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.

Learning Goals Need To Be Everywhere!

Between the books I've been reading and the webinars I'm attending, one thing has come through loud and clear.  It is important to do more than just post learning goals on the board.  It is important to do more than just have students write them down in their notebooks.  

As we all know, learning goals are the ideas or concepts we want our students to learn in each section.  We usually phrase them as something like "Students will be able to" followed by the goal.  We might also include success criteria for each goal so students can determine if they've learned the material and reached the goal.

When I went to college to become a teacher, we included learning goals in our lesson plans but nowhere else.  Many years later, I was instructed to write the goals on the boards as "I can" statements for students but that was about it.  Then I read a teacher needs to create success criteria so the students can determine if they mastered the material. Recently, I learned it is important to revisit the goals on a regular basis.

Furthermore, one should highlight learning goals on a regular basis such as listing the part of the learning goal being covered by the current lesson, or at the end of the direct instruction, or as part of the introduction to an activity or as part of the homework.  For homework, identify the learning goal associated with each problem.

If you use choice boards, it is important to list both the learning goals and success criteria at the top and identify which activity is associated with each goal so students are aware that every choice is going to help students meet the learning goal. 

You may be wondering why one should emphasize the use of learning targets throughout a lesson.  The idea is for students to use the learning goal as a guide to help with understanding the lesson itself.  The learning target identifies the important ideas within a topic and students won't know what they are unless they are told.  When students are reminded of the learning goals throughout the unit or section, they know where they are headed in their learning.

In addition, learning goals guide students and allow them the opportunity to see where they started and help them gauge how far they've moved towards the goal.  It allows them to determine if they've met the goal, and it helps them take ownership of their learning.  The constant reminders also help students answer the question "What are you studying" or "What are you learning". 

So overall, learning goals provide goals for students and by revisiting them on a regular basis, students can see how well they are meeting the goals and learning the material.  Since learning goals establish a purpose for the lesson, it helps prime students to learn new material and increase their learning because the goals provide a set of expectations.

Now, I'm working on reminding students of the goals by asking students to read the statements and comment on how they related to what they learned the day before, or have them connect the goals with what they already learned in an earlier section, or I ask them what they can tell me about the material we covered so far in regard to the goals.  I just have to start connecting the goals with the activities.  I am learning.  Let me know what you think, I'd love to hear.  Have a great day.

The Importance Of Why.

 

As a teacher, I am always working on finding better ways of doing things and finding out "Why" I'm having students do certain things. So why do we look at the "Why" in math. 

Why is it important to discuss the why in math class as we teach algorithms, rules, and everything else.  Most students can tell you that to divide two fractions, you have to flip one and turn it into a multiplication but they can't tell you why?  

Years ago, I watched an Algebra teacher show students they needed to divide by a fraction and then multiply both sides by the reciprocal to make the denominator equal to one.  She used the proper mathematical language rather than flip and multiply.

There are at least three reasons for explaining the why to students and the best way to do it.  The first reason is that it helps deepen student understanding.  The why helps students better understand the concept. As long as students just learn the algorithms, or process, they don't have the opportunity to understand the concept.  One example is trying to explain why a negative times a negative equals a positive.  Personally, that is something I could never picture on number lines until I finally saw a wonderful explanation I can now use with my students.

Think of the negative times a negative in this context.  You pay rent or a mortgage of $1200 per month, every month.  So each month $1200 is taken out of your account thus it is -1200.  Over a year you've paid out $14,400or -$14,400.  The next year, your boss offers to pay 12 months of your rent instead so every month  is considered a negative because you aren't paying or -12 months to you and the boss is paying out -$1200 per month or -12 times -1200 or you now have $14,400 more in your budget this year.  That is the first explanation I've seen that I can use with the kids.  The why can be done with an example rather than a mathematical proof.  

Second, knowing the why can help students retain what they are learning.  When teachers rely on teaching algorithms only, students are more likely to forget the process or misremember the steps because they don't know why they are doing things. The why helps students remember.  Third, knowing why, helps increase student confidence in their ability to do math.  Many students recognize that knowing why helps connect all the dots that the algorithm doesn't. Furthermore, knowing the why explains why students do certain things in the process.

Often times, when we try to explain the why, we resort to the long mathematical explanations.  When we do that, we loose student attention.  It is better to allow students to try problems before providing the explanation of why it works.  Research indicates that even the best students can feel overwhelmed when they've gotten too much information before they've had enough time to practice a specific topic.  In other words, don't try to give them too much information, too soon, so delay until after students have had a chance to practice or they ask for the why.

So the next time, give students a chance to practice something before you provide either a visual representation or something short and precise such as the example I gave on multiplying a negative times a negative.  Let me know what you think.  Another day, I plan to discuss teaching students shortcuts and whether it is good or bad.  Let me know what you think, I'd love to hear.

Warm-up

If the 57 links when connected make a chain that is 90 feet long.  How long is each link?

Warm-up

If a ship has an anchor attached to a chain made up of 57 links, each weighing 350 pounds, how many pounds does the whole chain weigh?

Quick Math Ideas

Yesterday, I ran a review for the upcoming test in my Algebra I class.  I had 5 minutes left, so I divided students up into groups of two, scribbled equations on pieces of paper, crumbled them up and threw them at the students. Their job was to work the problems on the paper until they got an answer.  When they brought the paper to me, I collected it and passed it out to a different student to check.  All the students were involved and active.

I vaguely remember reading about this somewhere, sometime in the past and it worked.  The students had a lot of fun.  Another way I could have done this was to have each student find an equation from the book and write it on a sheet of paper.  Then they could make a paper airplane from that paper and once everyone was done, they could fly the airplane to another person.  When the person got the airplane, they could open it up, solve the problem, write a new problem on it, fold it back into an airplane and send it off to someone else.  This could go on for several times so each student works a problem and adds to it.

I love keeping a set of index cards in my drawer for a couple of quick games.  For the first one, I've written a problem on the front with an answer on the back.  The answer does not go with the problem and I have just enough pairs for the students.  The idea is that each student is given one index card and they have to solve the problem on the front.  Once they have the answer, they have to find the person who has the answer.  I usually set it up so the problems and answers are in pairs.  For instance, on one I might have 2x + 1 = 7 one the front of one card with 5 on the back.  On another card, the front has the equation 3x + 1 = 16 with 3 on the. back and they would pair up.

Another quick game is a math version of Tic-Tac-Toe.  It doesn't take much to have a few grids set up and ready to go.  The idea is that two students are given a Tic-Tac-Toe grid filled with problems.  One student is designated as the starter and they choose a square to start such as the upper left corner.  This student solves the equation and checks their answer to prove it is correct.  Once they've proven it correct, they mark off the square with a circle or x.  The second student takes a turn, choosing a square and solving the problem on the square.  If they prove the answer is correct, they put down their mark and the students continue until they win or it's a draw.

There is also the QR code game which has a bunch of cards.  Each card has an equation with two QR codes on it.  One of the codes provides the answer and the other tells the students how many points they get if they got the correct answer.  So students work in small groups and one student selects a card.  They work the problem and once they have an answer, they check the answer.  If their answer is correct, they check the points and add it to their total but if they are wrong, they have to put the card back in the stack and a different student selects a card and works the problem.  They continue until they have finished all the cards or the teacher calls time.  The winner is the one with the most points.

The last one provides a physical result that students can see.  Create sheets of strips of paper with equations and cut them up.  The first strip has a problem on it and the student works it to find the answer.  They look for the answer on another strip, place it under the first strip and work the problem on the strip to find the answer. They again look for the matching answer, place it under the previous strip, complete the problem, and look for the answer on a different strip.  The student continues working through all the strips until they reach the strip that says finish.  When they have all the strips in order, they have the teacher check the work and if it ok'd as fully correct, they take the strips and make paper chains out of them.  The chains can be put together with other student's chains, until it reaches around the room.

It is always nice to have a few quick games available to take care of those odd bits of time that pop up or you need something to get students engaged or liven class up.  Let me know what you think, I'd love to hear.  Have a great day.

Help Build Mathematical Identify

The last webinar I took mentioned having students write a mathography to help the teacher see how they see themselves.  It gives us a bit of insight into their perception of their mathematical identity. 

Mathematical identity is defined as how a student sees themselves in regard to being able to do math.  Many will tell you  they are not "good at math" or "they can't do math" because too many believe that you have the ability or you don't. 

Instead, we need to help them see they can do math by helping them develop a mathematical identity that acknowledges they can do math.  There are many factors which contribute to students getting the idea they are not good at math.  They might have heard their parents saying they couldn't do it, or they struggled with certain new topics and concluded they couldn't do it so gave up.

It has been found that if a student has a good mathematical identity, they are more likely to succeed in their math classes.  Unfortunately, most students see mathematicians as older male geeks who wear glasses and are good at math.  They don't see themselves as mathematicians and that is an attitude that needs to be changed.  

Mathematical identity is connected to mindset.  If they have see themselves as good in mathematics, they often have a good mindset, one that is considered a growth mindset where they know they will get it whereas those who believe they are not good at math tend to have a fixed mindset because they don't think they'll ever be good at it.  Part of the process involves helping students adopt a growth mindset to help them develop their mathematical identity.

There are things that teachers can do to help students see themselves as mathematically inclined.  There are four things a teacher can do to help students.  First teachers should invest in maintaining a solid classroom community through out the year by having students work together doing worthy tasks and get all students to work equally together rather than letting one or two dominate.  Second, students should keep a math journal so they can write about warmups, classwork, open-ended reflections, and homework.

Teachers should facilitate classroom activities and act as co-learners with each other.  Finally, it is important to set high expectations for all students so they can learn math and help other learn it.  Students who develop a mathematical identity have teachers who see them as people, who take time to see how their lives effect them, and believe every student can do math.

It also means one has to redefine mathematical success because students need to believe they are capable problem solvers and thinkers and are able to contribute positively to the class.  This means going beyond thinking that success is only mastering algorithms or being able to calculate the right answers quickly.  It means recognizing when students do something right so they feel successful. It might be telling a student they did a good job by showing the idea in a new way, asking a good question, were able to restate a student's words after listening carefully, or talking about a new concept before they write it down, or they broke down a complex task into smaller steps, or they connected several ideas.  

It encourages low performing students when the teacher recognizes their contribution and it helps build their mathematical identity. We need to recognize that not all students learn math in exactly the same way and acknowledge not all of them use the same method.  In addition, we need to celebrate their mistakes because mistakes help us grow which helps a person grow as a mathematical person.

If we can help our students see themselves as "math" people who can do it with a good mind growths, we have done well. Let me know what you think, I'd love to hear.  Have a great day.

 

Google Meet and Jamboard Updates.

I just heard the other day that Google meet has released it's new version including breakout rooms but it is not available to everyone quite yet.  Google did announce the release but it will be for people who use Enterprise for Education and those who use G Suite will see the feature offered later in the year.  The breakout room feature is good news but I'd like to know why used of G Suite have to wait so long.

According to what I've read, Google Meet will allow hosts to divide attendees up into 100 smaller rooms for collaboration.  When the smaller groups are done, they can easily return to the mail room. Google is also giving moderators the ability to visit breakout rooms to check on things which is great and allows teachers to monitor the work in each room.  Moderators will also have the ability to place people in groups manually or randomly, based on need.  Although anyone with a google account can attend the meet, only the meet organizer can establish breakout rooms.  I haven't heard when the breakout room will be released for the general G-suite users but it is on the horizon.

Now for Google's Jamboard.  If you haven't seen it yet, Jamboard is a google product that allows real time collaboration of participates attending a meeting or working in the classroom.  With the distance classes in use or the required distancing in class, it allows more collaboration and interaction.  Jamboard is accessible by Chrome via an app, via an app for the iPads, or via the web based version directly at Jamboard.google.com.  

One can set up Jamboard to use in Google meet by having your admin person set things up so you can pair the two up and then use it during the class meeting.  There are several videos out there to help you get this set up.  In addition, Jamboard can be used with Google classroom since they both access material in google drive which means teachers can assign a jam to students in classroom as needed.  Furthermore, if you chrome, you can arrange for Equatio to be used with Jam by getting the extension.  In addition, Jam works with Screencastify which is another Chrome extension. 

So how do you effectively use Jam in your math classroom?  What can you do with it so it's not just the same old same old? On way which can be done either in class or by distance is to assign students to work in pairs to solve certain problems.  They could be asked to explain how to solve the problem by recording themselves and offering the product to others to see how to do the problem.

I saw Holly Clark of the Infused classroom books posted some suggestions on using Jamboard in different ways on Wakelet. There are a few for math to use on specific topics.  There were suggestions from early elementary to high school which could be used easily.  I especially liked the middle school ones.  Since I ended up on Wakelet and checked various collections on Jamboard.  I found some really nice ones with some great information.

Joanna Garza has a collection of instructional items including ones on explaining how to play live partner games on Jamboard, or running a live collaborative whiteboard session with audio using google classroom, meet, and jam board.  The one that caught my attention was the one on turning worksheets into interactive digital pages.  It provides a nice start.

This link takes you to the page filled with collections of ideas for Jamboard on wavelet. It provides a great list of collections to help you become the master of Jamboard.  Let me know what you think, I'd love to hear.  I can tell you , I'll be exploring these in more details to make the class more interactive.  Have a great day.

Warm-up

If it takes 3.5 pounds of grapes to make one quart of jelly, how many pounds of grapes are needed to make 2 gallons of jelly?

Warm-up

If it takes 4.75 pounds of tomatoes to make one quart of tomato sauce, how many quarts of sauce can you make from 87 pounds of tomatoes?

What is a Mathography? Why Use One?

 

Today I attend the first webinar in a series of four devoted to helping developing collective efficacy in math while engaging students in remote or hybrid settings.  I thought I could get some ideas to use in class to make it better and more interesting.  I came away with so many ideas after the first meeting.  

I came away with several things but they circled the concept of student math identity. Math identity is defined as how a student sees themselves in regard to their ability or lack of to do math.  Part of this identity is based on their perceptions based on the assignments they've had to do over the years.

One activity mentioned that helps a teacher learn more about how they see themselves is to ask them to write a mathography. A mathography is similar to an autobiography in that they talk about themselves and how they feel about math.  In the assignment, students are asked to tell whether they like or dislike math and explain why they fell that way.  They are asked if they are "good" at math and explain why they think that.

They could also share if there are any areas of math they like or dislike and what is it about that area of math that they like or if they don't like a certain type of math why.   Personally, I don't like statistics mostly due to not liking the instructor I had in college who wouldn't clearly explain things so I never took another stats class again.  I'm sure there are others there who dislike a particular area for the same reason.

They could be asked what makes math awesome or horrible for them.  They could also be asked what experiences they've had in math that made them like it or dislike it and why those experiences made them feel that way.  Let them take time to describe their most memorable experience in math either good or bad.  

One should also take the time to ask students how they feel about taking this particular math class and what do they think they might learn.  What do they fear about the class? Ask them that if they could set up a math class, what do they think should be taught in it?

If you want to delve deeper, you could ask them what do they remember about their early experiences with math?  Did they feel awesome at any one topic?  Did they show others how to do it? Were they proud of being able to show others how to do something? If they no longer like math, you could ask what happened to change things or did they struggle every year?

You might also ask them to talk about the things they like to do and have them explain why they like to do it.  You might also have them tell you what they are good at and what they aren't as good at because you can take the things they like to do or are good at and connect math to their interests to show them how math relates to everything in life.  

This writing assignment will give you a lot of information about the student, their past experiences, and their thoughts about their abilities in math.  With this type of information on each student, it gives the teacher enough information to look at ways to reach all their students.  It helps to have a starting point for every student.  Let me know what you think, I'd love to hear.  Have a great day.

Improving Engagement Via Breakout Rooms.

One of the primary ways used to teach students when schools are closed due to the coronavirus is by using some sort of video conferencing program.  It is admitted that using video conferencing programs can sometimes make it more difficult to have students gather in smaller groups to work on specific questions or problems.  Fortunately, there is something called a breakout room that allows students to gather in smaller "rooms" to do collaborative work.  

A breakout room is a smaller room where students are sent to do their group work.  If one is using zoom, this is fairly easy to do because breakout rooms are an inbuilt part of the program. The person setting up the meeting needs to enable the breakout room feature before trying to open any.  Furthermore, one can assign students to breakout rooms ahead of time so the teacher does not need to do it during class time.  The teacher, who is the host, is the only person who can set up the breakout rooms. If the meeting is being recorded locally, the conversation in each room can be recorded but if the recording is being done in the cloud, only the main room can be recorded.

Unfortunately, not every school uses Zoom, some use Google meet for class and it does not have an inherent feature allowing for breakout rooms.  I've heard Google is working on adding the ability to create breakout rooms but I've not heard they did it.  Fortunately, there are ways to work around this by creating several other hangout rooms labeled as breakout room 1, breakout room 2, etc.  Then create a google doc with all the links to the various breakout rooms so when it is time to split up, students can click on the link and head off to the smaller room.  

The other way to do breakout rooms in Google meet is to download one of two  extensions for the chrome browser.  The first is Google Meet Plus which allows people to create breakout rooms but everyone who is going to participate via this extension must have it installed on their computer.  In addition, the basic version is free but the Pro version requires a monthly fee.  It has received a four star rating based on 189 reviews.

The second one is Google Meet Breakout Rooms and allows the teacher to create breakout rooms based on nicks, can be viewed in tile or tab format, allows people to be pre-assigned or done during class, allows the host or teacher to broadcast video and audio to all rooms at the same time, integrates with Google classroom and quite a few other features.  The only person who needs this extension installed is the teacher. Students may download it if they want but it is not necessary for students to participate.  The person who created this extension recommends teachers try it out with friends first because there is a bit of a learning curve.  This extension has received a four star rating based on 69 reviews.  

You may be wondering what are some ways you can use breakout rooms in math.  Breakout rooms are great for small group work, jigsaw activities, turn and talk, think, pair share, or working together on problems where each person has a different problem but the same answer.  Any think you do in class in small groups, can be done in breakout groups.

Breakout rooms help increase student engagement in distance classrooms.  Think about using it if you need to teach by distance.  Let me know what you think, I'd love to hear.  Have a great day.

Back To School.

Just recently, my principal reminded the staff that although we are green, we need to plan lessons should we suddenly have to switch back to hybrid or remote due to cases.  I don't think we'll have a problem due to the restrictions the village has in place but it could happen.  

Last spring, when school suddenly went distance, we relied on packets that didn't have to be returned so most students didn't bother doing anything.  A few did some things and send in photos or texts to show their work but no-one chose the real world math assignments I provided.  The principal stated if we go red, packets won't cut it.

Although I've been researching the topic of teaching remotely, I do not feel I know enough so I went to the state website to see what professional development classes they off.  It turns out they are offering two classes that I think will be worth my while.

The first class is based on the newly published Distance Learning Playbook.  It is taught by the authors of the book over a four webinar series.  The first week looks at considerations for creating both units and modules that are engaging.  

Then the webinar goes on to explore synchronous vs asynchronous, learning goals and success criteria, aligning tasks appropriately, with another webinar on the health and well being of both student and teacher, and ways to improve student - teacher relationships. The final meeting covers ways to carry out assessment both formative and summative, and feedback effectively in a distance situation.  One of the other teachers suggested it because our school, like so many others, is open mostly but could easily switch to being totally online and I need to know more on how to do it.  So I'm taking the course.

The other one I'm taking is on teaching math remotely or in a hybrid model.  It covers building student math identity in individual and group settings, learning to identify areas where students need additional support and prioritizing methods of instruction to increase student learning as much as possible.  It explores creating situations for mathematical discourse in both hybrid and remote classes, selecting tasks that emphasize both problem solving and reasoning for these two situations, when and how to use multiple representations to help students connect ideas.

The first one is a general course while the second is math specific and I think the two combined will provide me with a better foundational knowledge should we move to online.  These two classes will give me that bit I need to improve my lessons for both in class or remote.  In fact, the middle school math teacher is currently taking three classes towards her masters degree and she asked me to share what I learn with her because she wants to know more about creating lessons for the uncertainty of the times.

As I go through the classes, I'll share the points which I think are great for use during lesson planning.  I know I'll be connecting pieces from each class into things I can use.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 How would you go about finding the volume of the fruit jelly if all you had was a 3 by 5 inch index card?

Warm-up

You have a ruler and a doughnut.  Explain how you would find the volume of the doughnut using only the ruler. 

How To Make Activities More Doable During Distance Learning.

Many of us have taken distance classes so we know for us, it often means sitting through a video based class for a couple of hours, scribbling down notes while trying to process everything the professor said.  We know that won't work with most of our students and it isn't necessarily a best practices method for teaching math.

We face the big issue of trying to construct lessons that will involve our students in something more than listening for 55 minutes while you lecture or at least try to have students reply. Fortunately, there are some ways to increase student involvement in class but it requires a bit of forethought and planning.

If you teach geometry, have students bring cereal boxes to class to measure calculate volume or surface area.  Ask them if they have soda cans, bottles,  or circular oatmeal boxes so students can relate formulas to real items rather than something out of a book.  If your school is sending materials home with lunches, see about including rulers, protractors, paper, and scotch tape so students can create their own nets for any of the standard 3 dimensional shapes.  

What about sending maps home so students can use ratios to calculate the distance between two cities using the key on the map.  If it is 1 inch = 50 miles, students can use the ruler to measure the distance between say Chicago and New York, set up the ratios to find the total distance a crow might fly to get there.  Take it one step further by having students look up the average speed of say a crow and let them figure out how long it would take it to fly the distance.

Let students plan a meal for their family and then using on-line sites or a printed list, let them investigate the cost of each item so they can determine how much a meal might cost.  In addition, ask them to scale up or scale down the recipe to feed say 2 people or 80.  Real life math.

Since most student have phones, let students call different phone copies to find out the costs of a couple of plans to determine which is better, or ask students to call the local cable or satellite companies to get the cost of various packages such as cable, internet phone, etc so they can figure out if buying them separately versus the whole package is a better deal.  Let them look at satellite costs to see if buying a package with everything is better cost wise versus buying a basic package and paying extra for one or two channels is better.

This is the perfect opportunity for the students to work together to create a "newsletter" to share various mathematical topics with their parents.  Each student can choose a topic and create an article to explain it so their parents can read about it.  Have your students select a stock from the stock market.  Each day, they can check the price and they can create a scatter plot over a two to three week period.  At the end of the time, they can calculate a line of best fit for these points.

This is the perfect situation to use twitter, facebook, or instagram type activities so students can share the results of various activities, questions, discoveries, impressions.  Matt Miller from Ditch The Textbook has templates for these social media outlets.  Take advantage of student knowledge of social media to engage them with questions, problems, etc.

Look around you.  Check on what the students have access to.  Look at what things students might have around the house to incorporate into the lesson so they are more engaged. Let me know what you think, I'd love to hear.  Have a great day.