Making Math Count

I can’t say exactly when I got off track with math, but it may have been the year I had to relearn long division after a hot summer of just being a happy kid and thinking no math thoughts at all.

It wasn’t until I had to take college statistics that I lost my “math phobia.” Portland State University math department legends, Mildred Bennett and her teammate, Ethel Lawrence, were ahead of their time with their highly effective teaching methods and student support.

Since that epiphanic time in my statistics classes, I have marveled at the importance and utility of mathematics in everyday life, from the complex economic models that determine the prime rate, to the use of algebra to solve fence-building problems. (I confess that I still don’t understand calculus, but I’m working on it — slowly.)

Today, over a half century after my difficulties with math, we still have students who struggle. The November issue of Educational Leadership is devoted to math education. Naturally, my favorite article is “Nine Ways to Catch Kids Up.” Access is free, along with some other great math pieces, so check it out.

Help someone catch up today!

Cross-posted on Straight Talk 13NOV2007

"All that is necessary for the triumph of evil is that good men do nothing."

You probably recognize, in the post title, the words of Edmund Burke (1729 - 1797).

He was an Irish statesman and supporter of American independence while a member of the British House of Commons,

The inscription on his statue (Bristol, England) reads: Burke 1774-1780. "I wish to be a member of parliament to have my share of doing good and resisting evil". Speech at Bristol 1780.

This blog is about education, but we're at a point where education and political activism may be running down the same track.

I'm not talking about partisan politics, I'm talking about educators taking their proper places in public life as leaders and persons of good example. We are some of those people Burke is talking about.

By now, the story of the Jena Six should be familiar to edubloggers worldwide. I posted about Lessons From Jena just a few days ago, hoping to remind teachers and administrators to bring some enlightenment about racial tolerance to their students (yes, looking to break or weaken the cycles of prejudice that infest entire families). The fallout from the Jena story makes me wonder if we ever entered the twenty-first century.

Today's New York Times carries a story about the Canarsie High School Principal, Tyona Washington, who received a package yesterday at school with a hate note and a noose. According to the article, "The Canarsie episode was at least the eighth time in the past few weeks that a noose was discovered in the New York area. In one instance, a noose was placed on the doorknob of the office of a black professor at Columbia University’s Teachers College."

The eighth time!?

And here's a story dated two days ago from the Times that deals with incidents that are on-going in Nassau County, where I spent most of my elementary and all my secondary school years. I'll be 63 years old next month, folks, and I assure you that this sort of crap wasn't going on there even in the pre-civil rights legislation days of the 50s and early 60s.

Looks like we need to do the thinking I was talking about on the move, pick the lesson plans well, and get to work now.

This is not something we can put off until our curriculum guides say it's time. The fallout is raining down now, and we have to step up to the plate.

Another reminder of our need to act comes from a poem by Pastor Martin Niemoller (1892–1984) about the failure of German intellectuals and other public figures to respond to Nazi bullying and terrorizing of the German population. Some of you may have seen a famous filmstrip that dramatized the poem.

When the Nazis came for the communists,
I remained silent;
I was not a communist.

When they locked up the social democrats,
I remained silent;
I was not a social democrat.

When they came for the trade unionists,
I did not speak out;
I was not a trade unionist.

When they came for the Jews,
I remained silent;
I wasn't a Jew.

When they came for me,
there was no one left to speak out.

Speak out folks, talk about race and racial tolerance. Teach about it.

What's "Fair"?

In a recent discussion with another teacher, I asserted that homework should be evaluated, but that evaluation, whether in the form of a letter or a percentage, should not be included in a report card grade if the purpose of the homework was to reinforce classroom learning (as in "formative assessment").

Then the teacher asked what they should do if the student decided that, because the homework mark didn't "count," he or she would not turn in their homework.

In the case above, most teachers would try to control the errant student with punitive grading: a zero, perhaps, for non-performance, and then averaging the zero along with the letter or percentage items that determine the report card grade. The teacher I was speaking with thought that zero was the only option.

I said, "No, it's not the only option. Stick with the principle of not adding homework evaluation to report card grades (summative evaluation)."

He said, "Then I should just let them skip homework."

"No," I said, "let's back up a second."

I asked if we could agree that homework should be thoughtfully assigned by the teacher, and the purpose of the homework should be to reinforce knowledge or skills taught in the classroom, and not assigned without consideration of the fact that students actually have a life in addition to school.

Yes, we could agree on quality homework.

Next, I asked if he would want to pursue every student who didn't do any homework assignment. He said he would, because otherwise it wasn't fair to the other students.

"Suppose," I asked, "that the student in question has an A in the class and doesn't need to do the homework?"

"Well," he said, "it just wouldn't be fair to the other students if I let that one go."

"Why not?" I asked.

"Well, it just wouldn't," he said.

"Can we talk about 'Fair'?" I asked. "There's two ways of looking at 'Fair.'"

"Okay," he said.

"First," I said, "'Fair' has nothing to do with anything. With regard to that particular student's achievement, it's all between the state standards, that student, and you. Other students don't figure into the equation. Remember, we're criterion-referenced, not norm-referenced, right?"

"Right."

"Second, and this is the way I prefer to think of it, 'Fairness is not treating all students the same. Fairness is meeting each student at their level of need.' So we consider each student, each case, one at a time, isolated from all the others."

"Besides," I said, "most well performing students are doing their homework anyway, and if they miss an assignment, there's usually a pretty good reason. You're a teacher, not a cop, so let it go."

"If you're concerned about the student who chooses to ignore homework because they may fail or perform poorly in the course without the practice, then you need to find a way to support them, and that takes some investigation into the reasons they are not doing the homework, as well as an enlightened administration that will provide before and after school, and lunch-time opportunities for students to have homework supervision and help."

"Okay," he said, "I get it. I'm a teacher not a cop. And I'm concerned with the value of what the homework produces for the student, not the process of making sure every kid does it or else. Homework is generally formative assessment, for practice, so it doesn't go into the report card grade. If a student who doesn't need the practice misses a homework assignment, I don't need to sweat it, but if a student who needs the practice misses, I find a way to help him or her get it done."

"Right," I said. "And besides, in all the years that I've observed those homework policies, I've never seen kids try to take advantage of me. The ones who will do it on their own, do it. If it's late, there's usually a good reason and it comes in later. If they're not going to do it, you have an opportunity to support them. And I've never seen that mythical stack of late papers on my desk at the end of a marking period."

Never. Honest.

Not Gonna Happen!

Does it hurt if your brain gets full? We'll never know, because even if we were able to learn 10 or 100 times what we normally learn each day -- even going to school -- none of us will live long enough to find out. Not even close.

Briefly, learning capacity, for the average person, is virtually without limit. The challenge is, how to use our brains more efficiently so we can be more effective in our daily lives.

The really big question for modern educators is, "Why don't we teach students brain-friendly learning techniques?" I'm talking about techniques that were familiar to the ancient Greeks and Romans, the orators and storytellers who had to remember tons of stuff without teleprompters or notes. How come we, as teachers, can't model the mind power of those classical folks we read about in the history books?

I don't know the answer to that question, but I do know that my Dad, who was a high school teacher and a scholar until the day he died, taught me about mnemonics -- techniques for making use of the associative power of memory -- so that I could more easily recall information teachers expected I would learn by rote, that is, repetition, aka banging your head into a brick wall until you make a dent.

The first of what I consider the most important brain-friendly learning techniques is the art and science of mnemonics.

From Merriam-Webster's Collegiate Dictionary (edited):

Main Entry: mnemonic
Function:adjective
Etymology:Greek, mindful, to remember
Date:1753

1 : assisting or intended to assist memory; also : of or relating to mnemonics
2 : of or relating to memory

Here's how I used to introduce the topic in my brief few minutes with eighth grade parents at Back-to-School Nights (which are happening around our district this forthcoming week)...

After an announcement about where parents could find our curriculum (in the student handbook!), I went on to discuss how I would teach their children to succeed in my class. I barely had time to introduce them to brain-friendly learning techniques and explain "grading for learning," but we alway had fun with mnemonics.

Imagine if you are a parent sitting in Mr. Repairman's eighth grade social studies class (American History through 1877) and he tells you that one of the state's onerous standards requires you to actually know, that is, memorize (for crying out loud) the names of the thirteen British colonies that became the original states.

Then Mr. Repairman says, "I can teach you to remember them flawlessly in five minutes or less, and what's more, you will be able to recite them, not only in the order you learn them, but backwards as well."

Then Mr. Repairman asks, "Now how many of you think I'm full of beans." Along with a few smiles, a few hands go up. Parents are more cautious that kids. When I do it in class during the colonies unit, the whole class raises hands!

Five minutes later, the braver parents are reciting the names of the thirteen colonies as promised. The ones who brought their children enabled a preview for those precocious rascals, most of whom competed at the Back-to-School class with the adults to show that they, too, could do the magic memory exercise, both forward and backward.

The students, for this first exercise, used my mnemonic, but later, when they had to memorize the goals of the US Constitution, for example, they used their own creations and drew their mnemonics as well.

Tomorrow I'll go into a little more detail and cite some references for teachers who want to help their students remember everything from mere facts to complex concepts, almost effortlessly.

By the way, when one of the parents asked another teacher during the same evening why they didn't teach students how to remember stuff more easily, the parent reported back to me that the teacher dismissed Mr. Repairman's mnemonics as "Mere memory tricks. Of no value, whatsoever."

I was probably overgeneralizing when I thought to myself, "What a moron."

The teacher, not the parent. ;-)

Cartoon Copyright 1986 by Gary Larson

Brain-based What?

Over on What It’s Like On the Inside, The Science Goddess is aptly referencing the Broadway musical Young Frankenstein in her discussion of “brain-based learning strategies.” You have to read her post for yourself and pay special attention to her links that will lead you to a short rant about the similarities between brain-based and butt-based learning strategies authored by Professor Plum, who may or may not still be stirring up the edublogosphere.

Maybe the reason I enjoyed her post so much is because I’ve always struggled with what to call my favorite focus (brain potential) on teaching and learning strategies (in addition to “grading for learning”). After all, we weren’t born with brain-use instruction manuals attached to our big toes…

I finally decided, after considerable deliberation over the years, to go my own way, depart from popular education research reporting, and call all the “stuff” under the heading “brain-based” by somewhat different names, to whit, “brain-friendly teaching strategies,” and “brain-friendly learning strategies.” My students could deal with that and so could their parents.

To be perfectly frank, my students and I never put much time into brain physiology, which seems to be an obligatory preface to discussing (and practicing) brain potential for learning, but in the end, useless.

What the brain can do is what lights up my Christmas tree. My students and I had lots of conversations about learning potential being virtually infinite, and old age being no barrier to continued learning (thank you, God). And, at the beginning of the school year, I promised to share with them ways to access this incredible potential.

Tomorrow, I’ll share the difference between the instructional and learning techniques, and some of those techniques that helped my students harness their own brainpower. It’s not your ordinary, everyday classroom stuff. Two of the ideas I’ll highlight helped me get a 4.0 in graduate school, without a brain transplant or any increase in I.Q.

I’ll include some references in case anyone is curious about how to maximize their students’ achievement potential by applying some of these concepts.

Educational Technology That Works...

...is the title of a promising wiki (like I know so much about wikis, novice that I am) that is devoted to classroom instruction integrated with Web 2.0 (about which I'm still learning).

I'm excited for several reasons.

Marzano's work -- featured on the wiki -- recognizes the convergence of education research and he emphasizes the practical application of the research.

This wiki may be a good model for the experimental Edubloggers wiki.

And most interesting of all, this wiki is an electronic version of six publications (plastic comb flip-books) that were put out by our district curriculum and instruction department back in 2000 to remind teachers of the main things to remember about the instructional strategies we were then beginning to promote: differentiated instruction; individualized instruction; cooperative learning; brain-based research applied to learning and instruction; multiple intelligence theory application; and assessment literacy (Stiggins, et al).

Those little books were fantastic -- they are collector's items now (for the geeks among us, anyway), but they were expensive and time consuming to produce. The wiki takes the place of all that and even spreads the joy of contributing around to whomever is willing and qualified.

All this discovery is total fun!

2nd Annual Conference on Sound Grading Practices

Educational Testing Service/Assessment Training Institute is holding the premiere international conference on standards-based grading December 6-7, 2007.

The continuation of this conference is a sure indicator that grading for learning has hit critical mass, and I'm way happy to say that our district will be well represented.

I'll be doing a couple of breakout sessions (those will be listed later) and I'd very much enjoy meeting any of you who can persuade your district to send you. At the risk of sounding like an old-time sales dog, "Last year was a sellout, so talk to your administrator today."

Don't Worry, We'll Make It!

The best of plans can run into rough water, but the deep pool coming up next is calm and has good fishing.

The wiki kick off has been revised and will not require so much attention that principal's will be shaking their collective heads saying, "So that's where my star teacher lingered instead of getting ready for the first days of school!"

We anticipate many different conversations on different education topics. Not everyone of us burns with the same enthusiasm for each of them, so appearances at all gatherings are not expected.

If you're an edublogger with an interest in instructional improvement and you're curious about what grading has do with it, speak up here and maybe join the conversation.

From this point RepairKit may reference the Edubloggers wiki occasionally, but my blogs on "grading for learning" will be independent. I'll be looking for you on both sides! ;-)

New Wiki In Town! 2

Here's an update on our wiki...

First, participants discussed wiki goals, use, and format. Then Eric edited and finalized the Front Page that outlines where we are at this point.

We'll begin our exploration of standards-based grading with a warm up wherein we analyze a couple of grading situations that made major metro papers. In SBG Warm Up Draft 1, we'll look at the articles separately, comment on each of them, then compare the situations and draw some conclusions about what's being described in the articles. (Articles are on this page.)

Standards-Based Grading, or SBG from here on, is also known as "grading linked to standards," and "grading for learning." (Thanks to Exhausted Intern for the new term and three-letter acronym!)

The end goal is to produce a document or series of wiki pages that can 1) serve as a primer for educators new to SBG, 2) facilitate a quick review for educators who have been exposed to the concepts, 3) be a training tool for professional development sessions.

This topic is red hot and ready to roll.

New Wiki In Town!

Eric Turner of Second Hand Thoughts has been hard at work constructing a wiki for edubloggers to share and polish thoughts about the education topics near and dear to their hearts.

While poking around in Eric's new construction zone, I came upon the above image. It's from Eric and it pretty well sums up the aim of the new wiki.

Any more conversation/ideas about how it's going to work? Let's hear from you!

Eric's my choice for ad hoc wiki foreman at least till it's up and running. How does that sound?

A Grading Conversation

I'll be off the grid for a couple of days, but was hoping to contribute something constructive prior to taking off.

Labels/categories/topics in a blog sidebar, although they may be a way to keep track of topical conversations, don't go far enough. A search function also helps. (There's probably an efficient Web 2.0 way to do it, like a topical aggregator, but it hasn't touched my mind yet.) So this is an experiment, a "sticky" post. (I'll figure a way to make it sticky!)

Eric, in Second Hand Thoughts, reinforced my desire to broaden and deepen the conversations on what the Exhausted Intern calls SBG or "standards-based grading," aka, "grading for learning," or "grading linked to standards." (Eric has in mind an idea for focusing conversations that goes beyond what I'm hoping to do here.) Here goes...

So far, I've talked about SBG with the following folks who have "grading" listed on their topic sidebar...

The Science Goddess of What It's Like On the Inside
The Exhausted Intern of Not Enough Hours

...and folks who don't have "grading" listed as a topic, but have addressed the issue in posts or "comments" either on RepairKit or their own blog:

Miss Profe from Hardknock Teacher's Life (See today's knock-your-socks-off post.)
Miss A of Confessions from the Couch
The Midwest Teacher of Teach Me, I Dare You

This is also an open invitation to join the conversation.

If I left anyone out of this conversation, my sincere apology and please mention it in a comment to this post. I'll cut and paste your link above.

My goal is to list, in one place, all of you with whom I exchange ideas about SBG. (If this is a dumb idea, or there's a better way to do it, please tell me!)

A Hidden Third Factor That Influences Math Scores?

I'll be very interested to read what The Science Goddess has to say about intrinsic and extrinsic student motivation to succeed relative to grading linked to standards, and how it sorts out with regard for a student's orientation toward either comparative performance or sheer subject mastery.

I'm thinking it will be a complex set of complex questions, and I would love to see the study design!

Prior to SG posing the question of how grading student output relates to motivation, I pretty much thought of student motivation to achieve being either encumbered or unencumbered by a teacher's grading philosophy. In other words, poorly informed, idiosyncratic grading practices have the potential to crush student motivation to achieve, and enlightened grading practices simply unencumber the student, but eventually become transparent or invisible and are taken for granted like breathing fresh air.

I spent a lot of time trying to analyze what in the classroom stands in the way of student achievement. For example, for years we tried to improve math scores. It was like banging our heads against a brick wall. We used Northwest Regional Ed Lab's "Onward to Excellence" model, a no-foolin' piece of work, to guide us. Our principal was on fire and had the intellect to lead the charge. We barely budged those scores. My thinking lead me to this some years later...

Question: Can classroom assessment issues block motivation to achieve in math?

Possible Motivational Challenges:

1. Formative assessments are included in grades (no room for mistakes).

2. Homework is treated like a test – marked and included in the grade (students develop
“coping behaviors,” a euphemism for cheating).

3. Infrequent processing opportunities during instruction.

4. Sparse student-involved assessment.

5. Zeros or 50% given for late and missing work.

6. Teacher uses mean average (with outlying scores) to compute grades.

7. Make up policies are one-size-fits-all.

8. Missing or unclear exemplars for classwork/homework (should match instruction).

9. Recency of learning not considered in grade.


Solutions:

1. Analyze syllabi, grading policies, classroom rules. Check for research-based “best practices”.

2. Check understanding of computer grading program mechanics.

3. Check for mean averaging with extreme scores that skew the mean. Compare to median average of scores.

4. Check grade printouts.

5. Analyze homework policies.

6. Do classroom observations with focus on classroom assessment and processing as part of
instruction (including student-involved assessment).

7. Develop a processing activity/formative assessment “bank” that teachers can draw on.

8. Emphasize Assessment Literacy and grading for learning in professional development activities.

Note: Many of these challenges and solutions will apply to classes in other disciplines. Anyone care to add to the list?

Are We Moving Too Fast in the Pursuit of "Rigor"?

While in elementary school, I forgot how to do long division the summer after we learned it. Thanks to my paternal grandmother, a saint in her own right and a 6th grade teacher at PS 199 in Brooklyn, NY, I got the proper brushing up.

As a high schooler, I struggled with algebra, aced geometry, and took "fusion math" in the eleventh grade from a strange duck who one day looked at his well-behaved (really) class of eleven students and said, "I hate you kids. If there was anything I could be doing besides teaching, I'd be out of here." That was my last day in a high school math class. My Dad, also a high school teacher and WWII combat vet, decided that it was neither a healthy environment, nor physically a safe place to be.

And the math struggle goes on.

Today I read that Lehigh Valley (Pennsylvania) math professors are among the many nationwide who complain that rushing through high school algebra and geometry courses, or following an integrated math curriculum, is leaving too many students currently entering college unprepared for college math.

Their concerns -- that students are not developing strong basic math skills because of the rush to move on -- are well-founded, in my opinion, and I'm burning to know how our district sees this news item.

After a full year of college level statistics and studying algebra for the GRE, I lost my math phobia and even begged my principal(s) to assign me to a pre-algebra class where kids were struggling. (They never did take me seriously. I'm not math certified.) So I'm convinced now that although some kids might be somehow more predisposed to either math or verbal high achievement, all students who are well-taught can succeed in math and develop strong skills useful over a lifetime.

A fellow edublogger noted that although we seem to know what to do to achieve pedagogical excellence as measured by high student achievement, we just don't seem to do it. There's a connection here.