Math And The Oscars.

 

Just recently, I ran across several articles about a man named Ben Zauzmer who has been using statistical analysis methods to create a mathematical model that could be used to predict the winners of the Oscar. He has been using his model since 2012 to make these predictions and is still doing it. 

When Ben was studying applied mathematics at Harvard, he decided to use statistical methods and data to handicap the Oscars.  Since around 2011, he has been using his models to make predictions with relatively good results.

It started back in 2011, when Ben watched a film called Moneyball. The movie was about how the Oakland A's baseball team used math to pick a winning team. He was really interested in the topic and it lead him to looking for the same type of prediction system for the Oscars but there wasn't anything.  

He says he uses anything he can that can be quantified such as Rotten Tomatoes scores, previous award shows such as the Golden Globes and BAFTA's, and any other aggregate data bases such as Metacritic. In the end, he chooses the films that have the best statistical chance of winning.  Since some of the voting is based on human nature, his predictions are never 100 percent but he has done reasonably well. Furthermore, he only makes predictions for 21 of the 24 categories and never makes any predictions for the three short film categories.  In 2018, he predicted 20 of the 21 winners but he is not usually that accurate.

He also looks at the previous year's Oscars to see how well each of the different factors effected the accuracy of the results and uses this to adjust the weights of the predictions. Every year, he looks at this and readjusts the weights for his current calculations.  Most people think that box office numbers would be a good indicator but it turns out there is really no correlation.  Since he began doing this in 2011, he has had a 77 percent success rate.

He has also released a book explaining the whole process.  His book, Oscarmetrics:The Math Behind The Biggest Night In Hollywood, talks about the process of how his models came about, the history of the Oscars, and he tried explaining everything so you don't need a degree in math to understand it.  So check it out if you want.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

A rat can survive a fall from the top of a five story building.  If a 5 story building is 52.5 feet, how tall is one story?

Warm-up

 Did you know that your heart pumps enough blood to fill 40 bathtubs every day.  If it takes 80 gallons of water to fill a bathtub, how may total gallons of blood does heart move every day?

Newest On Studying For Tests.

I'm sure you remember your days in school.  You used to highlight important material in your books and notes, you studied all your notes till you knew them inside and out. Then you took the test and didn't do as well as you thought you would.  Quite soon, Daniel Willingham, a psychologist will be publishing a book on what he considers the best ways to study for a test.  

According to his new book, most students study incorrectly when they prepare for tests.  He says we are doing it all wrong.  In fact, most of the traditional ways we learned are wrong.

To begin with, he feels the traditional methods used in class are bad to begin with because the lecture style class makes some assumptions that may not be correct.  The style thinks that students know how to establish priorities and they know how to schedule, they can read independently,  they are willing to work rather than procrastinating, and they can memorize material.  

Students are not born with these skills and most are not taught them in school.  In fact, by the time they reach high school, teachers assume they know how to do study. When it comes to preparing for a test, the number one method used by students is to read over you notes.  It makes you feel prepared because you have gained a comfortable familiarity with the notes but you haven't really learned it.  

A much better way is to create questions  that require you to remember the material since this is closer to the way your brain works.  You also provide the answers but the answers have to be separate so you don't look at them. These questions could be set up as flash cards with answers on the back or as a practice test. This is one of the best ways to prepare for a test.

He points out that if you are unable to remember it, it means you didn't learn it in the first place. Fortunately, there are things one can do during a test to help coax the material out.  Since memories are organized by theme, it is possible to do a brain dump such as listing all the animals you can remember in 30 seconds and then give a nudge with a word such as Australian animals which helps your brain narrow the choices. You can do this by listing everything you know on the topic and then using the question to help remember and narrow down the choices.

On Monday, I'll share what he has to say about reading difficult text and textbooks.  Let me know what you think, I'd love to hear.  Have a great day.

Math and Algebra By Example

 I visited a site called Serp Institute the other day. They have a couple of  free programs, Math by example and Algebra by example which can easily be incorporated into the classroom.  They are free if you download them directly which is nice.  I'll be looking at both today o you get a chance to see how they work and how they might provide supplemental help to the class.

The idea behind the two programs, is to help students learn to solve, analyze, critique, and discuss problems by looking at examples. In addition, the selected problems are designed to help students overcome misunderstandings both small errors, and fundamental. 

Students are provided with examples both correct and incorrect.  They analyze the correct ones to learn how to do the problems and the incorrect ones to figure out what was done incorrectly, so at the end they are able to work their own problems.  

Math by example is designed for fourth and fifth graders and addresses 125 topics and concepts from place value, fractions, and decimals, to geometry and ordered pairs, and more. The assignments are such that they are not required to be given in any particular order so they can be used to supplement assignments or be given instead of a normal assignment.  There is an assignment list which breaks down the assignments designed for fourth and fifth grade and provides the actual topics available.  

Algebra by example is designed to help teach algebra and looks at 40 different topics.  These examples are designed to specifically target normal student misconceptions, remediate errors especially repeated ones, provide flexibility while meeting common core standards, and promotes mathematical discussion.  

The example given on the example card gives the directions for the problem "Using the distributive property, rewrite in simplest form".  The examples shows the work which is 4w(5+12) = 20w + 48  with the statement "Pablo didn't rewrite this expression properly".  Then there are two questions. The first says "What did Pablo forget when distributing the 4w? and the second is "What should Pablo's final expression be?"  Finally, students are given a similar problem to correct on their own.

This site comes from Temple University in conjunction with several school districts.  It states the material is based on research so it provides what is needed to help students.  All you have to do is sign up and you'll have access to downloading any and all materials for free. If you need more material to help students learn to analyze errors, check out this site.  Let me know what you think, I'd love to hear.  Have a great day.

New Resource

 I was looking for something on the internet this morning and stumbled across this site with over 1900 resources for teaching math.  I love having resources available so I can find the perfect one.  This site, the Scitech Institute, out of Arizona has a list of math resources for grades K to 12.  Imagine having access to a list so long.

The list is subdivided into the strands of Algebra, Arithmetic, Calculus, Geometry and Trig, Stats and Probability, and other.  The calculus section only has 23 resources listed but the rest range from a couple hundred to over 600 for the topic.  Talk about having fun checking out things.  I selected algebra since I'll be teaching it this semester and it has 406 listings.

There are the usual ones like prodigy and Khan academy but they also have the not so usual ones like Kennedy Center.  Yes, that is right, the Kennedy Center with something on "Patterns across the day - Fibonacci in nature and art."  I pulled this one up so that I could check it out. It has everything from preparation to instruction. It has the standards, the websites, materials, everything and it provides the openers, the lesson, and the closing for the lesson.  It is quite complete. 

In addition, there are links to online free textbooks, links to youtube videos for short videos from Arizona State University, Mathalicious, and others.  The mathalicious videos often show real world applications of topics such as using piecewise functions with candy consumption or coupon clipping with percents and proportions.  There are links to Inside Math from the University of Texas at Austin, Geogebra materials, and so much more.  34 pages worth of links so it takes a while to go through them but the list seems quite comprehensive and it has a good search engine.

If you go to advanced search, you'll find a search bar that allows you to narrow things by grade level, math topic such as estimating and rounding, imaginary numbers, order of operations, and the list tells you how many resources they have for each topic.  There are 21 entries for negative numbers but only one for imaginary numbers.  In fact, you can narrow by both grade and topic which helps because certain topics such as geometry are listed together and you need to use the advanced search to help narrow things down.  Furthermore, you can narrow it down further by type of resource such as lesson plans, online game, etc, or you can go for the specific organization that produced it.

This site is almost like having Christmas hit because it has so much.  I plan to use some of these resources in my classes this semester.  Check it out and let me know what you think, I would love to hear.  Have a great day.

Warm-up

 

In 1912, the first person was arrested for speeding.  They were going a fast 12 miles per hour in a 10 mile per hour zone.  How long would it have taken them to drive from Los Angeles to San Francisco?  (The distance is 382 miles.)

Warm-up

 If the amount of paint needed to cover the worlds largest airplane can cover 10 basketball courts, how many square feet of paint is that? Hint: A basketball court is 94 feet by 50 feet.

Activities To Do At Learning Stations

 

Now that you know more about learning stations and how to introduce them into your classroom, you need a list of activities to use.  So today, I'll be reviewing quite a few activitieors to help you get started.  Sometimes, it is difficult to come up with activities so I'll help with that.  

One station should be the teaching station where the teacher works with students in a small group either providing scaffolding or enrichment.  The lesson here should consist of a hook, guided practice, and a check and review on assigned work.

As stated earlier, one station can have task cards. Cards that have the problem so that students can work on each problem and the answer should be easily available so they can check their work.  

Another station can have games that involve dice or cards.  I've used dice before to help set up the numbers for a binomial multiplication problem, or a trinomial.  The cool thing is you can find dice that have up to 20 sides. If you have four to five dice, you can use them for students to practice order of operations.  

On the other hand if you have cards and students who need some practice with cards, try gains and losses where students start with 15 points. Then one student flips over the top card of a deck that has had all the face cards removed and if the card is black they subtract the value from 15 but if it is red, they add the value. At the end of the game or time period, the one with the most is the winner.  You can also do the multiplication of binomials with cards so black is negative and red is positive and you count the face cards as 11, 12, and 13. 

Have a station that has real world applications of the topic or concept students are learning.  For instance, students can calculate pitch for a roof, grade for going down a mountainous road or looking at what happens when you change the dimensions of a room using algebra.  It takes a bit of looking but these activities can be found. Check out Illustrative Mathematics, Yummy Math, YouCubed, or look for real world activities that have them collect and interpret data.  

One station should include some sort of online activity be it Desmos, Khan academy, have students create a flip grid video talking about how to do something, IXL or other site.  The lesson can be practice, learning how to do something, a quick quiz either in Khan academy, IXL, or even google forms.

These are just a few ideas that will help you get started with Learning stations.  Let me know what you think, I'd love to hear.  Have a great day.  

More On Learning Stations

If you remember, I mentioned learning stations as one of the ways of differentiating instruction.  This is something I've had to learn to implement because it was not part of my teacher training.  In fact, learning stations and learning centers were something done only in the elementary classrooms.  This year I have 12 students spanning grades 7 to 12 with abilities from quite low to fairly high and this is a way I can meet the needs of everyone.

Learning stations can be used for differentiation, providing spiral practice for concepts, while helping students learn to take more responsibility for their own learning.  In addition, technology can provide some of the activities for students. Don't forget, when you have students working at the learning stations, you can pull small groups of students out for specialized instruction or additional support.

One of the best ways to introduce learning stations is to do it once a week.  Set up one day a week such as Fridays so students have the whole period to work through the stations.  If you set Friday as the day, you can use it to have students review the whole week's material.  For instance, station one has them review Monday's material, station two for Tuesday, station three for Wednesday, and station four for Thursday.  You can have a fifth station that everyone visits so you can provide small group instruction, scaffolding, or extensions.  

As far as rotation goes, if your students have difficulty moving from station to station, you can move the materials from station to station or have the stations set up so they can all be done on the computer.  It depends on what is needed.  I prefer to only do one or two activities on the computer because it is hard to do a quick assessment as they work but if I can spend a bit of time with them, it is easier to do a flying assessment.  Make sure the groups are small so if you need to, you can do double or triple copies of stations.  For instance if you have 30 students, you might have two of each station so no more than five students are at each station.

When setting up the stations, think of having one where they work with the teacher, others with regular type assignments, technology based activities, and some hands on items.  Make sure to have a big, loud timer so when it goes off, students hear it.  If you plan to have students rotate stations, make them practice rotating by setting a one minute timer and explaining expectations before they move.  

When you set up the groups, let them stay in the groups for the first two or three weeks so they get used to working and rotating.  In addition, think about how long each activity will take. You want the activity to take as long or longer than the time planned at the station so no one finishes early.  You don't want one station to take 5 minutes while another takes 20.  It needs to be fairly even.

Always change things up while keeping them the same.  For instance, if you have a technology component, always have the technology component but change the program they use each week.  In addition, have some way for students to self-check work with an answer key, form, or QR code. Next time, I'll discuss some more details about what activities to use with learning stations for middle and high school students.  Have a great day.

More On Task Cards.

Using task cards in math is one of the suggested ways of providing differentiation.  You can always pop onto a paid site to find them or you can make some yourself.  Although making them yourself may take more time, you get cards that have the problems you want.  So today, we'll look at the different ways task cards can be used in class. It is always nice to have a variety of ways they can be used.  

A task card is a card about the size of a index card with one problem or task written on it. A set has between 10 and 20 cards and each student has a sheet to write answers on and access to the answer key so they can self check their work. Later on, I'll explain how to make task cards on power point.  In addition, task cards are a good way to have students practice what they've learned and provides independent practice.

One way to get students up and walking around is to place the task cards on the wall around the classroom or in the hall. Students can either work in pairs or alone for this activity. Pass out one answer sheet to each student or each pair of students.  Students can start at any place they want but if students need a bit more structure, assign them a starting number.  So they start at one card, work it, and move on to the next.  Eventually, they will end up back where they started. Once they are done, they can either check the answers with the answer key or they can turn it in for a grade.  It is up to the teacher.

Another use is to have sets of task cards in small baggies.  These task card are for the students who finish first and need something to do.  The material on the task cards is either what they have already learned (a review) or it is composed of problems for the material they are currently learning. They work through the problems, write the answers on the answer sheet, and either check it with the answer key or turn them in for extra credit.

Of course, task cards can be used as the warm-up or bell ringer as something different. They write their answers on the warmup paper and if you don't want to deal with 10 to 20 task cards, settle on between three to five to use.  Again, have the answers available for students to check their work.  Furthermore, task cards can be used as exit tickets so the teacher can do a quick assessment of where they are. If you don't want to collect all the exit tickets, have students write their answer to the task card on a sticky note and pop it on a piece of paper by the door. This way, you can check the answers later.

Remember, if your school is a one to one school, you can make all the task cards be digital so students can pull them up via google classroom or other learning management system.  They can do their answers on the computer or on a physical answer sheet.

If you use stations, you can place 4 to 6 task cards at each station for students to do. So what if you don't have tables in your room, you can group student desks into clusters of 3 to 5 desks so you have stations.  Students begin at one station and work on the problems.  The teacher has a timer going and when the timer goes off, students rotate to the next station and work on those problems.  This continues until students have completed all the stations or the time is up.  One thing, if you allow students to work together at the stations, they get to practice cooperative learning.

Task cards can also be a nice part of direct instruction.  Show a task card on the board or digitally.  Allow students to complete the problem, and when they are all done, work the problem so students can check their work. You can have students work the problems on white boards and show the answer to you when they are done.  On the other hand, if you want to use only physical task cards, spread them out on a table, have students come up and take one card to work on. When they are done, they return the card to the table and choose another one.  After a certain amount of time, go over the answers with the class.

What about doing Quiz, Quiz, Trade with your students.  Give each student a task card and they work that problem out.  After everyone is finished, they partner up so person 1 asks the other person the question on their card.  The other person either works it out and shares the answer or is allowed to say "I don't know" if they don't. Person 1 either says good job if the other person got it right or explains how to do the problem.  Then person 2 asks the question on their task card and person 1 answers it. Person 2 praises the correct answer or explains the answer if it was incorrect.  Then students trade cards and find a new partner and do this again.  10 to 15 minutes is a good amount of time to schedule for this activity.

Make a Jeopardy game out of the task cards.  In addition, if you complete your lesson and there is time left at the end of class, think about pulling out the task cards so students can practice working problems.  So now you have a variety of ways to incorporate task cards into your math classroom.  Let me know what you think, I'd love to hear. Have a great day.

Warm-up

 There are about one trillion (1,000,000,000,000) web pages on the internet.  If that is about 140 pages for each person on earth, how many people are there on this planet?

Warm-up

When glass breaks, the cracks move faster than 3,000 miles per hour.  How many feet per second is this?

 

Differentiation Strategies To Use In Math.

 

Last time I looked at differentiation in general and this time.  Although the general framework is the same,  I'll be looking at strategies you can use in the math classroom to meet the needs of your students.  Sometimes what works in Language Arts or Social Studies doesn't always work in math.  It is important to have an arsenal of strategies to use in the classroom. 

One of the easiest strategies is to use task cards.  The task cards have different levels of problems so students can work on cards that have the appropriate problems that are just a bit challenging. If you color code the cards according to level, it allows students to move to another level when they feel as if they are ready.  I'll do more on task cards a bit later in the month.

Remember to give students a choice in how they will show they learned the material or as a general review.  They might write their own test questions, create a test review, play games, or make flash cards.  Yes, we can have students create flash cards in high school such as binomial multiplication, trinomial factoring, factoring in general, formulas, etc.  

Another possibility as far as choices is either using menu's or choice boards so students are able to select what they want to do.  Menus are better for assignments because you can offer a choice of which problems they do while choice boards are more for showing what they learned.

Think about using learning stations in the classroom. Learning stations and centers are considered different entities.  Centers are used to refine a skill or extend understanding of a concept while a learning station work on on different tasks that are all linked.  Students are not required to visit all learning stations, only the ones that have activities or tasks related to reach mastery.

Also consider using guided notes because it makes it easier for many students to copy down notes from the board.  If you have a student who has a lot of difficulty copying notes off the board, the notes will be more filled in before being given to the student but if they are great at copying notes, their paper will have more blanks. One way of using guided notes is by having students create an interactive notebook filled with foldables. The notebook can include a table of contents and/or be used during a test to help those who need a bit more.  In addition, it is an activity that has students folding, cutting, gluing, and writing so it helps keep hands occupied.  

Don't forget to look at technology because many apps and programs offer differentiation based on the students pre-assessment. Students who need more help will get the remediation while those who are more advanced will be given more challenging problems.  Technology also offers games designed to improve certain mathematical skills or have a chance to practice certain skills while receiving immediate feedback.

When talking in class speak slowly and clearly, especially if you have any English Language Learners.  This allows students to hear and process everything you say rather than tuning you out because you are speaking too fast.  

Think about using open ended projects.  Give students a list of projects to choose from so they can select the project that interests them.  Include the rubric or rubrics that will be used to grade student work.  The rubric might be different for a student who struggles versus the one who whizzes through all the assignments. 

This is just a few suggestions to get you started.  Remember, if you aren't using any of these strategies, you can start with just one.  I love using interactive notebooks because students have fun filling them out and sometimes they even add color to make their notes more interesting.  Let me know what you think, I'd love to hear. Have a great day.

General Introduction To Differentiating In The Classroom.

 
It seems like we have math classes with such a variety of abilities hat it is natural to want to differentiate.  I know that I want to differentiate especially since I usually have students who range from needing lots of help to those who can whiz through any material I put in front of them. 

Ideally, we should be able to tailor instruction to meet the individual needs of the students but in reality we can't always manage that so we'll look at what we can do.

To begin with there are four elements involved in differentiated instruction.  The first is content or what skills, knowledge or understanding do we want students to learn, second is process or how do we want students to understand or make sense of the material.  The third is the product or how will students show they have learned the skill, the knowledge or gained understanding and the fourth is the affect or how do their emotions or feelings impact their learning.

Lets go into those a bit deeper.  For content, we look at formative assessment to see where they at, think about using materials that have different reading levels, have materials on tape/cd/or computer read to them so they can follow along, present the ideas in a variety of manner, assign reading buddies, use multi-leveled questions, use small groups to monitor or reteach the material, use modeling, or flexible groups.

When talking about process, look at tiered activities, stations, manipulatives, time lengths that are variable depending on ability of students since some students need more time to finish and assignment than others.  learning or math journals, graphic organizers, use jigsaw or think-pair-share, learning menus, web quests, or labs, and manipulatives. 

Students can show their understanding through the use of choice boards, quiz, test, podcast, blog, presentation, use rubrics that are at the level of the student,  or encourage the student to come up with a way to show what they learned. 

Differentiated instruction does require that teachers plan ahead. It is suggested that teachers decided exactly what knowledge or skills students are expected to master due to the instruction. Then the teacher should conduct a pre-assessment to see which students have already mastered the concept or skill and which ones will need additional support.  Finally teachers need to determine which strategies will help all students learn. 

If you look at the process in more detail, the teacher sets the learning objective, conducts the assessment, introduces the topic, uses various effective teaching strategies, assign learning activities, have resources available, think about the product students show their mastery, how will students be grouped and possible extension activities for students who either have already mastered the material or master it quickly. 

This is a general introduction to the topic.  Friday, we will look at this topic in more detail.  Specifically how to implement it in the math classroom because sometimes that can be much more difficult.  Let me know what you think, I'd love to hear.  Have a great day.

Flash - At Least One Of Euler's Equations Does Fail!!!!!!

 For the past few centuries, mathematicians have been striving to create equations that model the motion of fluids.  Some of these equations such as the one that models the ripples that cross a pond, have been used to predict the weather, help design better airplanes, and help explain how blood circulates through the body.  

Although the equations can appear quite simple, the answers can be a lot harder to explain, in fact, almost ridiculously difficult. One of the oldest of those equations was formulated over 250 years ago by Leonhard Euler. It described the flow of a fluid with no viscosity, no internal friction, and can't be compressed into a smaller volume.  Practically all of the equations dealing with nonlinear fluids have been derived from this formula.

Unfortunately, no one is sure if the equation actually models ideal fluid flow.  Mathematicians have been looking to see if there are any points at which it fails, where the equation breaks down.  Now there are two mathematicians who have shown that one particular set of his equations sometimes does fail.  It does not solve the problems with the more general version but offers hope.

The 177 page proof is the result of 10 years of computer based research. This does make it hard for other mathematicians to check the proof and it has people looking at the question of what makes a proof along with the idea of how viable is it if the only way to prove something is with the use of a computer.  

As far as Euler's equations, if you know the location and velocity of each and every particles in the fluid, it should be able to predict how the fluid changes and evolves over time but mathematicians want to know if this is true for all cases. If at any time the values shoot up to infinity, this singularity then blows up at that point and fails.  Once that singularity is found, the equation no longer can calculate the fluid's flow.  Everything becomes more complicated if you try to model a fluid with viscosity. 

In addition, it is very hard to prove a singularity of this type because most computers are unable to compute infinite values. A computer is able to get close but cannot compute the actual values so it is not an actual proof. Instead, mathematicians have to go back to a previous point that gives them a self-similar solution.  Two mathematicians came up with a possible point but were unable to prove it so they went back, looked at things and developed a hybrid approach.  

They decided they were proving that if you took any set of values close to the approximate solution and put it into the equation, the results wouldn't be that far off.  So they had to define closeness before they could create a complex inequality using terms from rescaled equations and the approximate solution.  They also had to make sure that everything came out balanced to something small. 

They ended up breaking the inequality into two parts. The first part could be solved by hand using techniques from the 18th century but the second part required the assistance of a computer due to the number of calculations and precision needed. Using computers to help prove in this particular field is relatively new and will take a while before people are able to check their work.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

If your orchard produced 87,250 pounds of pears and each pound contains 2.5 pears, how many pears did you harvest?

Warm-up

 

If each pear tree produces 1,550 pounds of pears, how many pounds does your 23 pear trees produce?

Two Quick Assessments

Today, we'll be looking at two quick assessments that are quick and do not need much preparation.  At the same time, you'll have a chance to check for student understanding.  One I mentioned briefly earlier this week and the other is something that can be used at any time including as an exit ticket.  

Earlier this week, I mentioned Stop and Jot but I wanted to go into more detail and talk about different variations one could use.  Stop and Jot is as it sounds, students stop and jot down their thoughts. When students write their thoughts down, it helps promote both learning and retention.

The way to implement Stop and Jot, begin by having students draw a rectangle box on their notes or worksheet.  At some point during the lesson, stop and ask students to respond to a question that you pose. Once everyone has a chance to write down their thoughts, ask for one or two volunteers to share their thoughts or read the responses later.  

The stop and jot can be used at any point during the lesson as a way of providing time to process the information and to help students with their note taking.  If it is used before the lesson, it helps activate a students prior knowledge, if it done in the middle of the lesson, it helps students make sense of the material, can be used to check for student understanding, and after the lesson, it helps students clarify their thoughts, make connections with previously taught materials, and find relevance. 

Best of all, there are several variations of this activity available.  One is Jot-Pair-Share.  In this one, students jot down their thoughts individually.  Then they break up into pairs to share their thought and the last step is to share with the whole class.  Another variation is the quick jot in which students have between a minute and a minute and a half to record their response to a specific prompt or question.  If students need to record important information from the textbook or from a video, use the stop and fill. Students are given a sheet with blanks so they can fill in the material.  One can always do the group jot which as students broken up into larger groups and they share their thoughts from the stop and jot activity. Students are expected to expand their own notes based on this discussion. Lastly is the jot survey where students write their responses on sticky notes and place the notes on a poster containing a question or topic.

The second activity is called Triangle - Square - Circle which you may have seen before with a different name. This one offers students to opportunity to reflect on their learning while they are processing information from the lessons. This is used at the end of the class period to close the lesson or as an exit ticket. It can also be used right before an assessment so the teacher knows what students need to review most. When the lesson is done, have the students draw a triangle on their paper where next to the triangle they will write down three things important points from the lesson or the reading. Then they will draw a square and next to it they will write down anything that "squares" with their thinking or understanding.  Finally, they draw a circle on the paper and next to the shape, they will write down anything that they have questions about.  

A slightly different way to do this activity is to have students write down three things they need clarified next to the triangle and for the circle students can write down how the topic either connects with prior knowledge or with the real world. 

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

Evidence Based Math Instruction Part 2.

This past Monday, we explored the first two strategies recommended for evidence based math instruction. Today, we'll look at the other two.  I love learning new things.  Friday, we'll look at a couple of activities to help teachers do a quick assessment.  

The third strategy is schema based instruction.  This is considered one of the most effective strategies to help students learn to do word problems.  This also helps students who struggle in math. 

The idea behind schema based instruction is to teach students to recognize patterns in word problems rather than key words.  There are two types of schema for word problems.  The first is additive which includes addition and subtraction type problems while the second is multiplicative which includes multiplication and division problems.  They use the way the word problem is written to identify which scheme it is.  Schema based instruction helps students identify the pattern so they can connect it to the best way to solve said problem.  Once they've identified if it is additive or multiplicative, they then use either a diagram or an equation to represent the information. 

Research indicates that students who have been taught using schema based instruction are more likely to be able to solve both familiar and new multistep problems.  Students are taught to identify the pattern by looking for unique features.  They are also taught the vocabulary associated with each type of schema.  In addition, students are taught how to represent the information in the problem visually and show multiple ways to solve the problem.

The last strategy is by using peer interaction where you pair students up to work together and discuss the math.  Working together might happen after they've completed independent practice, or during.  These discussions help students develop student mathematical language and vocabulary. In addition, the discussions can help them become more aware of problem solving via the way they solved it or how others solved it.  

It is important to teach students how to conduct peer-to-peer discussions.  Take time to establish class rules for these discussions and establish some prompts to help students get started.  Encourage students to compare the ways they solved the problem while contrasting their approaches.  

If you've never used any of these techniques, start with one until it becomes part of the routine.  If you can implement all of these, your students should do better.  Let me know what you think, I'd love to hear.  Have a great day.

Evidence Based Math Instruction Part 1.

Evidence based math instruction is quite the same as data driven instruction even though it sounds like it.  Evidence based math instruction is defined as practices and strategies that have been identified as the most effective ones based on rigorous research.  Based on the results, it appears that students have positive math outcomes, provides data to show improvement, fewer wasted resources and less wasted time, and it is easier to convince students to use a program. 

There are four suggested strategies to use in class to help all students learn at all grade levels and abilities. The first element is to use explicit instruction with cumulative practice. This is because explicit instruction models a skill, has the teacher verbalize their thinking, and uses both guided and independent practice.  It should include both the new skill and previous skills learned.   It allows students to see how the process works.  

Research shows that using explicit instruction helps students improve their ability to perform operations and to solve word problems. One reason explicit instruction works is because students see exactly what they have to do and it keeps the older skills fresh in their minds.  In addition, it helps students to develop a working memory so they are able to quickly retrieve information.

Students should know exactly what the goal is for the lesson.  Teachers should include "Do now" at the beginning of class to revisit the skill they learned the previous day.  When teaching the skill or strategy, use crystal clear explanations and provide multiple examples showing more forms of the problems.  Instead of always teaching a linear equation as x + 2 = 7, show it as 7 = x + 2 or 2 + x = 7 so they understand they are all the same problem.  Always use think alouds so students understand the thinking behind solving the problems.  

Rather than always calling on one student, think about using choral responses, stop and jot, or thumbs up thumbs down.  If you 've never used stop and jot, it is a technique where you have students stop and jot down what they are learning at that point in the lesson to check for understanding.  Always, always, always, include problems dealing with a previous skill and finally, give students immediate feedback.

The next technique is to provide a visual representation of the skill or strategy because it allows the students to "see" the math.  A visual representation might be a number line, a tape or bar model, picture, graph, manipulatives or graphic organizer.  These help students understand abstract concepts better. One reason visual representations work is because they remove language barriers.  In addition, if students create the visual representations, they are showing their understanding of the skill or strategy.  In fact, research shows that students who are able to create accurate representations are six times more likely to solve word problems accurately.

Teachers need to teach students to use the different types of visual representations.  It is also important to encourage students to use visual representations to show their thinking.  In addition, the teacher should introduce and show the new skills using visual representations. Then model the concepts and skills using numbers, variables, and symbols. 

On Wednesday, I'll share the other two techniques.  I hope you find them useful.  Let me know what you think, I'd love to hear.  Have a great day.

Welcome To 2023