Saturday, March 23, 2019


Louvre, Pyramid, Paris, Tourism, France
The base is 116 by 116 by 70 feet high.  What is its volume?

Friday, March 22, 2019

These Are Not The Best Study Strategies.

Glasses, Read, Learn, Book, Text Yesterday, I looked at the best study strategies but there are two that should be thrown out completely and they are ones that I grew up with and I'm sure many of you did too.

First is rereading the material.  This is a very popular strategy with 84% of surveyed students using it but it does not enhance student learning because this method does not transfer the information into long term memory. 

This is one of those techniques, I learned when I was in high school but a lot of research has happened since I graduated and its one I tend to use when I'm making my own notes so I restudy the information.

Next is the use of highlighters to illuminate important passages.  This does absolutely nothing and according to one study, students who did this, performed worse on tests that required people to make inferences.  It is thought that when they highlight something they are not making connections with other parts of the text. 

I admit, this was a technique I never did because I hated messing up the perfectly white page with yellow.  The other thing is that if you ever bought used textbooks in college, they were often highlighted and the material highlighted was never what I thought important.  I'm sure many of you felt the same.

Summarizing the main ideas of the text appears to work if students are taught how to effectively paraphrase the ideas.  The key here is that students need to be coached in this strategy.  The training begins with students learning to summarize short paragraphs, before moving on to longer sections, eventually learning to do complete chapters.  The amount of training needed may make this strategy one that is not taught immediately.

This was never considered a study strategy when I was in school because its something you did in your English class, never when preparing for a test.  So its not one I ever learned.

Another technique requires students to visualize the content of the material they are studying.  Linking a visual with the content can help retain the material a bit longer but it only works with text that is too complex.  Unfortunately, it only appears to work for a short time after reading the material and the benefits do not last.  It is also harder for younger children to do because they often have trouble coming up with images for certain things.

The final technique is called keyword mnemonic where people link images together for words or idea. This often works well when taking a foreign language or working on vocabulary.  Otherwise, it doesn't help students for more than a short time.

I hope you learned something new in this today.  Let me know what you think, I'd love to hear. Have a great day.


Thursday, March 21, 2019

The Two Most Effective Study Strategies.

Laptop, Woman, Education, Study, YoungWe all know a way to study, especially when tests are upon us.  When I was in college, we highlighted, we read and reread the books, we deciphered our notes, all the night before in the hopes we'd remember enough to pass the test.  Since then research has been done to determine which strategies are the best.

One of the best ways to improve student performance is to provide frequent tests/quizzes rather than one for the end of the unit.  Students who used this method to study for their major tests, discovered they'd perform better than their classmates who used more traditional ways of study.  With the internet, it is easy to find all sorts of practice tests, either paper or online, to try.  As teachers we shouldn't be afraid of interweaving short ungraded quizzes throughout the unit.

In addition, a quizzing oneself does not just use traditional quizzes or tests but can include where the student hides information and tries to recall it or creates 3 x 5 cards or digital cards with questions based on the material they can use to test themselves. They should continue using these flash cards until they can easily answer the questions. As a teacher we can encourage students to leave space in their notes either to the side or on the backside where they can try a practice test based on the notes.  The same can be said of notes.  If a student keeps testing themselves on their notes until they can recall the material, they stand a much better chance of recalling the information during a test.

Next is distributed practice which in math means instead of doing all the same type of problem at once before moving on, they work one problem, then the next type of problem, then another type of problem until they've worked their way through all the types of the problem before starting again.  This has a much better chance of having students really learn the material.

This can be applied to preparing for a test by reading and rereading notes over a period of several nights rather than cramming the material in over a span of several hours the night before the test.  Research has found that if students take the time they'd spend cramming and spreading it out over several nights, they will learn the material better.

Although students might disagree, feeling they know the material well using traditional methods, research indicates actual learning takes much longer and if a child struggles, they are learning the material better.  The cramming method just has them recognizing the material for the moment but they have not had the time to properly transfer the material into long term memory

If you take time to teach study skills in your math class, these are the two that should be taught first because research shows they are the most effective ones.  Tomorrow, I'll look at those strategies that are totally ineffective.  Let me know what you think, I'd love to hear.

Wednesday, March 20, 2019

The Math Design Collaborative

People, Child, School, Genius The other day, I was searching for something quite specific and ended up at the Math Design Collaborative from the Bill and Melinda Gates Foundation. 

The first thing I found were class outlines for grades 6 to 8, Algebra I and II, and Geometry.

These outlines begin with outlines comparing the material in grades 6, 7, and 8 or Algebra I, II, and Geometry and a list of the eight mathematical practices.  Then you get the actual list of content with formative assessments and how long each section should take.  In other words it has a nice pacing guide built in.

Once you get to the main part of the guide, it gives additional break downs for each lesson from a general introduction to the lessons, links to the appropriate material, tasks, books, and information on the formative assessments.  Everything you need for the lessons.  The best thing about the lessons, is they've listed the standards each lesson addresses so you don't have to sit there and figure that out.

Every lesson has tasks associated with them.  The tasks are all labeled so you know if they are designed for the novice, an apprentice or expert so you know who they are suitable for and if you need to add some scaffolding.

Under each grade level or course outline there is a list of each individual formative assessment. For instance in the Algebra I course, there is a section on linear equations with something on simple and compound interest rates where students compare a linear function with an exponential function.  The outline provides an overall view but when you click on the comparing interests link, it takes you to the actual lesson module.

Although there are links for every section of the lesson, not all of them work correctly. The one link I found that did work, was the one that sent me to The Mathematics Assessment Project lesson on representing Linear and Exponential Growth.  This comes with the necessary resources including the lesson and a power point. 

The other problem with the detailed lessons is they often refer to pages that are in the material from the Mathematics Assessment Project and if you don't know that, it can make you wonder where the material is.  Otherwise, the information is there to follow step by step from pre-assessment through to follow-ups. 

I like the whole concept because I don't always have the time to write a lesson from beginning to end.  I found a nice lesson on classifying systems of equations I can use next week in my Algebra I class. 

Let me know what you think, I'd love to hear.  Have a great day.

Tuesday, March 19, 2019

Times in Music

Drum, Hands, Music, Sound, DrumsI was at dance practice last night but its wasn't the usual dance practice you might be picturing.  It was a Cup'ik (Chewpick) practice.  That means they used a standard 4/4 beat with a slight variation but it was usually 4/4.

In the middle of doing a song about two men who went whale hunting one day and ran aground on a sand bar, my thoughts flittered to this piece that was rather complex.

It was like 2/4, then 3/4, back to 2/4, then 9/8 thrown in and it was crazy.  It was extremely easy to get lost in if you were not paying any attention.  In the middle of all this, I realized it's all a form of math.

In a sense, time signatures are a fraction where the top number or numerator indicates the number of beats in one measure of music while the bottom number or denominator indicates the type of note.  So a 4/4 means there are four beats in a measure and each note is a quarter note.

Not quite the same as parts of a whole but not all fractions are parts of a whole.  Look at ratios which are comparisons and time signatures which provide a different type of information. Neither one is really considered Part of a Whole.

Furthermore, musical notes and rests are the visual representation of the time signature.  Any musician can look at the music itself, count the number of notes, look at the value of each note to determine the time signature without looking at it.  This is much like mathematics where its numbers are like the time signature and the representations of those numbers are the notes.

There is a mathematical equation for determining the note value based on the number of flags on the note.  The equation is 2^(-2-n )where n = the number of flags.  If its a whole note, it is 2^0 power or 1 beat where as if it has 4 flags, it would be 2^(-2-4) = 2^-6 or 1/64.

In addition, most pieces of music have repeated sections in them denoted by a repeat sign.  Most pieces of music have some sort of repeating pattern just like math has.  I know I always take a few minutes to look for the repeating pattern in the music before playing it so I don't miss any.

Then you have the vibrating sound waves that are tuned to a certain standard of Hertz.  Middle C is found at about 262 Hertz while other notes are at a different frequency.  If the instruments are not tuned properly, they some times sound off.

Even Fibinocci contributes to music. If you look at a piano, you can see it with the 13 keys that make up an octave.  Five of the keys are black and eight are white and the black keys are grouped in a group of two followed by a group of three.  2 +3 = 5, 5+8 = 13.  Usually a scale is made up of 8 notes where the foundation of a chord is based on the 3rd and 5th notes.

It is said that Mozart based many of his piano sonatas on the golden ratio.  In addition, the violin's parts are also based on the golden ratio and provides the basis for saxophone mouth pieces, speaker wires, and even used when designing certain cathedrals.

So math is found in so many places in music.  Let me know what you think, I'd love to hear.  Have a great day.

Monday, March 18, 2019

Angles, Skiing, and Snow

Freerider, Skiing, Ski, Sports, Alpine Skiing is one of those wonderful winter sports that people with drive a couple of hours to do.  I tried it once but I proved to be quite unsuccessful in that I manage to go down a hill backwards.  The only reason I didn't go very far was this beautiful tree I ran into butt first.  I've never been again since that day.  Besides its intimidating to watch a 6 year old whizzing down the advanced slope.

The cool thing about skiing is it involves math, grades or slope, and so much more math.    In skiing, they refer to slope as Piste which is French for the marked run down the mountain.

First off, slope in downhill skiing is spoke of as percent slope also known as grade.  A 45 degree angle is actually a 100 percent grade.  If you can visualize it in your head or draw it on graph paper, it shows up as a 1/1 slope or a rise of one foot over a run of one foot.  In addition to slope, skiers must keep in mind that snow no longer sticks when the slope is over 75 degrees.

Furthermore, they must keep tract of the type of snow because the type of snow determines how fast a person can go down the hill. If the run is made of up ice, the person will ski harder than on powder snow.

In general the easiest trails have a slope between 6 and 25 percent while the next ones up are between 25 and 40 percent.  Most ski resorts have the majority of the trails in this range.  The more expert skiers prefer trails over 40 percent because of the challenge.  The hardest trails have slopes well above 40 percent and lots of obstacles.

Now for the question of how the type of snow effects skiing.  If it has not snowed in a while and people have compacted the snow by skiing repeatedly,  it becomes ice.  Ice is not well liked by many skiers because they cannot dig their edges into the ice and they don't have much control.

If the snow is soft, it is easily moved around by skiers and it allows them to dig their edges in so they have the most control.  In addition, if they fall, they won't be hurt because the snow pads them.  If the temperature gets too warm, the snow will melt during the day and refreeze during the night when temperatures drop.  This means the run can be quite icy in the morning but gets slushy later on as the temperature goes up.  Slushy snow lacks structure, has lots of ice, making it harder for the skier to control their run and they can get ice burns if they fall.  When snow is wet, the water can create a vacuum under the skies, they don't slide easily.  Its like snowing with breaks on so the skier finds it quite hard to go downhill.

So the type of skiing one experiences when going downhill depends on both the grade or slope, the type of snow, and the temperature.  Imagine the types of graphs students can create from this information.  They can graph the degrees of each type of slope to see how steep it is.  Then they can create the grade such as 1/1 for the 45% angle to meaning to the percent. They can also create a graph based on the temperatures for the different types of snow for skiers.  Finally, they can compare and contrast the classification of green, blue, and black slopes based in the United States or in Europe.

Let me know what you think, I'd love to hear.  Have a great day.