Today鈥檚 post wraps up a series in which 糖心动漫vlog share the worst directives they ever received from administrators.
鈥楲iving in the World as We鈥檇 Like It to Be鈥�
Larry Ferlazzo retired last month after 23 years as a classroom teacher.
It was the summer after our schools physically closed down because of the COVID epidemic.
Our district鈥檚 superintendent, who later resigned with 鈥渆ncouragement,鈥� issued a number of edicts about how our schools would operate during distance learning in the fall. Few鈥攊f any鈥攖eachers, particularly those of us who had managed to do remote teaching the previous spring, were consulted.
One of these unilateral commands was that high schools would start distance learning classes at the same time we would have if schools were physically open.
We teachers knew that this was just not going to work.
It was difficult enough for our students to get themselves to physical schools on time. With society in a state of flux, our students were staying up even later than usual. Even though it might seem counterintuitive to some, we knew from our distance learning experience in the spring that it was likely that many more of our students would miss the beginning of remote teaching school if we kept to the same schedule.
Most of us felt it would be better to start the school day 30 minutes later and, in our informal conversations with parents/guardians, they agreed. Interestingly, a year later, the state of California implemented a law requiring all middle and high schools to regularly start later in the morning.
However, the superintendent wouldn鈥檛 budge during that distance learning year.
In response, teachers in most of our district鈥檚 high schools just ignored him and started our classes one half hour later.
After all, we were teaching from home, and students were learning from home. How could he enforce this arbitrary decision?
He later filed a rather humorous complaint to the state claiming that teachers wouldn鈥檛 listen to him, which was accurate, and nothing came of it.
The superintendent violated some key basic leadership rules. One was the community-organizing adage that 鈥渨e live in the world as it is, not as we would like it to be.鈥� And then, of course, there鈥檚 the quote attributed to Gen. Douglas MacArthur, 鈥淣ever give an order that can鈥檛/won鈥檛 be obeyed.鈥�
In my classes, at least, first-period attendance during distance learning that year was higher than when physical school had been in session.
No to Repetition
Pam Harris is a former high school math teacher, university lecturer, and author of Developing Mathematical Reasoning: Avoiding the Trap of Algorithms. She believes everyone can do more math when it is based on reasoning rather than math as memorizing and mimicking because math is actually figure-out-able:
The worst directive I received as a teacher was to teach math by helping students get answers that repeated correct step-by-step procedures. Textbooks were clear. State clearly the rule. Demonstrate the steps. Have students do an example problem with you and then practice with exercises 1-29 odd in the textbook. Doing math meant memorizing and mimicking to get answers.
Imagine my surprise when I began to realize that math-ing, doing math the way naturally math-y people do it, isn鈥檛 about rote-memorizing and mimicking procedures at all.
As a highly successful mathematics student and beginning teacher, I had begun to wonder about the memorize-and-mimic directive when my young son began to learn math. He reasoned his way through problems, using relationships that made sense. But, you should do it the 鈥渞ight鈥� way, I would counter. He just shrugged, 鈥淲hy memorize when you can think your way through?鈥�
For example, I once asked him in 4th grade if he knew his multiplication facts. 鈥淒o you know your 5s?鈥� He looked up at me, shook his head, and said, 鈥淣ot really.鈥�
As a high school math teacher, I began to panic. If my son doesn鈥檛 know his multiplication facts, how will he do in higher math?
He calmly said, 鈥淢om, you don鈥檛 have to know 5s if you know 10s.鈥�
鈥淲hat do you mean?鈥� I asked, 鈥淕ive me an example.鈥�
He explained, 鈥淪ay you don鈥檛 know 5 x 9. Since 10 x 9 is 90 and 5 is half of 10, then 5 x 9 is half of 90, that鈥檚 45.鈥�
鈥淕ood heavens. Does that work all the time?鈥� I asked, 鈥淕ive me another example.鈥�
He sighed. 鈥淥K, how about 5 x 23?鈥�
Not an example I was thinking about! I was wondering about single-digit multiplication facts, and he was reasoning using a relationship that would get him far more than just those facts. Goodness, using that connection, we could find 5 times anything! If 10 x 23 is 230, then 5 x 23 is half of 230, so 115. If 10 x 242 is 2460 then 5 x 242 is 1230. (I bet you鈥檙e trying your own x 5 problem right now!)
With this and many more experiences like it, I wondered if we could purposefully teach kids to reason mathematically like he was. He was doing it on his own. Could we open up the world of real math to all of us?
So, I dove into research. I read journal articles and studies. At the same time, I dove into my own children鈥檚 classrooms and experimented. Because of my background in higher math, I was able to sift through the less helpful research and find that there is a real math, math-ing way to teach.
Math is actually figure-out-able, and we can teach it that way!
Try this: Can you use 48 + 30 to help you think about 48 + 29? How about using 100 x 17 to find 99 x 17? How can you use 录 of 24 to find 戮 of 24?
What does it look like to purposefully teach all students to math, going through the mental actions that naturally mathy people have been doing?
Instead of telling students to rote-memorize and mimic the steps of a procedure, we can engage them in high-dose patterning. This can look like giving students problems like 64 - 20 and then 64 - 19; 156 - 100, 156 - 98; 6832 - 1000, 6832 - 995 and discussing how they relate, why you might want to use the first to solve the second in the pair, and then giving students a final problem without a helper, like 6.7 - 4.9 and asking them to apply the pattern to make their own helper. This isn鈥檛 about choosing problems that are easier, it鈥檚 about choosing problems that make recognizing and learning the patterns of mathematics easier. This is making learning easier.
This is not fuzzy, dumbing-down math. This is actually the way math-y people math. And it is super good news, that we can let everyone in on the secret of what math-ing is. Math is figure-out-able!
Thanks to Pam for contributing her thoughts!
Today鈥檚 post answered this question:
What has been the worst rule or directive you have ever experienced as a teacher, why was it such a bad rule or directive, and what should have been said, instead?
In Part One, Bobson Wong, Larisa Bukalov, Douglas Fisher, Nancy Frey, and Alexander F. Tang shared their experiences.
In Part Two Vernita Mayfield, Marcy Webb, and PJ Caposey offered their choices.
In Part Three, Rebecca Alber, Amber Chander, Ryan Huels, and Cecilia Gilliam wrote about their less-than-delightful experiences.
Consider contributing a question to be answered in a future post. You can send one to me at lferlazzo@epe.org. When you send it in, let me know if I can use your real name if it鈥檚 selected or if you鈥檇 prefer remaining anonymous and have a pseudonym in mind.
You can also contact me on Twitter at .
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