Happy Halloween

Don't forget to turn your clocks back one hour tonight!

 

The 2/10 Strategy

I just finished the second webinar on learning to teach better via distance.  Thanks to the series of classes, I'm learning more.  My district is still having classes in person but two schools had to go totally virtual due to an increase in Covid-19 cases.  Somewhere during the webinar, the question came up on how to build relationships with students, especially the students who display avoidance behaviors.

Someone mentioned the 2/10 strategy which I'd never heard of before.   The idea is that you spend 2 minutes a day for 10 days in a row getting to know a student and at the end of the time, you'll have a relationship with the student.

The time should be spent talking about general topics like sports, fashion, or what ever the at risk student wants to talk about.  These short interactions are designed to build relationships because it allows the students to see the teacher cares about them.  When a student sees the teacher cares they are more willing to work and their behavior improves.

At the end of the explanation on the 2/10 strategy, questions rolled in on how to do it when everything is distance.  Good question because it's easy to implement it in person but a lot harder when it has to be done via some sort of device.  People made several suggestions which created additional discussion on the topic. 

One person suggested they ask one or two students to check in about 5 minutes early to just chat or arrange for them to stay a bit later to have the conversations.  This only works if your students have access to enough internet for either google meet or zoom.  Another suggestion, one I like a lot is to make calls to individual students later in the day so they don't feel like they might be in trouble.  

There are however a couple of issues that might arise if you try to implement this strategy.  For instance, a student might not want to talk to you, it might be better to have general conversations with small groups of students.  Let that one child see you talking to others on a variety of topics that are not on school work, or anything.  Sometimes, you might need to suggest a topic to get the student talking to you such as if you overhear them talking about a particular team, read up on them and be willing to discuss stats with them.

Don't worry if the student doesn't want to talk for two minutes but do try for at least one non-academic interaction a day and keep interacting and eventually, those interactions will turn into a full two minute conversation and you'll have had 10 days worth of conversations.

Sometimes, as a teacher, it's hard for us to find time to talk to students individually especially if we feel as if we have to "make" time to do it.  Why not just take a couple minutes during class to stop and talk to students for a few minutes off topic rather than stopping class to address a disruption.  If taking time to build relationships during class helps decrease the amount of misbehavior, why not? 

The other day, I took time to ask students who watched the last game of the World Series.  I had one of my challenging students tell me the Dodgers won.  I let out a bit of a cheer and told him I was born in Los Angles. Then I asked him if he'd heard the 3rd baseman was taken out due to having tested positive to the coronavirus and another student shared that the guy was out on the baseball field celebrating.  After that short interchange, they went back to work.

Finally, teachers don't always know how to begin a conversation with a student.  It is suggested the teacher listen in on conversations students has with others for ideas of conversation starters.  Last year, I had a senior who had trouble settling down when class started because he wanted to talk politics, so I began learning about politics and discovered that if I spend 30 seconds to a minute talking about the latest in politics, he'd immediately settle down and work.  

Another way is to commiserate with the student over something such as when something happens at home and they don't get enough sleep the night before, or how they missed a basket at the last game.  Conversations don't always have to begin with a question.

Although many interactions will be done virtually, they can still be done and as a teacher, you can spend two minutes with the at-risk student every day for 10 days.  Give them a call and check up on them.  It is worth two minutes of your time to help a student become a better learner and less at risk.  Let me know what you think, I'd love to hear.  Have a great day. 

Real Life Examples Are Not Always Real!

 

I've come to the conclusion that so many "Real life" examples we find in books or on the internet are seen by students as fake.  Look up real life uses of fractions and you always get recipes showing up.  The idea behind that is when you want to change a basic recipe to feed more or cut it so it feeds fewer people, you will either multiply or divide by a specific number.  The problem with this scenario is that people seldom actually do that.  

For instance, my father is the dump it in until it tastes right and looks like it should feed everyone while my mother takes the measurements in the recipe and just makes two of them rather than multiplying everything by 2 or dividing the materials in half physically.  She never bothered with the math.  Most of the people I know, fall into one or the other although I actually do know an engineer type who does sit down and mathematically adjusts all the measurements before he prepares the food.

A more practical example using fractions for my students is the idea of needing to purchase wood for a project such as building a bookcase or a bed, or a house where the measurements include fractions.  It is easier to use a drawing with measurements and have students calculate how much total wood they'd need to purchase at the store.  This is something they can relate to because people around here build houses, and other things.  Another area that uses fractions is sewing where one has to buy enough fabric to create dresses or clothing. Often the measurements are in given in fractions so when one has to read the back of a pattern, they are encountering fractions.

The standard example of a pizza is something most people do not really talk about in terms of fractions.  They see pizzas as having pieces.  Yes you might eat a half of it if you are rather hungry but few people go out and talk about eating 3/8th of a pizza which is what some problems have you calculating. 

As for inequalities, the textbook we use doesn't give any real life examples my students can relate to.  I ended up asking them about their ATV's and the amount of gas they held.  I asked if they always filled the tank with the exact same amount each time they needed gas?  I also asked them what would happen if they tried to put more gas into the tank than it could hold?  Eventually we ended up with the idea that filling a gas tank is an inequality.  If the tank takes 8 gallons and x represents the amount of gas being put into the tank is the inequality x < 8.  If you try to put more than 8 gallons, it will overflow and spill all over the ground. That was an example they could relate too.

I took time to mention budgeting in regard to inequalities such as planning a certain amount for rent so that you don't end up spending more than that. Or how much you budget for eating out might be no more than $180 per month. A person has determined they should not spend over a certain amount such as the rent < $1500 per month, or entertainment < $200.  

As far as using integers, there are so many real examples such as temperature changes such as a rise of 23 followed by a drop of 25 degrees or money deposited or withdrawn out of an account.  Or one getting paid money for doing a job and the person who pays the salary is having to subtract it.

No matter what type of real life example you use with students, make sure you include context as you teach the math so it makes more sense to the students.  Let me know what you think, I'd love to hear.  I'm attending another webinar on distance teaching and I hope I get something I can use and share with everyone.  Have a great day.

Celebrating Halloween With Math

When I look for things to do with my high school students around Halloween, I have to search diligently because it is too easy to find those worksheet with word problems with spooks, pumpkins, or other such items.  I want more interesting material because most high school students find those types of worksheets - boring in one word.

So one thing I do is look for interesting graphs dealing with halloween candy.  I've found two so far that show which states favor which candy and use them as warm-ups for "What do you notice?", What do you wonder?" and I add in "What can you conclude from the visual?"  It was fun listening to their "Who even likes candy corn?"  or "I thought that state would prefer....."  Lots of conversation.

Halloween is a great time to explore probability using candy.  For this activity, you will need a larger bowl of M & M's or Skittles for students working in groups to predict the number of each color in the bowl.  Once predictions are made, have students sort through the bowl, placing the candies into  piles based on color.  Then they count the candies to see how many they have of each color and they mark it down on the group sheet.  After they've tallied their numbers, figured out which color had the most and which one the least, pass out small packages of the same candy.  Let students make predictions based on the results of the big bowl.  Once they've made the new predictions, have them open the packages, divide the candies into color and count the number of each.  At the end, students can comment on how their predictions matched the actual number of candies in the smaller bags and propose why the percentages might be different.

Another activity is to apply the exponential growth formula to the population growth of Zombies.  There are several Youtube videos on this subject including one by MathMashup.  These videos make a wonderful introduction to the topic.  Then this lesson from Better Lesson provides a physical representation of growth by beginning with the teacher being the only one infected. The lights are turned off and on to indicate the passing of time.  On the first day it is only the teacher, on the second day the teacher infects one student so two are infected, on the third day both the teacher and student each infect another student so now four are infected.  On the fourth day, all four infect four others for a total of eight until the whole class is infected.  At the end, students will think about how the rate might change is say seven are infected. 

On the other hand, CU Denver has a similar activity but it is designed to show how a Zombie infection looks if it is following a linear infection rate, an exponential infection rate, or a logrithmic growth, so students can see how each one looks.  In addition, the activity provides some extensions and discusses mathematical modeling in relation to this activity so students get a better understanding of modeling in general.

Finally for today, Desmos has a lovely activity on the Zombie Apocalypse.  It starts inside of a biological research facility where something has gone extremely wrong and two new strains of the Zombie virus emerge.  Students are required to graph the growth, make predictions, and all of the usual things associated with Desmos activities.  It even asks students to identify the type of growth they are witnessing.

I'll be back later in the week with a few more activities to include in your class that incorporate math with halloween.  Have a great day and let me know what you think, I'd love to hear.  

Warm-up

If 4.5 pounds of cucumbers produces one quart of relish, how many quarts of relish will 1099 pounds of cucumbers make?

Warm-up

If you are given a bushel of cucumbers and it takes about 2 pounds to make a quart of pickles.  When. you are done, you have 24 quarts of pickles, how many pounds of cucumbers are in a bushel.

Should We Teach Students To Use Tricks And Shortcuts?

 

As a high school teacher, I get students who ask me which way the alligator bits when referring to inequality signs.  I usually give them a funny look because I've never figured out how the alligator thing is supposed to work.  When I was younger, I developed my own visual clues to help me remember which one was the less than.  I decided the less than sign was the letter L slumped over to become <.  That helped me but if a student is asking me about the alligator, that tells me they never learned the basics originally.

I'm assuming the thing about the alligator is a trick to help students remember which one is less than and which one is greater than.  Then there is the trick of adding a zero to the number when multiplying it by 10.  Yes it works but when students rely on shortcuts and tricks too much, they never actually learn the concept, only the process.  Once a student has mastered a concept, the shortcut becomes more useful because they know what is happening.

In addition, when a student learns a shortcut before learning the concept, they often are unable to apply it properly or are unable to do a problem if it is presented in a different way. Furthermore, when they do not learn the concept instead relying on the shortcut, the missing understanding of the concept becomes a learning gap in the student's knowledge.  

Unfortunately, shortcuts may not always apply to a every situation.  Returning the idea that if you multiply  any number by 10, you add a zero at the end only applies if it is a whole number such as 5 x 10 = 50 but it does not apply if you multiply a decimal such as .056 x 10 is 0.56, not 0.0560 as one might assume without knowing the concept, proving the shortcut does not help with students learning the knowledge conceptually.

Another reason for not teaching shortcuts till after students have established conceptual understanding is that they often try to apply the shortcut without fully reading and thinking about the problem.  One needs to take time to determine if it applies to the situation for instance, we always teach students the order of operations using PEMDAS or Please Excuse My Dear Aunt Sally but there are times when it is better to divide before adding or subtracting, or that minus 5 is the same as adding a negative 5 so you can apply certain rules you couldn't before.  

In addition, teaching students shortcuts before they understand the concept and regular rules means they are not using their critical thinking skills, the same skills needed when problem solving.  When I teach binomial multiplication, I don't focus only on the FOIL method with the letters, I actually show students 5 different ways to multiply ranging from multiply just like we do a two or three digit number to a distributive method, to a pictorial method because not all students understand the FOIL method.

I do use rise over run when discussing slope because those are the terms they are used to but I equate rise to the change in Y, and run to the change in X along with a pictorial method to try to tie it all together and help students gain better conceptual understanding.  Oftentimes in high school math, I have to work on conceptual understanding by starting with the trick they learned earlier in their school career.  Let me know what you think, I'd love to hear.  Have a great day.