Related to the benefits of flashcards are the benefits of testing. Good tests provide feedback--to teachers and parents as well as to students. Good tests prompt retrieval practice by students, thereby solidifying learning. And, finally, good tests motivate teachers and students to be teaching and learning what they should be teaching and learning about anyway.
Tuesday, May 31, 2011
Sunday, May 29, 2011
Flashcards have gotten a bad rap by people who criticize pushy parents and drill & kill teaching. Epitomizing this, eponymously, is the still-popular 2005 book Einstein Never Used Flashcards: How Our Children Really Learn--and Why They Need to Play More and Memorize Less.
Friday, May 27, 2011
|Solving equations in the Olden Days vs. the 21st Century|
|I. Wentworth's New School Algebra (published in 1898), Chapter 2, "Simple Equations," final problems [click to enlarge]:|
|II. 8th grade Connected Mathematics, Unit 5, "Say it With Symbols," Investigations 4: "Solving Equations", final problems [click to enlarge]:|
III. Extra Credit:
Compare the skill sets necessary to complete these problems. Think about your answer to this question, discuss your ideas with your peers, and then write a summary of your findings in your journal.
Wednesday, May 25, 2011
Tuesday, May 24, 2011
Indeed, there's actually more emphasis than in pre-Reform Math days on so-called "addition and subtraction facts"--facts that I don't remember ever having to learn as such. Why, in this day and age, are people more concerned with addition and subtraction facts than ever before?
The answer becomes clear when you contrast Reform Math with more traditional programs. If you compare both the number of problems per worksheet, and the number of individual addition and subtraction operations per problem, you find that Reform Math has students doing only a tiny fraction of the quantity of addition and subtraction operations that traditional math used to require.
Where a traditional math worksheet might have had 20 or more arithmetic problems, a Reform Math worksheet might have only a handful, with most of the space taken up with words, pictures, and room in which to explain your answer in words or pictures.
Where a traditional math worksheet, starting with second or third grade, would have had multi-digit problems in which students must conduct multiple individual addition or subtraction operations per problem (up to n × m operations in an addition problem involving n numbers with m digits and multiple instances of regrouping), Reform Math worksheets don't routinely involve multi-digit problems until 3rd grade and restrict themselves to fewer digits and fewer numbers added together per problem (in general, n and m are much smaller).
Sunday, May 22, 2011
One of these stories appeared as a front page, May 18th Philadelphia Inquirer article. The other one is made up. Which is which?
Some teachers swear that the best way to establish their authority is to avoid smiling for the first two weeks of class.Story B:
David Hall takes a very different approach with his students at North Penn High School by cracking self-deprecating jokes and pretending to be the dude who thinks he is hip but so is not.
In the classroom, Hall brings social studies alive, bypassing textbooks in favor of original sources and creating his own lesson materials. Inside and outside the classroom, he spends time getting to know students, hoping to connect with them and inspire them.
Now in his 13th year of teaching, Hall, 37, recently received a "Teacher as Hero" award from the National Liberty Museum in Philadelphia, the latest in a long string of teaching laurels. The Liberty Museum cited Hall's field trips to courtrooms and prisons in Philadelphia and his work as an adviser for the school Gay-Straight Alliance. During summer vacations, Hall does corporate training on workplace diversity issues.
Lauren Ewaniuk, 28, who graduated from North Penn in 2001, called Hall her "all-time favorite teacher by far."
"The best thing about his class was we didn't use the textbook very often," said Ewaniuk, now a teacher in Cheltenham. "He taught us in different ways. The classroom was set up as a circle - it was all class discussion. We read court cases, we did interactive things, watched videos - it was very engaging."
Some teachers swear that the best way to engage with students is to crack jokes and relate to them as peers.
David Hill takes a very different approach with his students at South Penn High School. He spends most of his time standing in front of the class and rarely goes off topic
Hill brings social studies alive by ensuring that students can make sense of it. His approach bucks what has become a common trend among award-winning teachers: creating lessons from scratch out of original source materials. Noting that students often find such materials confusing or overwhelming because they lack the necessary background knowledge, Hill makes teaching this knowledge his number one priority.
"My job is to get them ready for the kinds of serious, primary source research that occurs in college and graduate level courses," Hill explains.
Now in his 13th year of teaching, Hill, 37, recently received a "Teacher as Teacher" award from the National Liberty Museum in Philadelphia, the latest in a long string of teaching laurels. The Liberty Museum cited the well-informed essays that Hill's students wrote about the history of prison reform in Philadelphia and Hill's own original research on Gay-Straight relations in Philadelphia high schools. During summer vacations, Hill seeks out the most informative, interesting history texts and conducts workshops for teachers in what he calls "Textbook Resuscitation."
Evelyn Lemaniuk, 28, who graduated from South Penn in 2001, called Hill her "all-time favorite teacher by far."
"The best thing about his class was how he renewed my interest in reading history," said Lemaniuk, now a teacher in Cheltenberg. "Most of the approved textbooks are incredibly low-level and boring, and so the better teachers tend not to use them. The problem is that, without a textbook, we're really at a loss when it comes to understanding primary source materials and how they fit into the bigger picture."
Friday, May 20, 2011
I. From 5th grade Investigations "Skill Check 5", administered in mid November:
Wednesday, May 18, 2011
One of the challenges among scientists is to describe the work they do in language the rest of us can understand. That's the idea behind a new program at the University of Tennessee that uses music to bridge that communication gap.
Jay Clark is one of five Songwriters in Residence... Each has one month to write two songs that put the scientific experience into words and music.
The Songwriter in Residence program is the brainchild of NIMBioS director Louis Gross. Gross noticed that the scientists and mathematicians with whom he works aren't always that good at communicating their ideas in a concise, accessible way. Moreover, he says, most people don't really have the time or patience to wade through complicated explanations of scientific theory. As a result, we don't always have a good sense of what scientists are doing.
"The better that we are at getting the ideas across without going into all the detail that often people are not that interested in, the better off we are as a nation and as a community of scientists," Gross says.Science is not in the business of making anything more complicated or obscure than it needs to be. Everything else being equal, the simpler theory wins out. But the natural world is very complex, and any simplification for the sake of simplification is oversimplification.
...To test out his first stab at a song about the evolutionary process known as sexual selection, Clark dragged one of the NIMBioS scientists, Erol Akcay, down to a conference room. Ackay's response was about what you'd expect from a scientist:
"Well, it definitely sounded good," Ackay told Clark. "But, you know, from my research, that's kind of an oversimplification of what animals actually do."
That's the point of the whole program. The scientists watch the songwriters and learn how to make their ideas more accessible. The songwriters watch the scientists unravel the mysteries of the natural world — and then write songs the rest of us can understand. At least, that's how it's supposed to work.
Monday, May 16, 2011
Where right-brain skills trump left-brain ones... at least if your audience is sufficiently right-brained:
As Mr. Gardner shows in his survey of expert prediction-making, the more you sound like you know what you are talking about, the more people will believe you. This point is driven home by another expert, the "renowned" Dr. Myron L. Fox, a specialist in "mathematical game theory as applied to physician education"—or, if you prefer, pure drivel. Dr. Fox was, in fact, an actor who, in the early 1970s, was chosen by three psychologists from the University of Southern California to be at the center of an experiment. They set out to test the responses of the audiences who attended Dr. Fox's lectures. The fabulous Dr. Fox was drilled "to present his topic and conduct his question-and-answer period with an excessive use of double talk, neologisms, non sequiturs, and contradictory statements . . . interspersed with parenthetical humor and meaningful references to unrelated topics."
All this he executed with aplomb. "He spoke with clarity, confidence, and authority," writes Mr. Gardner, and "that was all that mattered." Dr. Fox's meaningless lecture was a hit with three separate audiences composed of academics and graduate students; an overwhelming majority felt that he had stimulated their own thinking. One person even described him as "extremely articulate."
*From a recent WSJ book review of Dan Gardner's Future Babble
Perhaps this also captures why right-brainers are ruling the roost in education and why the humanities have gone off the deep end.
Sunday, May 15, 2011
Just learned that J's next year's school uniform shirt color is BLACK.
For a parent of a child whose pale blue/white shirts are hopelessly stained with tomato sauce within the first few weeks of non-parentally supervised, school cafeteria pizza consumption, this is truly wonderful news.
Saturday, May 14, 2011
I'm still waiting for Blogger to restore the comments that went missing after Blogger went down on Thursday. Meanwhile, here is a link to a post on the Common Core standards that I wrote for the Core Knowledge blog; the comments there are intact, as well as interesting (and, as usual, I call out the New York Times for its credulous, overly-enthusiastic education reporting).
Friday, May 13, 2011
I. The "Percent Problems" set in the 6th grade Everyday Math Student Math Journal Volume 1, p. 157:
I. The "Percent Problems" set in the 6th grade Everyday Math Student Math Journal Volume 1, p. 157:
Tuesday, May 10, 2011
One interesting thing about this model is that it suggests a tradeoff between deficits and strengths: Emphathizers tend not to be Systematizers, and vice versa. Some evidence for such a tradeoff between social and analytical skills comes from a study that recently showed up in my gmail account, entitled "Mathematically Gifted Adolescents Have Deficiencies in Social Valuation and Mentalization:"Popularized by Simon Baron-Cohen (The Essential Difference), this model holds that autism is caused by excess exposure to testosterone in the womb, and/or by "assortative mating" in which highly unsocial, analytical people are more likely to find one other in today's interconnected world, to intermarry, and to produce even more extremely unsocial, analytical offspring (concentrated in areas like Silicon Valley).
This model best explains those children whose primary deficits are social, and who excel in things like engineering and computer programming: the Temple Grandins of the world.
Many mathematically gifted adolescents are characterized as being indolent, underachieving and unsuccessful despite their high cognitive ability. This is often due to difficulties with social and emotional development. However, research on social and emotional interactions in gifted adolescents has been limited. The purpose of this study was to observe differences in complex social strategic behaviors between gifted and average adolescents of the same age using the repeated Ultimatum Game. Twenty-two gifted adolescents and 24 average adolescents participated in the Ultimatum Game. Two adolescents participate in the game, one as a proposer and the other as a responder. Because of its simplicity, the Ultimatum Game is an apt tool for investigating complex human emotional and cognitive decision-making in an empirical setting. We observed strategic but socially impaired offers from gifted proposers and lower acceptance rates from gifted responders, resulting in lower total earnings in the Ultimatum Game. Thus, our results indicate that mathematically gifted adolescents have deficiencies in social valuation and mentalization.While this may not come as any great surprise to those familiar with the math world, the notion of a tradeoff between math skills and social skills raises the possibility of a more general tradeoff between autistic traits and intellectual skills. Even this, however, may already be part of our collective unconscious, underlying, for instance, the common notion that being a genius entails being highly eccentric.
Sunday, May 8, 2011
Just in time for Mother's Day (though a tad pricey), a book I co-edited with Etsuyo Yuasa and Tista Bagchi is now out: Pragmatics and Autolexical Grammar: In honor of Jerry Sadock.
Friday, May 6, 2011
|I. From Sessions 2 and 3 of the first "Investigation" in data analysis the 2nd grade TERC/Investigations curriculum, p. 153:|
|III. Extra Credit:|
Which involves higher-level thinking: actively creating your own representations of data, or passively reading off someone else's?
Wednesday, May 4, 2011
Once again it's the season of the Pennsylvania Middle School Computer Science Fair. Here are some of this year's top awards:
1st Place - Logo DesignNot a single category, it would seem, for actual computer programming. No sense that computer programming involves anything more that the consumption and marketing of computer technology. No sense of the tremendous analytical skills that go into the coding that makes all the rest of this possible.
2012 middle School Computer Science Fair logo symbolizes the integration of technology in our lives and features a Quick Reader ta to the fair's website for smart phone users.
1st Pace - Desktop Publishing
Inspired by Laura Crawford's books on New York City, Washington DC, and Chicago, this children's book features cheery postcards written by a young girl during a trip to Philadelphia. Each page features a popular designation in our city for families. Look closely and you'lll notics that the names of Amy's friends help the reader to spell Philadelphia--Penelope, Holly, Iris, Belia, Alexis, Danny, Ella, Lisa, Pam, Holly, Isaac, and Alex. Quick Reader tags are included to give the reader with a smart phone internet access to each destination's website.
1st Place - Digital Video
This jazzy music vieo is in appreciation of Philadelphia as a popular designation for families with teenagers. The vieo features an original score, choreography and lyrics sure to please teens as well as their parents.
1st Place - Multimedia
This mutimedia project is about the history and impact of volunteerism. The project features the efforts of the University of the Sciences, families and other organizations to transform a trash-filled vacant lot in West Philaelphia into the Lower Mill Creek Garden. With 3,000 vacant lots in Philadelphia alone, the impact of a community-building beautification project could have a significant impact on our city.
1st Place Web Page
Pollution Solution is a website designed to motivate young adolescents to take better care of our environment making small changes every day.
2nd Place - Graphic Design
Based on the organization Tree Tenders in Philadelphia, this project features a complete marketing package of logo, leterhead poster and business cards for a fictional organization, "Earth Strength." The theme of the design is to inpire community members of support tree-planting projects, which will improve the beauty of our city, and enhance the environment.
And yet another area that has been hijacked away from the most left-brained of our students.
Perhaps there's some virtue in this contest, but could we possibly call it something other than a "Computer Science" fair?
And could we possibly have a city-wide Computer Science Fair that's actually worthy of the name--i.e., one that showcases the work of those who do actual programming? I'm thinking, in particular, of autistic spectrum students like J, who spent about an hour writing up a program in Python that lists all the different ways to create a given amount of money using pennies, nickles, dimes, and quarters:
No one showed him how to do nesting while-loops, or even suggested this strategy to him: a novice programmer, he wrote this code all by himself.
The reason I keep harping on this is that it's in output like this where I see J's potential for earning a living, for feeling happy and productive, and for giving something back to the world.
Wouldn't it be nice if today's schools gave young programmers like J even a fraction of the recognition they give our young graphic designers and desktop publishers?
Monday, May 2, 2011
In my two previous posts on this topic (see below), I've argued that:
Kids are novices who depend on direct, structured instruction in basic skills and fact-rich core knowledge before they're ready to start taking charge. Absent such direct instruction, there will, indeed, be "very little learning by the students." 59% of students not achieving a basic level on a standardized science test isn't proof that they don't understand the phases of the moon; it does, however, suggest that, on average, students are receiving a very low level of direct instruction of basic scientific knowledge.And that:
Perhaps it's simply too difficult for people to believe that the reason why kids today can't locate Iraq or the former Iron Curtain or the relative positions of the sun, earth, and moon when the latter is full is that no one has ever even attempted to teach them these things.I've had some great comments in response, and a few have raised some objections. One is the fact that some children learn things on their own. As HappyElfMom writes:
Franklin was a school dropout, so I can't see him freaking out about some state test scores. He might, however, freak out that there is a state test to score.
I'm not sure that it really matters if a child thinks that Iraq is in Central America. I guess having a severely disabled child changes it for me, but I read that and thought it was nice that the children understand the concept of country and continent. If that's a given, one can simply point to the map and say, "It's not over here; it's HERE" and maybe show a few pictures of the Babylonians, ancient civilizations, early writing, etc.
Any kid with a calendar and a window can start to learn about moon phases WITHOUT much adult input!
Do you know what I think is a travesty? Kids being required to just attend school and SIT rather than construct their own education plans within certain parameters.As Anonymous points out, however:
In a classroom setting, learning is done as a group (with choices about what to research for special projects as the final part of a unit). This is unavoidable, because young children need instruction and guidance as they learn, even in the most creative classroom. And some types of knowledge build on other types; the order does matter.
I've personally given direct instruction, together with guided practice (I show, you watch, you do I watch), and yet, the next semester, you'd never be able to tell that they'd ever seen it before at all. I also know that it's quite possible to explain something quite clearly to the whole class while my daughter is there, and she won't remember any of it (the ADHD meds help).
How much is that they lack basic reading/writing/math skills and so are unable to demonstrate their knowledge on a test?
The people who are ultimately responsible for the upbringing of a child are the parents. In far too many cases, they are failing to do so.
A big fault with today's curriculum designers/teachers, in my opinion, is that they seem to assume that merely exposing children to a topic through access to written or digital materials will make them retain the material. Not so; most of the time, children (and adults) need to process the material by practicing with it. That is, in essence, what note-taking is; it's what problem sets are; it's what writing book reports is; it's what writing up a lab is.And as Anonymous (the same Anonymous?) points out:
Also: children vary in the degree to which their minds are "sticky." For some kids, for some topics, they retain a lot just by being exposed to a glancing explanation, whether oral, visual, or electronic (by this comment, I'm agreeing both with Katherine and with Lsquared). The same kid, on a different day, or the kid next to the first kid, will need a much more extended engagement with the material in order for it to "stick."