that this definition has gotten quite widespread:

A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer then 25 numbers. It is a quick, simple way to organize data. []

A line plot shows data on a number line with x or other marks to show frequency. []

A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer than 25 numbers. It is a quick, simple way to organize data. []

This page contains worksheets with line plots, a type of graph that shows frequency of data along a number line. []

Of course, no one outside the elementary school teachers uses that term, which is confusingly similar to the standard term “line graphs”.  Even the superteacherworksheets site acknowledges the terrible confusion that the “line plot” term generates:

Line Graph Worksheets Line graphs (not to be confused with line plots) have plotted points connected by straight lines.

“Line graph” is a common term, even among educators:

Line graph is a graph that uses line segments to connect data points and shows changes in data over time. []

Line graph: A graph that uses points connected by lines to show how something changes in value (as time goes by, or as something else happens). []

line graph definition: a diagram of lines made by connected data points which represent successive changes in the value of a variable quantity or quantities. []

Was it just because they couldn’t spell “histogram” that elementary school teachers had to invent a new term confusingly close to an existing standard term?  I feel sorry for the kids subjected to this poor choice of nomenclature, as they will have to do more unlearning before taking high school or college tests, where they will be expected to know what a histogram and a line graph are, but not anything about “line plots”.

2012 April 16

Squishy Circuits, for family science night

Mylène recently posted a good description of an electrical building project suitable for young kids (she did it with a Brownie troop): K-12 Engineering: Squishy Circuits Tips and Tricks.

A few years ago, when my son was in 5th and 6th grade, I helped run a Family Science Night at his school.  We did a lot of fun activities, but never tried squishy circuits.  I did keep on-line notes about what we did do and web resources we found at that time.  Perhaps these notes may be useful to someone planning a family science night at an elementary or middle school.

2011 June 5

Analysis of Common Core Standards

Filed under: Uncategorized — gasstationwithoutpumps @ 09:59
Tags: , , , ,

The article

Common Core Standards: The New U.S. Intended Curriculum by Andrew Porter, Jennifer McMaken, Jun Hwang, and Rui Yang
doi: 10.3102/0013189X11405038 Educational Researcher 40(3):103–116, May 5, 2011.

has an analysis of the new Common Core Standards, comparing them to existing state standards, standards in other countries, and a few well-known assessments or standards documents. (I’ve blogged about a different comparison almost a year ago in California standards vs. Common Core.)

The method published in Educational Researcher attempts to reduce the complexity of comparing huge, complex documents down to single numbers measuring similarity, which loses a lot of the information. Saying that California shares 0.27 similarity (on a scale of 0 to 1) with the Common Core for kindergarten math standards, or 0.31 for high-school math, does not tell me whether the Common Core is better or worse, just that it is different.

The similarity measure is computed from comparing the weights given to each of 1085 cells of an array in math (815 for language arts). The arrays are 2-dimensional, crossing topics with cognitive demand. The projections onto the cognitive demand axis are shown for “state” standards (which I assume are the sum over all grades and states for which they have data) and the Common Core.  Later on in the paper, they imply that the tables are just for grades 3–6, but they failed to have any caption on the table (so much for “Data displays” being taught to educational researchers).

level state CC
Memorize  12.11%  9.50%
Perform Procedures  48.82%  43.74%
Demonstrate understanding  28.66%  35.65%
Conjecture  7.78%  5.96%
Solve non-routine problems  2.63%  5.16%

Of course, this comparison is for all states and some subset of grades, not specifically for any one state, which is where the comparison might be useful. Still, I’m glad to see an increase in “demonstrate understanding” and “solve non-routine problems”, and a decrease in “memorize” and “conjecture”. (Note: conjecturing is a useful thing, but grade schools and high schools confuse it with guessing, so students are better off not being taught to do it wrong.)

A more informative table is the one that breaks things down by major topic area:

Topic state CC
Number sense 13.84% 32.75%
Operations 15.08% 22.72%
Measurement 0.00% 17.79%
Consumer applications 11.58% 0.05%
Basic algebra 0.03% 13.40%
Advanced algebra 14.47% 0.00%
Geometric concepts 0.24% 5.73%
Advanced geometry 9.27% 1.64%
Data displays 2.83% 2.76%
Statistics 4.72% 3.16%
Probability 0.15% 0.00%
Analysis 0.03% 0.00%
Trigonometry 0.64% 0.00%
Special topics 0.32% 0.00%
Functions 1.09% 0.00%
Instructional technology 25.71% 0.00%

This table tells me more about the weaknesses of their method than it does about the standards, though.  I see no way that one set of standards can be all “basic algebra” and no “advanced algebra” while the other is all “advanced” and no “basic”.  I also have no idea what they mean by “analysis”, but it is almost certainly not the topic that mathematicians call “analysis”, which is a more advanced form of calculus.  The numbers in both columns look ludicrous (25.7% on “instructional technology”, which probably means use of calculators?  32.75% on number sense?).  Quite frankly, after seeing this table, I do not believe anything the authors have to say about the standards—the numbers look cooked to make their point, rather than being a dispassionate analysis of the data.  Looking further in their paper, I see that this is just incompetent proof-reading, as their graphs show low “advanced algebra” content in both  columns, and do not show  huge bump for “instructional technology” in the state column

So, the one interesting table in their paper is clearly garbage.  What a waste of effort, doing all that work then failing to proofread the paper and printing trash. Other incompetent editing: some tables have states labeled with names, others have “State A”, “State G”, … .

I think that Educational Researcher needs to retract the paper and have the authors redo the paper with proper proofreading and captioning of their tables and figures—this is unacceptably bad work for an academic publisher.


2010 November 18

Math game competition

Filed under: Uncategorized — gasstationwithoutpumps @ 00:10
Tags: , , , , , , ,

The Games for Learning Institute have announced a contest for games that teach 5 of the New York State geometry standards for 6th grade. There is a flier at if you want something to post on the wall.

Register by: December 12, 2010
Game Submission Deadline: January 12, 2011

Unlike many game designers, the organizers here seem to be aware that schools don’t have cutting-edge equipment. The game has to run in a browser on a commodity PC or Mac (no special hardware or special plug-ins). I believe that Scratch games should qualify, via the Scratch Player (a Java applet), so beginning programmers (even 6th graders!) can get in on the action.

I’ve posted about Scratch before (Computer Languages for Kids) and the Build-Your-Own-Blocks extension to Scratch.  I don’t know whether BYOB has a Java applet player, which would be necessary for entering this contest.

Next Page »

%d bloggers like this: