Why I Left Public Education

In early June I took retirement from the district and High School where I taught for over 12 years. However, I did not retire from teaching. I started right away as the chair of the math department for a brand new, international, boarding, private school in Los Angeles. The school will get its first intake of students this September and I have spent my summer preparing the curriculum and learning all kinds of software.

This is a big transition, especially for a “person of a certain age” like myself. William Bridges wrote in his book, “Every transition begins with an ending.” Why did I end my career in public education? Why did I actively seek to get out from where I was? In one sentence: I’ve had enough.

I came to the conclusion that academic success in high school depends largely on only one factor: home environment. Home environment – call it socio-economic status, or demographics – trumps everything else, including teachers. In a New York Times article titled “No Rich Child Left Behind”, Sean Reardon points out that “There is a lot of discussion these days about investing in teachers and ‘improving teacher quality,’ but improving the quality of our parenting and of our children’s earliest environments may be even more important.”

It did not matter how much effort or innovation I put into teaching my lower level kids (Algebra 1) – they did not do their homework, did not pay attention in class and did not care they were failing. This was a general pattern – all teachers who taught Algebra 1 observed the same performance and behavior. Not that our school did not have good students – we sent about 12% of our graduates to the University of California system. The good students did not take Algebra 1 – they had done that in middle school. They had a different attitude toward school – they cared to succeed.

However, if one measures success by the number of kids understanding (or even trying to understand) the material and going to the next course, then we failed. If this school was a hospital and we had the same rate of curing our patients as we had of kids succeeding in math, the state Board of Health would close us down.

The Principal and the Assistant Principal made things even worse. Why is it that high school administrators do not have high school teaching experience? Even more, why is it that they do not have teaching experience in one of the core subjects: math, science, English or social sciences? Instead of solid thinking and teamwork with the teachers we got top-down instruction, clichés and bombastic slogans. The motto of the school used to be “home of scholars and athletes”. The new principal changed this to “home of scholars and athletes, where ALL students succeed”. Really? ALL? Isn’t this a statistical impossibility? Or are we now defining success as just staying out of jail? But this is typical of this principal’s style and vocabulary. He let go a teacher because she was not a “rock star” (said that to her face). If he likes a department, that department is “awesome”. I wondered often what is worse – that he really believes in “awesomeness”, “rock stars”, “focused instruction”, “positive reinforcement” or that he just mouths these words?

And the teachers? They may be dissatisfied, but they do not do anything about the situation. Teaching is by the book – no innovation or questioning takes place. Partly this has to do with the fact they are not specialists in their field: in a math department of 12 only 2 were math majors, the rest math education majors. In Japan all math teachers are math majors and so are those in most countries at the top of the international rankings in math. Our teachers are also – in general – not the tops of their class. The best and the brightest science and math majors do not generally end up in education.

Well, I was fed up and I did something about it. It’s a risky move – career wise – but it opens the possibility of doing education right and, in the process, providing a lot more personal satisfaction. More about this in the next posting.

 

 

 

 

Five Observations Regarding Teaching Similarity According to Common Core

For the last two months I taught geometry according to Common Core, at least as it is interpreted by EngageNY in its Module 3 (Similarity and the Pythagorean Theorem). I am “off the reservation” in the sense that I am the only geometry teacher who is not following the book and is “going common core”.

Based on my experience, limited as it is, there are a number of observations that I would like to share. These observations pertain only to my experience in my school and with the students that I have. These students are largely freshmen and sophomores who have gone through Algebra I and, if they are sophomores, through Algebra II.

First, there is dearth of common core curricular material. As far as I can tell, EngageNY is the only entity that publishes a teacher edition on how to teach Similarity and the Pythagorean Theorem in the SPIRIT of common core standards.  There are other places on the Internet where one can find problems and projects geared to common core, but to come as close to a text as we are used to, EngageNY seems to be it.  I should add that the EngageNY module I taught from is for 8th graders – there is nothing for High School Geometry. (Professor Wu’s notes regarding High School Geometry are geared to future math teachers and they are extremely useful as to the common core approach, but they do not constitute a text).  However, given that we are in a transition period to a full blown common core curriculum, and given the mathematical preparedness of most of my students, I saw no problems using this Module.

The second thing that stands out is the unity and the internal logic of the common core approach. Similarity, the Pythagorean Theorem and even trigonometric functions are all based on geometric transformations, specifically dilations. While as a teacher I appreciate the consistency of the approach, I wonder if it truly enhances significantly student understanding. The approach that we choose in teaching math goes directly to the fundamental question of what do we want our students to get out of high school math. Do we just want them to be able to solve problems? In that case a drill and kill could work (more or less). If we want them to think mathematically, then yes – a math course with logical consistency will probably be superior to the current texts. However, students, especially at this age, rarely take the long view and can stand back and appreciate the beauty of a consistent approach to math teaching. In the absence of a randomized, control study, I don’t think that we have yet a clear cut answer. Personally, I am pleased that when I teach, I feel that there is a logical continuation and unity to my teaching.

Third, I have observed that, at least the EngageNY modules are not problem rich.  At the end of it all, math students should be able to solve math problems and being successful at that comes from practice (as well as teacher guidance). My hope is that future texts will have a significant number of problems in them and that those problems include some challenging ones.  I have had difficulty finding challenging problems in similarity. (An example of what I would consider challenging High School problems in similarity can be found here. These are a very far, far cry from the problems we find in our textbooks).

Fourth, common core puts emphasis on students being able to explain their reasoning. I have asked questions that require explaining a result and the outcomes are sad, if often funny. Students (at least mine) have difficulty in answering in complete sentences. Responses are terse as if the students are afraid that a longer paragraph will show that they are not sure of their answers. Because of this, I found that asking “why” and “explain” questions are a good diagnostic tool for assessing students understanding, perhaps more so than checking the results of their problem sets. However, I keep in mind the fact that students have never before been asked to explain their answers, and that gradually, by modeling complete answers in complete sentences, students will improve. I hope.

My last observation has to do with modeling. In common core there is also emphasis on students being able to apply their math knowledge to more complex, real life situations – to do mathematical modeling. Once more, this is not something my students have been asked to do in the past. All previous student experience in math has been structured and structured rather rigidly. The “real life” problems in textbooks are so contrived, they are laughable. They are also duplicates of “regular” math problems. An unstructured project is a challenge for my students. I gave my students their first project – the rolling cups project from the Shell Center. The project is part of their exam in similarity and is the take home part of the exam. We will see what happens.

All in all, teaching similarity according to common core has been interesting and challenging. Part of the challenge is that I am the only one doing this and that the school-wide assessments are written by the other teacher who are teaching the traditional way. They have more time to practice “standard” problems than I  do, because of the time we spent in class going over dilations and how they form the basis of similarity. Also, their assessments do not require explanations of the results – they are simply “find x” problems. The other big part of the challenge is that both I and my students are new to this common core business. we still finding our way, but I think it is a worthwhile endeavor.

Diane Ravitch and Market Forces

One of the more discussed recent books on education is Diane Ravitch’s “Reign of Error”.  Ravitch argues that poverty and socioeconomic inequality produces kids who enter our educational system handicapped in their ability to learn.This poor start translates in poor performance as the individual moves through primary and secondary education.

I do not agree with Ravitch – the immigrants to the US, say in the 1880s, were poor and they were discriminated against on religious and/or cultural grounds. Yet those immigrants made sure their children, although raised in poverty, got the best education they could afford. These children became engineers, doctors, or lawyers. I am proud to count myself as a graduate of an excellent school – The City College of New York – that was developed for the very purpose of offering a free (and excellent)  education to the children of poor immigrants. Therefore, I do not see poverty by itself as being the source of a sub-par educational system.

I think that cultures and nations that develop good educational systems do so because education is one of the few, or the only path to an individual’s financial well being.

When there are other avenues for achieving financial success, education takes a back seat. In the US, you can be a mattress salesman, with very little education and still be financially successful. We do have a society in which we can become wealthy in many ways – entrepreneurship, salesmanship – and, in addition, we are a wealthy country (from the point of view of natural resources that one can exploit).

In other countries, there may be many barriers to individual financial success – lack of capital, a hierarchical social order, or generalized poverty. In these societies, education becomes important to the individual primarily as an avenue for achieving financial security . I am thinking especially of the Asian countries where education has been the “classic” path to success – those who became mandarins started with the civil service examinations.

An alternative path to developing a good educational system may happen when a top-down,  autocratic society (e.g. Russia) starts compensating educated people because these people can strengthen the country’s military and industrial infrastructure which is weaker than that of its neighbors’.

In summary, my thesis is that a good educational system develops due to market forces – education is a sure path to an individual’s financial well-being and there are few other paths available to achieve this well-being.  In this thesis, poverty by itself, does not lead to a poor educational system.  A sub-par educational system comes about when education is not the most important  path to financial security.

Perhaps there can be another driver to a good educational system. After all, there were quite a few rich merchants in medieval times in Asian countries and these merchants did not get wealthy because of their classical education.  It could be that a good educational system, or more precisely a selective one, also develops when education is seen as a “noble” profession, in the sense that it leads to relative wealth without physical effort. However, this is not an American concept – we actually value physical effort and one can see a proof of it every Sunday until the Super Bowl.

If I am right, what does this mean for how education will develop in the US? I don’t see much improvement soon – say on a 10-year horizon. As long as we  have a high degree of elasticity in our economy – meaning that we have many paths for achieving individual financial success – education will be not be a priority for us as a society.

It may be that increasing international competition will drive us to educational reforms. After all, the genesis of Common Core was when industry and the Chamber of Commerce started going to the state governors and saying we are losing jobs and contracts because we do not have a sufficiently well educated workers. Common Core developed from an industry initiative. That’s market forces at work!

Justin, Tom and c2396

  • Justin                DC

I am a science and engineering professional who seriously considered teaching as a career change. I am the son of a teacher. I understand and value the profession, and have a passion for imparting knowledge to others. I have taught as a graduate assistant in a university setting, and enjoyed it.

But I didn’t choose to become a teacher, despite this. Why? Largely because of the abuse of the profession of education that I see. No, it’s not the typical line about new standards and grading teachers and throwing out the bad ones that I object to. I would far rather that we demand the highest caliber of individuals as teachers and weed out anyone who can’t cut it.

The abuse I speak of is what is asked of teachers relative to what is given. People have this idea that teachers spend only a few hours a day teaching, and have the summers off. Nothing could be further from the truth. Today’s teachers work 10-12 hours days regularly, including the summer, and for what? Less than half of what I am currently making as an engineer.

On top of brutal hours for little pay, teachers are under-appreciated by parents and administrators alike. They are harassed for every demerit, subject to immense pressure for grade inflation. They are tied down by administrative rules that interfere with the core mission. They are expected to be substitute parents, substitute cops, and substitute priests.

In short, being a teacher in America today is asking for abuse. Thank those who do it.

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  • c2396                           SF Bay Area

People who are really good at mathematics and the sciences are no different from anybody else. They want good pay and good working conditions. And they often have the talent and in-demand skills to secure them.

Teaching is a stressful, demanding and important job, with lots of second-guessing – by parents, by administrators, by school boards, and by the general public. The idea of dealing with today’s hellish mixture of hysterical helicopter parents, as well as uninvolved parents who set a poor example for their kids, is probably a big turnoff to people who value the structure, self-discipline, intellectual rigor, and logic the fields of mathematics and science require.

Want more people like this to go into teaching? Raise the pay and treat teachers with more respect, for starters. I managed IT projects for years before I retired, and it was a high-stress job, but I enjoyed it. Would I become a teacher in the average classroom today, at current pay rates? No way.

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  • Tom                             Midwest

When those in math and sciences can earn as much as a teacher, they will become teachers. When state departments of education require a math or science teacher to be a math or science major, we would get better math and science teachers. However, as a now retired scientist/mathematician who took the require education classes to obtain certification and was still denied to teach in some states because I was not an education major, sorry. All too many scientists and mathematicians who might be teachers will never enter your ranks. The system, both for teaching requirements, as well as the pay, are institutionally incapable of hiring and retaining math and science majors as school teachers.

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On December 9th, The New York Times published an op-ed piece titled “Teachers Tell Us How to Fix Science and Math”.  As a former engineer with a Ph.D. in Fluid Mechanics and a minor in math, who after retirement switched careers to high school teaching, I found the previous readers responses sadly true

Can These Kids Be “Saved” by Common Core?

There are moments in the life of a teacher when a student says or does something that takes you aback and makes you think about education as a whole.

Last week, while reviewing exponents and the rules associated with them in an Algebra I class, I overheard a student ask another: “How much is 9 x 3?”  This is a student who failed Algebra I with me last year and who had something like “General Math” in middle school. She is not an exception in lacking the very basic basics – many students in my Algebra I classes use their fingers to do simple computations.

By coincidence, a couple of days ago, I received a response to a review of an Algebra 2 Glencoe textbook – supposedly “Common Core” – that I posted a year ago on Amazon.  In agreeing with my critique, Bruce G. Frykman wrote, “What I face is simply appalling. First, students come to these classes without the proper grounding. I have tutored kids in algebra II who cannot multiply or divide at even the simplest level. How did they get into these classes?”

Can these kids be “saved” by Common Core?

I happen to believe that Common Core is a step forward, in that the tests by which student performance is to be judged include a lot more critical thinking and communication than the previous state tests – at least this is how it appears to me from the released. According to these released questions, we will have to ask students to master the material with deeper understanding and the ability to communicate their knowledge.

But if Common Core will demand more critical thinking what will we do with the kids Mr. Frykman and I referred to? Granted that Common Core is supposed to start early – in elementary school – and therefore give us better prepared kids by the time they reach high school. However, the performance of the kids, as many other performance measures, will form a normal distribution. What will happen to the left side of the curve?

Kids in middle school will continue to be promoted, regardless of their performance – Common Core does not touch on promotional policy. Common Core will not transform demographics, poverty, a culture of not valuing education (except as a ticket to a better job), and any other sources of poor educational performance. Common Core is a set of teaching and assessment standards, but it is not educational policy.

Common Core is supposed to give high school students that are “college ready”. The dream is that students who have passed through Common Core K – 12, will not need to take remedial courses as do 30% – 40% of the current college freshmen. But we will always have the left side of the normal distribution and if those kids continue to be promoted despite their poor academic skills, we will face the same situation as before Common Core: a significant percentage of kids who enter high school without the basic academic skills and knowledge that they need.

In the absence of an 8th grade assessment that tests for basic academic knowledge and a vocational track that provides a success avenue for those who do not show sufficient knowledge, we will face the same situation as we have now – Common Core or not.

 

 

What is Rigor?

As mentioned in my previous post, I am looking at various publishers’ textbooks for high school integrated math – Common Core compatible. Common Core prides itself on being a rigorous set of standards and the textbooks all mention that they are rigorous. (Pearson’s books are stamped “Rigorous, Engaging and Data – driven” directly under the title). But what is rigor, more specifically what is rigor in the context of a curriculum and a math textbook?

The dictionary defines rigor(s) as “the difficult and unpleasant conditions or experiences that are associated with something; the quality or state of being very exact, careful, or strict”. Of course, we are not going to introduce a course to our students by saying it is difficult and unpleasant. In the context we are interested in, rigor has more to do with exactness, and with a logical and data-driven presentation of the concepts. In other words rigor refers to how the material is presented to the students and it has the connotations of validity and cogency. This is the interpretation of rigor that the publishers and the Common Core authors refer to.

But other definitions of rigor have synonyms such as “hardness”, “difficulty” and “stringency” .  In our context we can perhaps call this “depth” and add this dimension to those of exactness and logic with which we present the material.

None of the curriculums I have seen have much depth to them. None of them offer high-level, challenging problems to the student. Granted, not every student is going to go into a math or science career, but why not include challenging, critical thinking problems – if only to have them available for those students who want a challenge?

As an example, consider radical expressions as introduced by Pearson’s Integrated Mathematics, SIMMS Integrated Mathematics and an European collection of problems. All three texts address 9th  to 10th graders.

Pearson’s text starts with simple binomial radical problems such as

Rigor 1b

and then progresses to solving equations such as

Rigor 2b

The SIMMS text is less traditional in that it develops mathematical concepts entirely within a set of applications. For example, some simple radicals and exponent rules are introduced in a module where students learn about carbon dating, while much more sophisticated radical equations show up in the context of conics with students using a flashlight to create different conic sections.

The SIMMS text does not appear to have “drill and kill” problems similar to Pearson’s and the more sophisticated equations appear rather abruptly.

The European text starts with problems such as:

Show that

Rigor 5b

and continues by asking for solutions of equations such as:

Rigor 6b

Both the Pearson and especially the SIMMS text have multiple activities, investigations and projects, the European text has none.

In terms of rigor defined as “difficult” or by “challenging” problems, the European text is far ahead. The American texts however engage students in activities where they either apply previous knowledge or develop that knowledge in the context of working some “real-life” situations. Under the influence of Common Core, math textbooks will increasingly have activities and/or problems in which students will have to justify and explain their solutions. The hope is that  students will achieve deeper understanding, become used to group work and to presenting  their results.

It appears that in the process of doing projects and modeling, American students lose strictly mathematical rigor – i.e. depth – and do not encounter very challenging problems. (This is perhaps unkind. American texts have lost that kind of rigor since the 1960s.)  Perhaps the argument is that with all the projects and the modeling there is simply not enough space or time for truly challenging problems .

What is better for the students? Why can’t we have both?

Dreams of an Integrated Curriculum

We are in the midst of a transition year.

We have the luxury of experimenting, while we are in transition to Common Core. We are not sure if the state and the feds will agree to give a state exam – the state has voted not to –  but in the meantime, we are tweaking the curriculum with more freedom than we ever had before. Practically, this means eliminating a lot of stuff that teachers feel the kids do not need. (What it actually means is that we are eliminating things we feel our kids will not get.)

We are also looking for materials for an integrated curriculum that meets Common Core – we have decided as a department that we want integrated. The integrated books labeled Common Core are really not, so we are staying with the old sequence (Algebra 1, Geometry, Algebra 2) until decent textbooks appear. (My fellow teachers also want the ancillary materials – they want to be able to make tests automatically, not to make the problems themselves. Too much work I guess.)

These two circumstances led me to research what a decent Common Core integrated curriculum would look like. I have done some “Googling” and SIMMS, put out by Kendall- Hunt, caught my attention. In my opinion, SIMMS (Systemic Initiative for Montana Mathematics and Science) has two attributes that deserve attention.

First, SIMMS not only integrates the different branches of mathematics, but it also does so within applications and projects. Second, for me the most important attribute is that SIMMS is divided into levels geared to different kinds of students. There are levels “recommended for all students”, those “recommended for students in non-mathematics and non-sciences fields”, and those “recommended for students who plan to major in mathematics or sciences”. There is the possibility for students to change their minds, i.e. go from the more “non-mathy” levels to the more “mathy” ones and vice-versa, so the curriculum does not track students.

This is an immensely appealing idea for a teacher like myself, who works in a school where there is a broad spectrum of students. Currently, in our school, we are forcing students to take Algebra 1 and Geometry even if they have not done well in middle school. We are mandated to do this because the state wants to “expose” ALL students to as high level of mathematics as possible. Did they get a D in Algebra 1? No matter – let them take Geometry. Did they get a D or F in science in middle school? No matter – we are not going to put them in Earth Science in high school, we are going to put them in a laboratory course – Biology.

The results are as one might have expected – lots of D’s and F’s in Geometry and Biology. So the students are exposed to a science and math course they are not ready for, they fail and they incorporate in themselves a sense of failure, a sense of “I am not good at this” and worse, a  feeling of dislike for math and science.

In Geometry, which I am currently teaching, when are students going to use congruence of triangles, if they do not major in math or science? When are they going to use proofs? For these students, calculating areas and volumes are probably the most useful applications of geometry.

Even for a dyed-in-the-wool math person like me, proofs are beginning to look like a form of torture for most kids. I know the argument that proofs are a way of teaching logical thinking. But, are they the only way or the best way of teaching logical thinking? I can envision a case-based course that would teach elements of logic more successfully than two-columns proofs can.

Same thing in Algebra. If I am not going into math or science, do I really need to know the difference between slope-intercept and point-slope? Why are we doing all these line problems? The real reason is that lines offer the simplest predictive models for a variety of situation, but this gets lost in the dicing-and-slicing that we do in Algebra 1. Much better to offer a course where we take data, make a scatter plot and see what a straight-line model does for the data. We can talk about slope and y-intercept and residuals in that context.

In a way, it seems to me that transitioning to Common Core offers us an opportunity to do truly differentiated teaching – not the one about different learners types (visual, tactile, etc.) which has been shown to be cognitively false, but differentiated by aptitude and attitude.

One can only hope. In the meantime, I am going back to grading the latest Geometry exam on proofs  and marvel at the inventiveness of students who make up non-existent properties.

Nicholson Baker, Algebra II, Lurking Variables and Making Shakespeare Elective

calvinIn a recent article in Harper’s magazine, “Wrong Answer – The case against Algebra II”, author Nicholson Baker argues against having Algebra II as a required course in the high school math curriculum. He points out that when we force students to take such abstract and rarely used concepts as rational functions or Fourier analysis, we do nothing but produce thousands of students who not only hate algebra, but math in general.

Baker marshals an impressive array of witnesses, many of them mathematicians, who support the view that Algebra II should be an elective. Towards the end of his article, Baker writes: “Math-intensive education hasn’t done much for Russia, as it turns out.”  In other words, Russia is an example of an inverse correlation between math-intensive education and…what? Material benefits? Political freedom? Democracy? Let’s say the general well-being of the population.

I would argue that Baker’s statement is an example of a lurking variable.

Russia’s math prowess was originated from above, when Peter the Great modernized Russia by force. Since modernization implied a strong army, engineers were sought for armaments, fortifications and building a navy. Mathematics therefore became a prized skill/profession, one encouraged and compensated by the government. Mathematics thus became an avenue for an individual’s material progress, increased freedom and respect.

Peter’s tradition continued in Communist Russia, where engineers were needed for another round of forced industrialization, building an armaments industry, including a nuclear arsenal and a rocket force. (The hard sciences did not escape Stalinist purges, but in general mathematicians fared better under Stalin’s murderous repression than other professions).

Therefore, the “math-intensive education” variable in Russia was associated with government support, support that over the years morphed into respect for math in the general population.  If the explanatory variable is “math-intensive education” and the response variable is “the general well being of the population”, government directed activities are a lurking variable that affects both the explanatory and the response variables and hence the correlation. A certain type of actions, forced by the government through coercion or financial rewards, is the one variable that in Russia affected both the direction of the education and the well-being of the population.

The “command” style of Russian political life affected both an emphasis on math education and (negatively) the well being of the population.

Baker continues:  “But historical counterexamples don’t seem to interest the latest generation of crisis-mongers. We’ve once again gotten ourselves caught up in a strangely self-destructive statistical cold war with other high-achieving countries.”  Perhaps, but a recent report suggests that American workers are becoming less productive because they are falling behind in math skills when compared with workers from other countries. I quite agree that, as Baker mentions, carpenters and plumbers probably do not need Algebra II. However, I would venture to say that the executives who are the bosses of these carpenters and plumbers most likely have gone college and therefore through Algebra II in high school.

Baker’s solution is to “… create a new, one-year teaser course for ninth graders, which would briefly cover a few techniques of algebraic manipulation, some mind-stretching geometric proofs, some nifty things about parabolas and conic sections, and even perhaps a soft-core hint of the infinitesimal, change-explaining powers of calculus. Throw in some scatter plots and data analysis, a touch of mathematical logic, and several representative topics in math history and math appreciation… Make it a required course…Then turn the rest of algebra, geometry, and trigonometry into elective courses, just as music and art and biology are. Pay math teachers better and — this is important — stop requiring Algebra II for admission to college.”

I have no quarrel with paying math teachers better. However, where is that line between required and elective? Shakespeare’s English is difficult to read (and sometimes understand) by today’s readers. Would Mr. Baker make Shakespeare elective?

Common Core (Geometry) – The Good, The Bad and The Ugly

GoodBadUgly3Common Core Geometry was sprung on us this year, without any kind of preparation. In addition, the State of California, in its politically-driven-wisdom (a great example of an oxymoron), is asking us to offer Geometry to all of our students who have finished Algebra 1 – even if they had “passed” it with a D. This is to create “opportunities for all”.

So how is Geometry faring in Common Core?

THE GOOD.  There is no doubt that Common Core envisions a superior Geometry course compared to what we teach now. The projects, the modeling and the writing components will require more critical thinking from the students.

In addition, the sample problems that I have seen from the two national testing consortia are better (i.e. they require more thinking) than what our current textbooks offer.  I have always believed that a math textbook can be judged by its sets of problems – by this criterion, Common Core Geometry does indeed promise to be a better course than the current one.

Common Core Geometry also wants to be more mathematically rigorous – for example it defines congruence as the result of a sequence of rigid motions that map one object identically into another. This approach also has the advantages that it helps students “see” motions in space and deals with constructions at the very beginning – certainly a good way to draw kids in.

THE BAD. I am not aware of any Geometry textbook that is truly “Common Core”. Most textbooks labeled as Common Core are old textbooks with perhaps very few modifications. Pearson’s and Glencoe’s Geometry textbooks are good examples of this “quick-to-the-market” (but not good) products.

It took about a month into the course before I hit upon engageNY’s Module 1 for geometry. To this date, as far as I am aware, it still is the only published coherent and complete material aligned to Common Core (Geometry).

And here is where the problems begin.

It is difficult and (at least temporarily) unproductive to ask students to explain the reasoning when nobody has asked them to explain their reasoning before.  It is difficult and (at least temporarily) unproductive to ask students to do investigations, when they have not been trained in investigations. So the first two major problems with Common Gore Geometry are lack of materials that form a complete, coherent course and the fact that teachers and students have been thrown in the “critical thinking” pool without any swimming lessons.

However, with time, these difficulties will likely be resolved. More disturbing to me is the fact that I have doubts about the rigor claimed by Common Core – Geometry. Certainly, requiring explanations of one’s reasoning process does strengthen students’ critical thinking skills. Certainly the problems that I have seen in engageNY’s module are a step (or may be two) above those in our current textbook. However, these problems are not on the level of Weeks and Adkins or Moise and Downs. Why can’t we go back to the level of rigor of 1960s American textbooks? Is it because now Geometry is taught to many more students than to the “elite” few of those times and therefore many of today’s students are not as well prepared?

Another problem I see is that, besides defining  congruence as the result of mapping through rigid motions, there are no other “math-pedagogy” new ideas in Common Core Geometry. In an article titled “Teaching Geometry According to the Common Core Standards”, Professor Hung-Hsi Wu (U.C. Berkeley), one of the originators of the Common Core curriculum, states that ”…once reflections, rotations, reflections, and dilations have contributed to the proofs of the standard triangle congruence and similarity criteria (SAS, SSS, etc.), the development of plane geometry can proceed in the usual way if one so desires.”

Kind of a letdown, if you ask me.

Therefore, despite an abrupt start and a lack of materials, Common Core appears to be a step in the right direction, but it does not reach the levels of academic rigor that we asked of our students in the 1960s. We seem to have tilted the balance away from solving truly challenging math problems towards communications and investigations. One wonders if this is such a good change of emphasis.

THE UGLY. Alexander the Great is quoted as saying that “An army of sheep led by a lion is better than an army of lions led by a sheep”. Well, Alexander need not lose any sleep – at our school we have an army of sheep led by sheep.  I have never seen so much confusion, mixed and often conflicting directives.  First, we were all told to march in step, teach the same thing at the same time and give the same exams. The only concession to Common Core was to move the chapter on transformations towards the beginning of the course. (No mention however of why we were doing transformations at the beginning of the course, before congruence). Then the teachers said it was not practical to march in lockstep and the department decided that each of us will follow our own pace provided we cover the same material by the midterm so we can give a common midterm exam. Then we decided not even to give the same midterm exams.

Admin has no idea of what to do with Common Core except to tell us that Common Core is the Promised Land and to pepper their dialogue with new buzz-words such as DOK-4 (depth of knowledge – level 4). They (the administrators) however, will not provide a map of how to get to this new mathematical Zion or the resources needed to get there.

Our teachers are not better. We are supposed to have weekly meetings to exchange ideas about how to “get to Common Core”. All I hear is a bunch of old women (they are in their late 20s and early 30s actually) moaning and groaning that there is no textbook, no resources and no training. This in the age of the Internet! They are truly more comfortable with the old ways then they are trying to teach in novel ways.

And so, once more I go my own way. I dig stuff up from the Web, maintain my own pace, give my own exams and pass only the kids that deserve it. C’est la vie.

The Smartest Kids in the World

Last week I read an immensely interesting and I think important book: “The Smartest Kids in the World: And How They Got That Way” by Amanda Ripley. The book looks at a comparison of educational systems in various countries (Finland, Korea, Poland and the US) through the eyes of American teenagers studying abroad as exchange students

Two conclusions stand out from reading this book. First, teacher quality is the primary determinant of how successful an educational system is. With very few exceptions, the US among them, most countries have national educational system with uniform curricula across all the schools. Therefore, the quality of the teachers is controlled nationally in these countries.

Control is achieved in various ways, but the one common thread is selectivity. To quote: “… all of Finland’s teacher-training colleges had similarly high standards, making them about as selective as Georgetown, or [U.C.] Berkeley in the United States. Today, Finland’s education programs are even more selective, on the order of MIT.”  To put some numbers on this, in 2011 the Georgetown acceptance rate was about 18%, U.C. Berkeley about 25%, while MIT’s acceptance rate in 2011 was about 9%. I doubt very much that undergraduate admissions to colleges of education in the US approach these numbers.

Not only is the selectivity level high in these countries, but so is the training. Ripley mentions that teacher education in Finland means getting a master’s degree – the program is six years long – and that it entails doing original research. This is followed by a year of mentored teaching and the mentors’ criticisms are honest and unsparing.

The second conclusion is that the kids take school seriously, because they have to. Most nations have a matriculation exam at the end of the high school years that determines whether a student will go to the university. Here is a telling passage from the book. (Kim is the Oklahoma born and raised American exchange student in Finland).

“So, [Kim] collected her courage and blurted out the question that had been on her mind.

‘Why do you guys care so much?’

The girls looked at her, confused. Kim felt her cheeks flush, but she barreled ahead.

‘I mean, what makes you work hard in school?’

It was a hard question to answer she realized, but she had to ask. These girls went to parties; they texted in class and doodled in their notebooks. They were normal, in other words. Yet they seemed to respect the basic premise of school, and Kim wanted to know why.

Now the, both girls looked baffled, as if Kim had just asked them why they insisted on breathing so much.

‘It’s school,’ one of them said finally. ‘How else will I graduate and go to the university and get a good job?’ ”

Note the unspoken implications of this answer. University is not for every one – not all of us are going to go to college – only those who have passed a rigorous and comprehensive exam.  There are no alternative pathways – no junior colleges with transfer possibilities to 4 – year colleges. There are no remedial courses at these universities. Because of this, Finnish kids (and those in other high performing countries) have a significant stake in the results of their matriculation exam. In California, where I teach, passing or failing the state test has absolutely no consequence for the student – so why care about it? There is an additional implication to having an exam that really counts at the end of the high school years.  If the exam is rigorous and it matters so much, then the training of the kids must also be rigorous and demanding.  The author gives many examples showing that kids in these countries are about 1 – 2 years ahead (especially in math) of the same age kids in the US.

However, in the US, we are number one in excuses. I can hear some of them now: one exam to determine one’s future? What if my child is not feeling well on that day?  Or: A national exam? That undermines local control of education! Or: My child has time to mature academically in college – right now he has to have a full life, social and sports.

The author does a great job of showing how these excuses don’t hold water and how they damage the education of our kids.

Reflections of what can be done in this country, especially at a local level are for another blog and for the readers’ comments.