Week 3 Post 2 (Boostrapping their Way to Mediocrity / Kitchen Table Math)

I did not so much respond to the blog entry as I did to some of the posts in the response thread. A constructivist mathematics program (IMP) had written some testimonials to its product. The teacher expressed approval at how students who were not inclined towards math could do algebra, trigonometry, etc. with the methods espoused by the program.

A poster remarked that in a college calculus class he was in, there was a huge difference in the quality of answers between students who had learned traditional mathematics and students who had learned reform mathematics. He said that even though reform math students could eventually arrive at an answer, they did so in 2 pages, with equations going in incoherent directions, and then going back, with diagrams, tables, arrows, etc. It took them 30 minutes to do what other students could do in 5 minutes on six lines. He said we are training students who can find answers, but who really can't do math.

He later likened it to a wonderful story written without any rules of grammar or spelling. It's great that a student could write a compelling story, but that student cannot be taken seriously in a vocation if he produced something riddled with spelling and grammar errors. He ultimately does not have any command of the written English language.

I echoed this poster's sentiment by suggesting that we no longer teach the "R's" in school these days - reading, writing, and arithmetic. The order of the day is inventive spelling, no grammar at all, and manipulative and calculator-based math, which have replaced essential arithmetic.

I recounted my own experience with Impact Mathematics, a program I described as constructivism on steroids. At no point does it give a step-by-step explanation for any mathematical procedure. It confuses and frustrates students, and ultimately I trashed it for a more traditional approach to math. It is a struggle, because I am constantly borrowing from other sources, and the students really do not have a reference for doing their homework aside from their notes. Then again, even if we used the textbook, they would have no reference for completing their homework.

Other posters later commented on how constructivism demeans students by not believing that they can learn the simple facts necessary for going on to higher planes in mathematics.

Week 3 Post 1 (Why Don't Students Like School? at The Core Knowledge Blog)

This week, the Core Knowledge Blog is being moderated by Dan Willingham, a cognitive scientist who wrote the book, "Why Don't Students Like School"? Appropriately, he responds to this question from a cognitive science perspective. I personally believe that the answers don't just lie in the field of cognitive science, and that cultural explanations would go a long way in shedding light on this issue. Nevertheless, his analysis is pretty compelling.

Willingham explains that the brain is wired to actually avoid thinking when it can. "Compared to your ability to see and move, thinking is slow, effortful, and uncertain," he notes. He admits that this is a pretty depressing conclusion, especially when considered by an educator. So how do we make the thousands of decisions that we confront on a daily basis? The answer is that we don't think; we rely on memory, which is actually much more reliable than thinking.

The vast majority of students are not "thinking" when they compute 7 + 7. They are accessing their memory. Because they have seen this fact countless times, they have reached the point of automaticity. Automaticity is very important in education, because it allows more higher level problems to be less taxing than they would otherwise be. In other words, our memory allows us to exert less effort. A student who must count by eights each time they see 8 X 7 is doing something much more burdensome than the student who is simply recalling the answer from memory. A student who cannot compute this automatically will have a lot of difficulty when they reach polynomials and they have to multiply (8x^2)(4x + 7x^5 + 9x^7). The student who is not automatic will be confounded by all the calculations that this problem entails. The automatic student will be able to solve this in less than 20 seconds.

Willingham contends that this discovery (an old one) in congitive science is the case for practice, which has more sinister synonyms in "drill and kill" and "learning by rote." He's not saying that all learning should conform to this arrangement, but that certain basic things must be memorized. I could not have agreed more. I echoed his sentiments by saying that the difference between a successful 7th grade math student and an unsuccessful one is the difference between knowing how to do the four operations automatically and not knowing this. I have students who still multiply by counting in their heads, or doing long-hand addition on their paper (strategies promoted by Everyday Mathematics and other constructivist programs of this ilk). They can compute the volume of a cylinder correctly, but guess which student gets it right more often? The students who know their multiplication tables and who understand the algorithm for doing multiplication with 2 or more digits are far more successful.

There were 34 posts in this thread, and just about every educator agreed with my assessment of the matter (and of course, Willingham's), which made me pause and think. How is it that constructivist education took off this decade when most educators (at least my colleagues, friends, grad school peers, most who I meet online) despise the ideology? Because students are not expected to master certain basic facts, they become frustrated when they must tackle more difficult subject matter. Maybe this is why students don't like school.

Week 2, Post 2 (First, Blow up the Ed Schools / Kitchen Table Math)

I later posted to a patently inflammatory thread about the state of education schools in the country. While I do not agree with the sentiment that education schools should be blown up (I do feel that St. John's offers a solid education), I can certainly identify with the thrust of her criticism leveled at education schools/colleges/universities. First, Blow up the Ed Schools started with the observation that teacher preparation has traditionally focused on process-oriented ed courses rather than content courses.

I chimed in by agreeing wholeheartedly. I expressed dismay that not once have I received direct instruction regarding the material that I am responsible for conveying to my students. I am a seventh and eighth grade math teacher, and while I have personally far surpassed pre-algebra, knowing does not necessarily equate to effective teaching. I feel that education schools should make teachers experts in their respective fields. I have been exposed to a whole lot of theory, which theoretically enhance classroom instruction, but have I ever received guidance from a professional regarding how to effectively teach algebra? No, not at the university level and not through professional development.

I do not understand. I concluded with this thought.

"Wouldn't we all feel a lot better if our elementary school teachers were actually taught "how" to teach fractions effectively, or are we all content to leave our educators to their own devices so that they can reinvent the wheel?"

There was actually a very instructive response citing an educator who graduated in 1956. Apparently, the NYC school she worked in brought in an expert to thoroughly teach a method for teaching spelling. The commenter snidely remarked that back in the day, professional development seemed to actually be professional development. An expert would come in to impart their knowledge, and then teachers would apply it. I believe that it is high time that education schools supplement theory with material that zeroes in on the nitty-gritty of teaching a particular course.

Week 2, Post 1 (P21 Still Doesn't Get it / The Core Knowledge Blog)

One of the controversies in education that has been stirring (quite frenetically these days) is the choice between content and skills in the classroom setting. Partnership for 21st Century Skills is an organization that is a vocal advocate of process-oriented education, which is manifested in widely-used programs like Everyday Mathematics, and in today's model of differentiated instruction (emphasizing group work and alternative activities for students with different learning styles, activities which hardly constitute mastery of a topic).

As a newly minted educator, it is my impression that the modern educational landscape is riddled with group investigations that relegate the teacher to the role of a facilitator. Direct instruction is foregone in favor of activities which are designed to motivate students to learn, but the second part of this equation, the "learning" part, takes the backseat. Everyday Mathematics does not conceal the fact that they do not value mastery of standard mathematical algorithms. But you know what they do value? "Critical-thinking skills." Multiplication, division, adding fractions - it's important that kids experiment with them, participate in fun activities which vaguely model the content, but mastery - the academic establishment should not be making such dictatorial demands.

I make no bones about eschewing the workshop method of teaching mathematics. I responded to a poster that said "content just becomes a delivery mechanism for the skill." I agree wholeheartedly. Everyday Mathematics (I use Impact, the even more awkward older brother of EM) lays an emphasis on constructing meaning out of multiplication and applying problem-solving strategies (arrays, partial numbers). The times tables are treated as a means to an end, and in the end, I inherit a substantial amount of students who simply cannot multiply - not because they can’t, but because they were never given the opportunity to master this skill. The de-empahsis of facts has tossed the multiplcation tables to the wayside, treating them as an afterthought that is essentially thrown in to develop other nebulous problem-solving skills.

Diana Senechal responded to my post and made a very insightful remark which captured the thought that I previously could not verbalize - that by teaching content, we are actually cultivating the critical-thinking, problem solving, and communication skills we are aiming for. She asserted that "you could address all these skills through the study of Edgar Allen Poe’s, trigonometry, Supreme Court cases, three-part harmony, French irregular verbs." Believe it or not, you can teach content, and kids won't be all the dumber for it.

Week 1...Second Post

I posted a second comment to an article about the downside of evaluating teachers using "value-added" measures. There is a growing movement to align pay with performance in the country, and evaluating teachers are how far along they've brought students (instead of against a set-in-stone benchmark, keeping in mind the educational disparities in the U.S.) seems to be the fairest method available.

"There's no I in "Value-Added" mentioned that this arrangment would create a dog-eat-dog world where teachers would not be willing to help each other given that one teacher must beat the next in order to raise his income. I do not believe that this is the case. If I were to be evaluated against other teachers, it would be city-wide, so I would feel no threat from my own immediate colleagues.

I also took the conversation in a different direction. I noted that the whole question is a moot point because I do not believe that there is a meaningful collaboration in schools these days. One prep period simply does not allow teachers to bounce ideas off each other in a way that substantially affects the quality of their performance in the classroom. In Japan, the school day is longer and stuffed with prep periods, and the system places a premium on teachers working together, whereas collaboration appears to be more incidental in NYC schools. How could "value-added merit pay) produce a disincentive to work together when there almost no opportunity to work together anyways?

Unfortunately, there were no further posts to this thread, but my post stood apart from others in that most others highlighted how unfair "value-added" approaches are. I personally think it is the lesser of all evils. There needs to be more accountability in schools these days, and this just might be the best way to go.

Week 1

So I ended up posting at the Core Knowledge Blog, a blog which delves into general issues facing today's educators, as well as issues surrounding the implementation of a national curriculum in the United States. Core Knowledge is a non-profit organization which advocates for a national curriculum for the United States. Nearly all European countries have a national curriculum, as well as Japan, whereas in the United States, states traditionally have had jurisdiction over what is taught in their schools.

I first commented on an article that was posted on March 3. In a nutshell, the article highlighted that the idea that the United States implement a national curriculum once was extremely taboo, but now, the nation's governors, a growing numbers of education leaders, and even the new Secretary of Education, Arne Duncan, are backing the idea. Having once taken an undergraduate class on education reform, I chimed in by saying that the highest performing countries (academically) have a national curriculum. I believe that there are many benefits to a national curriculum. So many states have standards that are deemed to be inadequate, and the incentive for state's to implement high standards are very low given NCLB's mandate that all school's make adequate yearly progress.

I added that there is a lot to be gained if 100,000 eighth grade math teachers (as an example) taught to the same standards. So many resources could be built geared towards improving performance nation-wide. We have thousands of competing curriculums in the United States, and this deters companies and organizations from profitably producing quality resources. One streamlined curriculum could ensure that all teachers be trained adequately in their area. It allows teachers from all over the country to share best practices, and given the mobility of our population, it ensures that students can pick up from where they last left off when they move. Also, parents can be brought on board in a more meaningful manner, since they will know exactly what their children are responsible for in each grade.

I cautioned that a national curriculum should mandate "what to learn" and not "how to learn." It would be a crushing imposition on the nation's schools if particular educational philosophies and programs be adopted. I, for one, would be very upset if the "workshop model" be universally adopted. As a math teacher, I believe very strongly that students must master the standard algorithms for each topic in mathematics. While discovery and experiential learning can make learning more meaningful, at the end of the day, students must be exposed to the right way (or ways) of doing things. I do not want a national curriculum to stifle the way I approach teaching mathematics.

A gentleman responded to my post, echoing my sentiment that "what" should be learned is the appropriate jurisdiction for the national government. He also said that the movement towards a national curriculum is heating up, as Sen. Chris Dodd has already drafted legislation towards that end. He said that the constitutionality of the matter is not in question, since the legislation does not specifically mandate that states adopt the curriculum (this might violate states' rights), but that it will withhold funding if states do not (a little loophole in federalism).