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A Rite (Triangle) of Passage May 13, 2014

Posted by mareserinitatis in education, family, gifted, homeschooling, math, older son, teaching, younger son.
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pythagorean_catThe younger son recently started his pre-algebra class.  Somehow, this has made math a bit better.  I think the fact that it has algebra in the title makes him feel very accomplished and that, in turn, has made him more enthusiastic about math.

The other day, he was doing some of his homework, and the lecture was confusing to him.  I listened to the lecture and then said, “It makes more sense if you draw a picture.”  He responded that, “Pictures always help me learn better.  I guess the math program doesn’t realize that some of us are visual learners.”  I was both amused and quite stunned.  I think I’ve been discussing educational theory a bit too much at the dinner table.  I can tell he’s listening to us.

Tonight, he hit a milestone.  He called Mike over, and I followed, so he could ask us how to pronounce “pythagorean.”  He was sure he’d heard us talking about it before (yeah, we discuss this stuff around the dinner table), and he wanted to be sure that was what it was.

“Oh, wow!” I said.  “You’re doing the Pythagorean Theorem.  That’s awesome!”  Suddenly, there was an impromptu round of cheering and high-fiving.  The older son even came over and gave his little brother a big hug, saying, “Woo hoo!  The Pythagorean Theorem is awesome.”

As the lecture progressed, it reiterated the terminology, focusing on right triangle legs and hypotenuse.  Given I’ve had ZZ Top in my head, I had to immediately sing, “She’s got legs!  She has a hypotenuse!”  I wasn’t able to come up with much more, though.

Yes, I have to admit that I realized how odd it was, in retrospect.  We were having a celebration that younger son had made it to the Pythagorean Theorem, and we were all making a huge deal about it.

But younger son didn’t think so.  He thought it was awesome and giggled continuously for the next few minutes. I guess he likes having a math cheer team.



The first two homeworks September 17, 2011

Posted by mareserinitatis in education, engineering, teaching.
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I’m almost done grading the first two homeworks for my classes, and I think the results were rather interesting.

The first homework consisted of reviewing the learning styles quiz.  I wanted the students to reflect on their results and discuss whether they thought their results were valid.  Further, I wanted them to discuss where they anticipated difficulties in school and what things they could do in those situations.  All of these were things I went over in class.

My first surprise was that a significant number of students did not address the questions they were supposed to answer, leaving their essays feeling…empty.  I think I need to be more clear that they need to answer all the questions, but I also think I need to provide a rubric so that they have a better understanding of what I’m looking for.

A number of the students felt they had gained no new information from the quiz.  A couple obviously didn’t understand what their results meant.  I was impressed, however, reading the essays where the students disagreed with the quizzes.  It seemed like those students were the ones who put the most thought into it, saying that perhaps the results applied in some situations but not others.  They usually were able to identify when they felt the results were valid.  I feel like those students really got the point of the exercise: they were supposed to think about how they learn, and they were able to analyze various situations and how their preferences interacted with the environment.

The second exercise had a more positive reception.  The students were supposed to attempt to take notes using two different methods covered in class.  There were five methods, one of which was to tape record the lecture.  The other four were written, although I’ll probably explain them in another post.

Most of the students felt it was useful to attempt to take notes different ways.  They did a nice job comparing and contrasting their experiences and feelings about the process, and very few failed to fulfill the requirements for this assignment.  I have to admit that my heart sank a little every time a student said something like, “I like to these types of notes because I don’t have to think about what I’m writing.”  Those are the students who I worry about.  However, a number of them said they learned something new.  A few said they liked their new notetaking method better while others said they might borrow one or two concepts to incorporate into their notetaking skills, even though they aren’t planning on changing their method a whole lot.

I have to admit that I found certain types of notes easier to read.  (I required them to hand in copies of their attempts.)  It does make me wonder how I can look at some of these notes and think they are far more clear, while the person writing them does not.  The primary issue is that I need to figure out a way to make them not feel guilty for using ‘too much paper’.  Some of these other notetaking methods require more paper than traditional notes because they use white space to organize things.  So many students seemed to think that using paper was a bad thing.  I need to make it clear that using paper to take useless notes is more wasteful than using more paper to take notes that are easier to study and comprehend.

Another issue I ran into is that several of the professors of freshman level classes provide their notes in powerpoints.  My experience is that upper-level classes will be significantly different.  I accepted writing on printed out slides as a possible notetaking method, but I found the evaluation of that to be very unsatisfactory.  Further, I think these students will not have the benefit of experiencing the other types of methods once they don’t have those slides available.  So I’m going to pretend those aren’t an option next semester.

We discussed people’s thoughts in class because I had students use only 2 of the four types.  I wanted students to get a feeling for the other types of notes.  I think that in future classes, I’m going to require they try the three non-traditional written methods themselves.  First, one of the methods the students tried was almost always traditional notes.  Not too many were willing to venture out of their shell and try two new types.  I think this limited their perspective because they were always comparing their new method against traditional notes, and they most often focused on how awkward it was to take notes differently.  Further, when we discussed things in class, only a limited number of students tried each of the new methods.  This reduced discussion to just a couple people, in some cases, and those students couldn’t provide a lot of different perspectives on the benefits and difficulties of the other methods.

I’m requiring my students to evaluate their learning so that they can become self-regulated learners.  I guess I’m trying to do the same thing with my teaching.  In that vein, I’ve concluded that my first assignment needs more clear guidelines.  I think I need to spell things out for the students.  Some students can do a good job with minimal instruction, but some really falter, so I need to be more clear for those students.  Some of the students didn’t seem to think the information was relevant, so perhaps getting specific about what they need to think about will help them understand the relevance more.

For the note-taking assignment, I think they’d benefit from getting more experience trying new things, so I’m going to change the scope of the assignment and have them try the three non-traditional note-taking methods.  Hopefully this will give them something to compare to…and fewer will go the route of not wanting to think about what they’re writing.

Finally, I have to say that this is giving me new insight into how students approach their classes.  I was a student who really didn’t think about how I learned and never had formal instruction in studying and how to learn.  I didn’t learn about a lot of these things until I had to face problems with my children’s learning.  Realizing how few of them have thought about it is probably going to make me think a lot harder about how to present technical information in the future.  I hope I’m able to make things more clear and understandable for my students.

The adventures of Stu Dent in the land of metacognition September 1, 2011

Posted by mareserinitatis in education, engineering, teaching.
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As many of you know, I’m teaching a class this semester on academic skills for freshman engineering students.

In doing this, I attempted to pick topics I thought would be relevant to engineering students, and I consulted with several working engineers about what I should teach.

My first set of lessons revolve around metacognition: the students need to learn to think about how they think and learn.  (Yeah, it’s kind of recursive.)  This week’s lecture dealt specifically with learning styles.

Because I’m planning my own curriculum for the course, I also am on my own for coming up with lecture material.  I decided to start with Bloom’s taxonomy.  If you’re not familiar with it, it’s a way to organize thinking skills.  It’s a hierarchical structure, usually shown in the shape of a pyramid.

After that I went into learning styles as described on Richard Felder’s site.  The students had to take the learning styles inventory before class so that we could tally up the results.

Ironically, talking about learning styles is very…verbal.  I also know that attention tends to wane after about 10 minutes.

My approach (at least this time) was to make sure I finished talking about Bloom’s taxonomy within ten minutes.  I tried to relate different levels of the taxonomy to different levels in engineering education.  Roughly, the three lower levels often relate to the first couple years of a college degree.  The top three levels will be encountered more in junior and senior level courses.  And it turns out that those thinking skills relate to learning styles – some find the first couple years are easier (usually the sequential and sensing individuals) while others, like the intuitive and global thinkers, will find the last couple years easier.

Rather than gathering results for all of the scales at once, we could take results from one measure on the quiz, talk about it, and then go to the next.  They could zone out  for a little bit, but they seemed to want to see how their classes were skewed.

I also had a ‘prop’: I drew a stick figure, whom I named Stu Dent, to represent the different extremes on each scale.  Yes, it’s goofy…but some of the students actually seemed amused by my cartooning.  (You’ll see “Intuitive Stu” below.)  In one class, someone observed that I always had a thinking Stu on the right and a doing Stu on the left.  In another class, one student shouted, “You killed Stu!” when I erased one of Stu’s personalities from the board.

I think I got the information across.  (I guess I’ll find out when I get their assignments next week.)  Some students seemed bored, some were very involved.  I don’t think it’s a coincidence that my class with the largest percentage of active learners was very talkative and involved, while the class with the largest number of reflective learners was pretty much silent the whole time.  I did ask a couple students after class if they thought the info was useful.  Some seemed lukewarm while others were enthusiastic.

The one thing I did notice is that after nearly an hour, most of the students still seemed awake, alert, and paying attention.  That’s an indication, I hope, that the lecture was at least halfway compelling.

Style versus substance December 14, 2010

Posted by mareserinitatis in education, family, homeschooling, older son, teaching, younger son.
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I think I spent the vast majority of the older boy’s elementary school years arguing with teachers who didn’t understand that a kid could be both LD and gifted. The arguments that they presented seemed extremely superficial from my perspective.

For instance, they told me he was not good at math, and they used the following as evidence:

“He doesn’t have his tables memorized.”
“He keeps flipping his numbers around. His numbers are malformed.”
“He has to think for a long time about his computations.”

The teachers used these arguments as justification that he should not be allowed to progress in math.

I come from a different perspective: thinking about how to do math is far more important than memorizing tables. If he understood what he was doing, no matter how slow, there was no reason to hold him back. Far better to learn the process to figure these things than mindlessly memorize a bunch of numbers. Tables can be printed out on paper and referenced.

When I finally gave up and homeschooled, that is exactly what I did: I printed out addition and multiplication tables. I explained how to use them. Then I started moving him very rapidly from single digit to multiple digit manipulations. I never made him memorize anything. However, he knows his times tables as well as any other kid his age. In fact, chances are he knows them better since he’s taking college algebra and trig as a freshman in high school.

The reality is that comprehension is more important than computation when it comes to math. Yes, getting the computation right is important, but that’s also why we have tools (ranging from calculators to mathematica) to check ourselves. Knowing how to do the problem is essential for fixing our errors: that is something a calculator can’t explain.

Unfortunately, now that the younger boy is in school, these arguments are coming on all over again. Interestingly enough, they don’t seem to be around math, which is the older boy’s phobia. No, the younger one is acknowledged to be quite adept mathematically. But they were claiming he is behind in reading.

The younger boy has quite a perfectionist streak, and so if he can’t do something perfectly, he doesn’t like to do it at all. And worse yet, he compares his abilities to his brother’s all the time. (He doesn’t realize that his brother has had a decade to master a lot of these things.) Reading has always been a bit terrifying for him.

When I mentioned to the teacher that the books they were sending home were far too easy (things he’d read in kindergarten), she told me that they were looking for comprehension. That was actually part of my problem: the books they were sending home had no plot, so if you ask him what happened, he couldn’t tell you. However, I started him reading Magic Tree House books, and he had no problem telling me what happened there.

Fortunately, the books coming home seem a bit better, but I got a note from the assistant teacher saying that one of the things they were working on was reading “smoothly”.

I have three issues with this. First, reading aloud is not as simple as just plain reading. While I can imagine that a child who reads well out loud is a good reader, I don’t think a child who may have difficulty articulating what they’re reading implies they aren’t a good reader. Even if the reading is choppy, if they aren’t struggling to read the words, then that’s a good indicator they understand the words. Saying ‘choppy reading indicates he’s having problems’ is like saying a kid who writes their numbers ‘funny’ is not good at math. Second, I feel that if you send a more difficult book home with a kid, they’re going to be exposed to many more words, which will give them more practice. This, obviously, will create a better reader than giving them books which are not challenging: increase the learning curve, and the rate of learning will necessarily be higher. If you don’t challenge them, they’ll continue to plod along at the same slow pace.

The final issue is that this will be very child-dependent. In this case, I have already had my son’s IQ tested, and one thing that came out of this testing is that he, like myself and his brother, is strongest in visual abilities. He may have a lot of difficulty reading “smoothly” for a while because, being a visual learner, he will need to translate every word he reads into a mental picture. This means he will read the word and have to pause after it to process what it looks like. Then he will read the next word and do the same thing.

The problem I have with all of this is that the focus is not on comprehension and higher-level cognitive skills. Kids are held back because of lower-level skills, the kind that require practice. Rather than giving kids stimulating work to practice on, work that challenges the higher-level skills, it’s easier to focus on the areas where there may be functional weakness, holding the child’s mind hostage to their motor functions.

As I was pondering this, an article on visual-spatial learning from the Eide Neurolearning Blog popped up in my reader. (Honestly, it was incredible timing!) After discussing ways to deal with visual learners, they ended with:

Be Patient Young visual thinkers are classic late bloomers. Yes, there are ways to help, but it’s also a good idea to understand big picture view of their growth and development.

It was good to remember that this too shall pass, despite the fact that I’m frustrated to be dealing with these same issues again.

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