Tips For Teachers

Documenting Classroom Management

How to Write Effective Progress Reports

Building Relational Trust

"Making Lessons Sizzle"

Marsha Ratzel: Taking My Students on a Classroom Tour

Marsha Ratzel on Teaching Math

David Ginsburg: Coach G's Teaching Tips

The Great Fire Wall of China

As my regular readers know, I am writing from China these days, and have been doing so four years so far. Sometimes the blog becomes inaccessible to me, making it impossible to post regularly. In fact, starting in late September 2014, China began interfering with many Google-owned entities of which Blogspot is one. If the blog seems to go dark for a while, please know I will be back as soon as I can get in again. I am sometimes blocked for many weeks at a time. I hope to have a new post up soon if I can gain access. Thank you for your understanding and loyalty.


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Thursday, December 29, 2016

When Are We Ever Gonna Use This?

Raise your hand if you have ever heard this question, “When are we ever gonna use this?” When I was a young teacher, I tried hard to answer. I used to give my students (junior high and high school) examples of math problems from various occupational fields. I bought a large poster that listed many occupations along the top and many mathematics topics along the side with black dots showing exactly which occupations use which topics.

Years passed. Film projectors gave way to Youtube videos. Mimeograph machines gave way laser printers. Whole new field of occupations emerged. I metaphorically threw up my hands in exasperation. When the inevitable question arose, I answered that I had no idea how they were going to use this information. I had no idea how their interests would develop, or which occupations they would pursue, or what the jobs of the future would be. All I could do was teach them a little bit of what had taken thousands of years for people to discover about math. My students were not always satisfied.

Then Paul Lockhart came along and wrote “A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form.” https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

Now I had an answer that captured their imaginations:

“In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide -- a relief from daily life, an anodyne to the practical workaday world….People don’t do mathematics because it’s useful. They do it because it’s interesting … The point of a measurement problem is not what the measurement is; it’s how to figure out what it is.”

The question of the usefulness of any particular subject stems from the mutual internalization of both the teacher and students of a questionable, yet unexamined assumption.

“To say that math is important because it is useful is like saying that children are important because we can train them to do spiritually meaningless labor in order to increase corporate profits. Or is that in fact what we are saying?”

Thus instead of teaching real mathematics, we teaching “pseudo-mathematics,” or what I have often called non-math, and worse, we use math class to accomplish this miseducation (See https://schoolcrossing.blogspot.com/2012/11/tricks-and-shortcuts-vs-mathematics.html and others). According to Lockhart, we teach math as if we think “Paint by Number” teaches art.

“Worse, the perpetuation of this “pseudo-mathematics,” this emphasis on the accurate yet mindless manipulation of symbols, creates its own culture and its own set of values….Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles?

Math is like playing a game. As with any game, it has rules to be sure. However, it is more fun and more elegant than all other games because it is literally limitless.

Physical reality is a disaster. It’s way too complicated, and nothing is at all what it appears to be. Objects expand and contract with temperature, atoms fly on and off. In particular, nothing can truly be measured. A blade of grass has no actual length. Any measurement made in the universe is necessarily a rough approximation. It’s not bad; it’s just the nature of the place. The smallest speck is not a point, and the thinnest wire is not a line. Mathematical reality, on the other hand, is imaginary. It can be as simple and pretty as I want it to be. I get to have all those perfect things I can’t have in real life. I can never hold a circle in my hand, but I can hold one in my mind. […] The point is I get to have them both — physical reality and mathematical reality. Both are beautiful and interesting… The former is important to me because I am in it, the latter because it is in me.

Mathematics offers infinite possibilities for storytelling. I tell many stories as I teach math. My students are positively enchanted and remember them forever. One of my favorites is the kimono story.

I tell my students how in old Japan, servants helped geisha to put on the multiple layers of kimono. Each layer has to arranged and offset just so in order to reveal the colors of each layer. I tell them we are going to start with a geisha like 1/3. First we put on the 2/2 layer. 1/3 x 2/2 = 2/6. Notice that the geisha looks a little different, but underneath it is the same geisha. How about another layer, maybe 3/3. Okay 2/6 x 3/3 = 6/18. How about another 2/2 layer. 6/18 x 2/2 = 12/36. We can take off the layers one-by-one as well. This is called “simplifying a fraction.” Simplifying a fraction is simply a process of finding out which geisha is at the bottom of all those layers. If we are in a hurry, we can remove all the layers at once. How would we do that? In the case of our geisha, dividing by 12/12. The students love it.

The most elegant math story is the proof.

A proof is simply a story. The characters are the elements of the problem, and the plot is up to you. The goal, as in any literary fiction, is to write a story that is compelling as a narrative. In the case of mathematics, this means that the plot not only has to make logical sense but also be simple and elegant. No one likes a meandering, complicated quagmire of a proof. We want to follow along rationally to be sure, but we also want to be charmed and swept off our feet aesthetically. A proof should be lovely as well as logical.

Wednesday, November 30, 2016

Teachers Should Teach to the Test

Should teachers teach to the test? Some say of course we should, in order to give students the best chance for achieve their highest potential score. Some have even made teaching to the test a lucrative business. Schools are sacrificing more and more instructional time to test prep. Others say that teaching to the test games the outcome in favor of some students without actually reflecting the acquisition of real knowledge or achievement. Who is correct?

First, we must be careful to distinguish between tests teachers write covering material they themselves taught, and standardized tests. Standardized test are not written by the teacher who is teaching the material, and indeed, it is considered cheating if teachers see the questions ahead of time. Teacher-written tests cover a specific subset of content. The purpose of the test is to evaluate the students’ learning of that specific knowledge. Theoretically, if everyone in the class masters the material, everyone can potentially score 100%. Practically, teachers try to have a mix of harder and easier questions in order to differentiate levels of mastery. However, there should not be any questions outside the subset domain.

Standardized tests are very different. Test designers try to ensure that half the students will score above the target median and half below. From the students’ point of view, they perceive right away that it feels like they do not know half the questions. The realization often makes them feel inadequate and creates much of the test anxiety surrounding standardized test. I have found that explaining the difference between the test I write and standardized tests relieves much of the anxiety.

There is, of course, no point in explaining jargon like normative evaluation, median, etc. It is sufficient to simply say that the people who wrote the bubble test wrote it for lots and lots of students who have been taught by lots and lots of teachers. The writers really have no idea what I taught or how I taught it. So the writers write lots of question that they expect no one will know the answer. In fact, they write the test expecting that students will miss fully half the questions. I reassure them that it is perfectly normal to feel as if they are probably missing a lot of questions. Go ahead and guess anyway.

I tell them that the test designers include questions from lower grades in the test and questions from higher grades. The test designers know which questions are which, but of course the students do not know. I tell them if they feel like they do not know a question, it is probably from a higher grade and not to worry about it. The test designers look at the answer sheet and can tell if the students correctly answered the questions from their own grade level. If they do, they will get at least 50. I tell them this does not mean 50 points, nor does it mean 50%. I tell them it is a different kind of scoring system because it is not a test that their own teacher (like me) wrote. With high school students, I discuss a little more statistics and the idea of percentiles.

This kind of explanation usually satisfies students, removes perplexity and frustration, and helps them do their best. If the teacher’s curricular philosophy and design is strong and the teacher is a skilled teacher, then there is no need to worry about the standardized tests. Simply teach, and the standardized test will take care of itself. If the curriculum is weak, teachers will feel a strong need to teach directly to the test. However, by all means, teach to your own tests.

Thursday, October 27, 2016

Can You Teach the Bible in Public Schools?

The short answer is yes, you can and should teach the Bible in public schools.

The long answer is more nuanced.

There are three subjects that benefit from the inclusion of the Bible: English, Social Studies, Political Science, Western Law, Art, Music and yes, even Science.

English:

We expect students to recognize and understand literary allusions. The vast majority of literary allusions come from four sources: the Bible, Shakespeare (who often alludes to the Bible), Greek mythology and popular culture. There is no good reason to deny students understanding of certain literary allusions, merely because they come from the Bible. The Bible is also a literary classic in its own right. Belief is not a prerequisite to an intellectually honest presentation of the Bible as literature.

Avoiding the Bible also leads to miseducation, such as the case of a fifth grade teacher who defended reading The Lion, the Witch and the Wardrobe by C. S. Lewis, by saying she intended to read it as a fairy tale. C. S. Lewis intended the story to be Biblical allegory, not a fairy tale. To teach otherwise is educational malpractice. Either the teacher should teach literature such as this honestly, or avoid the book entirely. The middle ground simply will not do.

Social Studies:

History education prefers primary sources whenever available. The Old Testament is the major primary source for the ancient history of the Jewish people. The history of the church had a huge impact on the history of Europe over the last 2000 years, and an understanding of the Bible informs our understanding of European history. The Boers drew their rationale from the Bible (although I would argue that deliberately or not, the Boers improperly applied the Bible to their situation). In fact, an understanding of the Bible is essential to an understanding of the motivations behind many historical events.

Political Science and Western Law:

Our public discourse constantly refers to the Bible, and yet most of the people who think they are quoting the Bible (both Christians and non-Christians alike) have near zero understanding of the Bible context itself or the Bronze Age time when most of it was written. Christians especially have a weak understanding of what a “literal” interpretation means. When I was much younger, I met a man who had been an Air Force pilot during WWII. After the war, he went to Papua New Guinea or Irian Java (I forget which) to be a missionary. The island people had a noun which meant airplane. Literally, the word meant “a bird with the skin of a machete.” We would be foolish to think that the island people really thought the airplane was a bird, yet Biblical “literalists” make this type of mistake all the time. Another example comes from Chinese. Their word for computer means “electric brain,” but clearly the word is not figurative, spiritual or symbolic. It is simply the word for computer. In English, we still say the sun rises and sets, but no one supposes that we literally mean the sun moves up and down. Many people who say they believe in taking the Bible literally fail to distinguish these types of expressions, leading to some of the ridiculous arguments we hear everyday.

As Christopher Gunter wrote :

So what are young people to think when they hear biblical passages taken out of context to both support and refute gay rights, or the Iraq war, or any highly charged issue? They must not be afraid to question and challenge biblically based sound bites. They must have the courage and the foundational knowledge to understand for themselves the source and context of biblical passages. Our reluctance to teach the Bible perpetuates its mysteriousness, which has grave consequences in our intellectual lives and in the wider world in which we live.

Art and Music:

Anyone who study art or music appreciation will not get very far before they run into cultural works illustrating, or inspired by the Bible. If we want to understand the cultural work, we need to understand the source material.

Mr. Gunter again:

... the Bible’s influence spreads beyond the literary realm into the artistic and the cultural. Any student of art or music will deal extensively with religious material. Moreover, biblical allusions in culture persist into the 21st century: in movie titles, song lyrics, newspaper headlines, billboards, and so forth—even television’s “The Simpsons” draws extensively from the Bible. In short, biblical knowledge enriches our understanding of both high art and popular culture.

Science:

The acrimonious debate between “creationists” and “evolutionists” would evaporate if both camps actually understood what the Bible says.

As Mr. Gunter concludes:

It is a sensitive endeavor, to be sure. But we first must recognize the value of undertaking that task. The Bible is a remarkable document, parts of which can stand with Plato in their philosophical depth, with Tolstoy in their political complexities, and with Shakespeare in their poetic beauty. The religious sphere does not have exclusive ownership over those important words. We should give our young people the tools to understand the Bible, both for their own enlightenment and to better inform their decisionmaking as citizens.