What Are The Best Assignments For Distance Learning?

After last semester, I needed to learn more about creating assignments for a distance class.  I tried but didn't have time to really learn about teaching distance classes because like most teacher, we were told on Friday that come Monday, everything would be online.

I needed to know more about creating assignments that would be effective for my students while making them so students could be more self-directed.  So I've assembled several suggestions to improve online assignments.

Before you actually sit down to write the assignment or lessons, it is important to know what you want your students to get out of it.  What skills are you hoping students can do at the end of the assignment.  When students know what they are learning via this assignment, they are more likely to do the assignment because they do not see it as "busy work".  Another thing to think about is the skill levels of your students.  If the assignment is too far above a student's ability, they are likely to get frustrated and shut down whereas one that is too far below their ability will lead to a lack of motivation and boredom.  The last thing to think about is which topics have students struggled with in the past so you can work on making those areas clearer through the use of videos, etc.

Our first instinct is to create the same type of assignment we would in class including all the directions.  In class, we are able to give the directions in small increments but when we do it online we tend to just write them all out in paragraph form.  It is best to use numbered lists or bullets with short simple steps anyone can follow.  Many times, parents will be trying to help their student and the listed format makes it easier for them too.  Furthermore, students and parents can check off each step as it's completed.

It is suggested one create a list of assignments, videos, class time, etc for the whole week in table form with a due date and a place to check each completed item.  This helps students keep track of what they are doing and helps them keep up with pacing.. In addition, for math, add some choice so they can choose say 5 out of 8 problems.  That way, they feel as if they can skip a problem if they don't know how to do it.  Also, other than class time, do not set a specific time of the day something should get done so that the family can work it in around what they are doing.

It is also suggested the teacher be consistent when it comes to posting material for the class.  It should be done at the same time  and the format should also be the same for each assignment so students are not scrambling to find everything.  A teacher might post daily with the daily work or weekly for one week worth of work, it depends on the age and school requirements. 

Make sure the layout of the assignment is the same every time.  Put the learning objectives at the top or bottom of every assignment and create a numbered list that has the same things in the same place. For instance, you might have a warm-up activity first every time, a video second with a fill in blank for notes, two practice problems where students fill in missing steps, and the problems last.  It is also nice to put in a time for "office hours" so students can log in and visit with zoom or google hang outs or via phone. 

For the assignments, it is also important to include multiple forms of representation such as making sure the videos have audio and closed captioning so students who have trouble listening can read as the person is speaking.  If the assignment includes a reading, make sure there are images, videos, and audio to go with it.  

If it is possible, allow students the opportunity to show you they can do the material via alternative means.  Perhaps you can have them explain how they did a certain problem via video so they don't have to write the explanation down.  Perhaps they want to create some sort of animation to show how the problem is solved.  

So keep all these things in mind as you create the assignments for the class.  On Monday, I'll be looking at some online things that might make it easier for students to work at home in math. Let me know what you think, I'd love to hear.  Have a great day.

7 Things To Think About If You Go Distance.

Some teachers will be back in the classroom while others will be teaching via some form of distance.  I know that many school districts have not yet decided which way to go, making it hard to plan ahead.  I'm still looking at ways to make the year more interesting should the semester start using online.  

I've looked at general information on distance teaching which can be easily used in the math classroom.  These tips should help one prepare lessons for distance learning.  When you have to teach via distance, the students do not have the chance to communicate with each other so they can't work together in the same manner. 

1.  Simplify instruction because everyone is not longer in the same room.  Students are unable to work with each other or ask for help as needed.  Now distance teaching has had to incorporate activities that require a much higher degree of self direction.  There should only be one or two activities associated with a class period and the activities need to have clear directions. Furthermore, there should only be one or two resources associated with each lesson and the resources should be easily accessible to a student when they want to use it.  Resources can include pdf's or slides, or even a video.

This would be a perfect time to use chunking.  Chunking is when the material is broken up into units or chunks which are much easier to learn and uses short term memory more efficiently.  In addition, chunking helps students "see" the connections between all the "steps". 

2. Make sure you have a home base set up for your digital classroom.  Rather than a classroom, use a digital place such as Google classroom or Canvas, to check up on the most up-to-date information.  All the information should be in one place so students don't have to jump around various programs and possibly miss important information.

In addition, it is important to set up clear instructions with checkpoints so the teacher can see what is happening and to help students continue progressing through the course.  Since distance requires more self direction, many high school students still have difficulty with that so they need the checkpoints to help them.

3.  Planning classes is going to take longer because you have to plan everything in detail.  If students are not engaged, you cannot suddenly change direction when doing a distance class.  It is better to plan longer assignments that are student driven so you have time to plan future units. Try to make the units so they are more student directed with check points so students keep on pace and arrange sections so students can discuss it with parents or other students via the phone.  In addition, set up choice boards or perhaps a choice of problems so they have a certain amount of engagement and ownership.  

4.  The thing that gets lost in distance education is the personal interaction.  The part where you say hello in the hallway, or ask a student about their last basketball game, or how their weekend was.  It is important to create points in the lesson for personalized interactions which can be done by e-mail, video messages, messages through Google, or phone calls but whatever method you choose, stick to it.  Cultivating those personal moments is going to take more energy than when in the classroom but it is worth it. 

5.  When the class first begins, take time to set your expectations.  Let the students know about the different types of activities they'll have, the amount of work you expect them to complete and deadlines along with checkpoints, how they will be assessed, and behavior guidelines including what will happen if cyber bullying occurs.

6. Make sure every resource you need for the lesson is on line and working.  Check the links to make sure they work as there is nothing worse than expecting students to watch a video and the link is broken.  It's not like being in a building where you can pop out and make extra copies or make new copies for a change to the lesson.  

7.  If you decide to make your own videos to go with your lessons, you need to keep it relatively short, in the four to five minute range.  Don't worry about making it look like a Hollywood movie, just make sure it covers the points that need to be covered.  Be sure to practice the lesson before you record it so it does not have a lot of pauses or Umsss.  In addition, if you aren't sure about managing the explanation while being recorded, there are several prompter apps available to use so you don't forget anything.

If you are going to be starting the year doing distance learning, these are some things you can think about as you prepare the class.  Let me know what you think, I'd love to hear.  I'll be exploring this a bit more on Friday.  Have a great weekend.

  

Preparing For A Possible Distance Fall Semester.

After a summer of not going anywhere, I'm still waiting to hear what my school district will be doing for the fall semester.  I just heard that the Anchorage School District will be distance for the first couple months because of the sudden spike of cases in the city.  They just hit over 150 cases for the first time.  In fact, this is the first time the in state numbers have passed 100.  Hopefully, I'll hear from my district sometime this week what they'll be doing.

I've been researching teaching virtually since last spring my district settled on packets that did not have to be returned.  I need to know more about how to do it and want to take some time to plan, just in case.  I'm sure there are others out there in the same boat.

The learning scientists have six recommendations they make for teaching virtually so students are able to learn better. This group researches topics associated with learning and make recommendations.  They have taken their six strategies recommended for use in the classroom and made adjustments for the virtual classroom.

1.  Spacing.  Spacing is where learning opportunities are spread out across a period of time.  In distance learning, students need to be a bit more self-driven and it is suggested they spread their study time over five days rather than trying to do it all in one day. Normally, in class, students have the opportunity to work on problems with the teacher there but with distance, the student has to take more responsibility to work independently.  This means they need to schedule enough time to complete the assignment using videos, reading the material, take quizzes, etc so they are not rushed and allow the brain enough time to absorb it all.  Since students often wait to the last minute to complete assignments, teachers can help by spreading the topics across several weeks so there is a built in spacing.

2. Interleaving.  Interleaving is mixing up the types of problems students work on instead of having them do all the same type of problems.  Most textbooks are set up so that the problems in the section correspond to the examples but it is more important to mix up the different types of problems so no two in a row are done exactly the same way.  In addition, one should add previous problems into the mix to continue spacing while interleaving current material at the same time.  Furthermore, in distance classes, it is important to pose questions which require students to integrate knowledge throughout the topics.

3. Retrieval.  Retrieval is where students are asked to bring memory forth from their memories.  The most obvious ways to do this is when students take quizzes or tests but there are other ways to do this.  Ask students to write down what they remember on a particular topic, or play a game like Kahoot, or other game.  When asking students to write down what they remember about a specific topic, let them know they are not expected to remember everything.  They can fill in missing information later, it is just a way of working to connect things in their mind.

When teaching by distance, it is good to include a lot of low point or no point quizzes but write the questions so they have to use what they have in their memory to answer it rather than just copy the answers.  The questions might require students to apply the concept to a specific situation or identify the parts of the answer.  Another suggestion is to create a large data base of questions that can be pulled so not everyone answers the same questions.

4. Concrete examples are much easier for students to follow than abstract ones.  Concrete examples are the best but there must be multiple concrete examples provided and the examples should contain different details so students connect with the concept.  Unfortunately students tend to remember the surface details but not the deeper details so by using a variety of situations in the examples, students do better remember the concept being illustrated.  It is easy to incorporate multiple examples in a video if that is the way your school is going this fall.

5. Use elaboration.  Elaboration has you asking students "How" and "Why".  When students work on answering questions dealing with how and why in reference to the concept, it helps them understand and learn better.  One can also ask students how this topic or concept relates to their own lives or ask them how two topics or concepts are similar and different.

6. Dual coding which is about combining words with drawings/pictures, or diagrams to make the material easier to understand.  In addition, students learn best when using multiple representations and students need time to digest both the words and the illustrations.  Furthermore, students should be taught to explain how the different representations show the same idea or concept.  When using this in a video, use words while presenting the illustration and take a pause to give students the chance to explain it to themselves.

Keep these things in mind when you return to classes this fall either in person or via distance.  I'll be discussing this topic in more detail later in the week.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If an average grasshopper covers 30 inches in one jump and the 30 inches is 15 times the length of it's body, how big is the grasshopper?

Warmup

If a grasshopper can travel 30 inches every hop, how many hops will it take the grasshopper to go one mile?

14 More Weird Math Facts

 Today I'm back to share more interesting math facts with you. Some of these facts show that math is all around us, while others show something interesting that would make the basis of a "What do you notice?" question.

1.  The first fact involves cicadas which are a type of insect we often hear on a hot summer night.  The cicada's life cycle is based on prime numbers.  For the first 13 or 17 years of their lives, they spend underground before emerging to mate.

2.  Usually when we talk about geometric shapes in real life, we discuss triangles, squares, or rectangles but if you look at a baseball playing field, the baseball diamond is actually a perfect rhombus.

3.  If you have a bunch of two dimensional shapes such as a square, rectangle, pentagon, circle, etc, all with the same area, and you calculate the perimeter, the circle will have the smallest one.

4.  Now if you take the same shapes mentioned in number three with all the same perimeter and calculate the area, the circle will have the largest area.

5.  Imaginary numbers are used in the real world to describe electrical currants among other things such as signal processing and radar.

6. If you begin at the center of the sunflower and work your way to the outer edge in a spiral pattern, you'll notice the petals are arranged in the Fibonacci sequence of 1, 1, 2, 3, 5, 8.....

7.  If you take time to really look at Roman Numerals, you will notice there is no symbol to represent 0 by itself.  You'll find 10, 50, or 100 but not 0.

8.  The written word for the number 40 is the only number whose letters are in alphabetical order.  Look at it - forty.

9. If you look at the spelled out version of odd number such as one, three, five, etc, every single word has the letter "e" in it.

10.  The written words for 11 + 2 is an anagram for the same written words of 12 +1.  So the letters in "eleven plus two" can be rewritten into "twelves plus one".

11.  We've all heard the saying "Back in a jiffy!".  Well jiffy is actually defined as 1/100 of a second.

12.  If you add up the two numbers on opposite sides on a dice,  the sum always equals seven. This is because the 1 and 6,  2 and 5,  3 and 4 are opposite.

13.  It should take no more than 20 moves to solve a Rubick's cube regardless of the starting position of the cube.  There are over 43 quintillion possible starting positions on a Rubick's cube.

14. If the clock you have hung on the wall uses Roman numerals, it most likely uses IIII instead of IV for four.

Just a few facts to use as warm ups this fall.  Let me know what you think, I'd love to hear.  Have a great day.

Math Also Found Pluto and Exoplanets.

 This past Monday, I spoke about how two different astronomers used math to find Neptune but that wasn't the only astronomical body calculations found.  The story picks up in 1846, just after Neptune's existence was confirmed.  There were still some issues in regard to Uranus's orbit that could only be explained by the existence of another astronomical body out there somewhere.

In 1894, Percival Lowell built his own observatory - the Lowell Observatory - in Flagstaff Arizona.  He began searching the skies for the mysterious Planet X but didn't find it in his lifetime.  In 1929, the observatory hired Clyde Tombaugh who joined the search.  He used a method where photographs were taken and he made comparisons between the photos to see which items had moved.  This lead to finding Pluto.

Now what is not generally discussed is the female mathematician who worked with Percival Lowell. She provided the mathematical calculations confirming the existence of Pluto and both Lowell and Tombaugh relied on the math to help find Pluto.  She noticed that the orbits of both Uranus and Neptune still were not where they should have been so performed the calculations to prove there existed another planet that influenced the orbits of both planets. She was the one who sent Lowell to look in a specific part of the sky and Tombaugh continued relying on her calculations as he searched for the body. She was fired from Lowell Observatory in 1922 when she got married.

If you follow astronomy at all, you know that in 2006, Pluto was demoted to a dwarf planet and at the same time, the number of recognized exoplanets or planets outside the solar system has increased.  In the last few years over 4000 exoplanets have been discovered by astronomers.  The process is based on many times astronomers notice something that indicates another astronomical body so they hit the math to calculate what it is and where it is.

An example of this is when Belgium astronomers noticed a dimming of the light out of a dwarf star which usually indicates a planet crossing it, so they began calculations to confirm there was a planet associated with the dwarf star. Consequently, we now have the TRAPPIST - 1 star system.  The astronomers used the transit method in which the light of the sun dims a bit as the planet crosses in front of it. They watch for this dip to be repeated on a regular basis.

Another technique to find exoplanets is to use radial velocity also known as Doppler wobble.  Astronomers look for small wobbles in a planets orbit. These wobbles are caused by gravitational pull of other bodies.   The third less common method is to use direct imaging which relies on the light from the planet but the problem with this method is that dimmer planets are not as easily found.  The final method is using microlensing in which there are two planets being observed. One passes behind the other and the planet in front acts as a lens to bend the light of the planet so it increases and decreases smoothly.

One of the first things they calculate is how far the new exoplanet is from planet Earth and the second thing is to calculate the mass of the planet.  They find the mass by using the brightness of the star and it's distance to get a number and they are able to determine the mass based.  Once mass and distance are calculate, scientists can then figure out the planet's radius, orbital radius, and density using standard equations.

If you want to give students the opportunity to use the type of math some of these scientists have used, there are some great activities available.  This one available from JPL has applying Kepler's third law to help determine the movement of known planets and then some exoplanets.  They provide a lesson plan with step by step instructions and the answers so you can spend more time with students.

This NASA page has a list of exoplanet activities for grades K to 12. It includes several transit activities and a couple more using Kepler's third law and even provides one activity using the same technique used to find Jupiters moon.

These activities connect math with astronomy to see how formulas are used to find mysterious planets and moons.  Let me know what you think, I'd love to hear.  Have a great day.

Math Found Neptune!

Students will often ask "What is math used for in real life"? and I think they would be surprised to hear that scientists knew about Neptune before it was ever seen by a telescope.  It was the first planet to be discovered using mathematical calculations.

Imagine the scene.  Three different scientists, all working independently, all using calculations only, discovered Neptune in 1846.  Since they all made the discovery at about the same time, it lead to an international dispute as to which one would get credit.

Neptune is a planet that cannot be seen with the naked eye from earth but Uranus could be seen but there were discrepancies between it's actual location and it's mathematical location. In other words, Uranus was being pulled out of it's mathematically calculated orbit.  Something had to be causing those differences but none of the general theories could explain it so they thought there might be another unseen body influencing Uranus's position.

Scientists needed a way to explain the motion of Uranus because it's position in relation to Jupiter and Saturn could not fully explain it's orbit.  Although they found Uranus in 1781 and scientists published tables of planetary locations, it was noted that Uranus was not where it was supposed to be so the scientific community hypothesized there was another planet out there, it took a while for anyone to attempt the complex mathematics needed to solve this problem.

In 1845, a French astronomer used mathematics to try to figure out the mystery planet's position while at the same time a British astronomer worked on the same problem but neither knew of the other's work.  John Couch Adams, the British Astronomer began working on the problem in 1843 and in 1845, sent his solutions to the Cambridge Observatory and to an astronomer in Greenwich, neither man recognized the significance of his work and disregarded it.  Furthermore, Urbain Jean Joseph Le Verrier of France began his work in 1845 and published several small papers on the topic in 1845.  Le Verrier sent his results to several astronomers in Europe including Johann Gottfried Galle in Berlin.

Galle received the paper on September 23, 1846 and two days later discovered the planet only about one to two degrees off of the predicted position.  Galle wrote back to Le Verrier to confirm the information was correct and also wrote the astronomer in Greenwich to share the information.  Since he'd let the paper languish, he took steps to assert the British had actually been the first to discover Neptune with Adam's calculations.

This lead to an international dispute as to whether the French or British scientist had "discovered" Neptune although the third one is given credit for having actually seen the planet in the sky.  The amazing thing is the scientists managed to do this at the right time in history to have the planet actually where it was predicted because they didn't know Neptune took 165 years to make one orbit around the sun. They used the idea that the gravity from the mystery planet effected the orbit of Uranus to find the location of Neptune and then they calculated the mass of the planet.

This discovery that marked the beginning of using mathematics to find astronomical objects rather than relying on observations.  Astronomers have used mathematical modeling to find exoplanets in today's world.  I'll address that another day.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If it takes 5 quarts of milk to make one pound of cheese, how many gallons of milk does it take to make each 84 pound wheel of cheese?

Warmup

It takes 5 quarts of milk to make one pound of cheese.  How much cheese will be made from 37 gallons of cheese?

Mathematical Models For Ice Skating.

 I've always loved watching ice skating.  Those athletes are so graceful and amazing with the way they make jumps look so easy.  I can sort of ice skate to the point of being able to stay up but that's about it.  I ran across an article on a mathematical model done at the University of Alberta which shows how ice skaters move across the ice.  The model could help professionals improve their skating while helping prevent injuries.

The model describes the movement of the skater so they know what part of the body needs to be moved to make the move optimal. In addition, the program will help an ice skater choose the right movements to create a specific look.

The model uses non-holonomic mechanics which is actually where they place constraints on the mechanics used in ice skating to show how the body moves in three dimensions.  The model also includes a list of movements and trajectories the skater can use on the ice.  This model can help people train better so they perform better and could lead to fewer injuries skaters get during training.  Eventually, this model could help improve the boots and skates to improve their design.  This model is more of an overall look at skating.

There are models out which look at the mathematics behind jumps done in the sport.  Let's start with the quadruple jump where the skater takes off from the ice, turns four times before landing.  In order to accomplish the jump, the skater has to build up a huge amount of momentum, strike the ice with the toe pick to propel themselves into the air, make four turns in under one second, and when they land, their body undergoes between 8 and 10 times their body weight in impact forces, stop rotating, and continue with their routine.

Back in 2010, none of the olympic competitions used quads at all in their programs but within one year, quads began appearing in skaters routines and now they are quite common.  Researches have used biomechanics which studies the movements of living organisms to determine how the quad is done and published it.  Now, trainers have a much better idea of what is needed to make a successful quad jump and what type of training the skater needs to become proficient at these.

One researcher at the University of Delaware spent ten years researching this topic.  He placed ten cameras around an ice skating rink to record skaters as they tried a variety of jumps.  He used motion capture technology to map the moves onto a computer model.  The researcher then applied a program to analyze the movements that took into account the individuals weight distribution and produced a computer model that showed how the move should be one as compared with how it was being done.  Since developing the system, over 80 skaters have used it including several olympic skaters to improve their ability to jump.

The researcher also noted the skaters could watch the computer simulation but few could actually do the movement straight off.  Often, the skater was spinning at 330 revolutions per minute (RPM) while they needed to up it to between 400 and 440 RPMs to give themselves the best chance of doing the jump properly.  So they had to show what needed to be done and explain how to do it to the skater.

These are just two ways in which mathematical modeling is used to help ice skaters improve their skating ability.  Let me know what you think, I'd love to hear. Have a great weekend.

MathDeck

 Every so often, I check out the latest in math news just to see what is happening around the world and I stumbled across something called MathDeck.  No, it is not a deck of cards students use to help learn formulas. Instead it is an easy to use search engine designed to create, edit, or look up formulas on the internet.

The idea behind this web based application is to make mathematical notation both interactive and easy to share.  It was created by an interdisciplinary team made up of both faculty and students at Rochester Institute of Technology.  MathDeck is free and available to the public.

MathDeck allows people to enter mathematical formulas using handwriting, an uploaded typeset image containing the formula, or text. The application uses image processing and machine learning to help the program identify the images and handwriting so people can enter complex mathematical formulas easily.

In order to write the program, they had to develop an understanding of how people input and searched for equations and create a way to distinguish the formula's nuances among multiple meanings and contexts.  The developers had to implement a way for the program to understand the nuances so the search was faster and more accurate.

Part of the area to work in allows the person to type in either the name of a formula or the formula itself and if you hit the search button, it sends you to the appropriate place on google. The work area allows you to handwrite the formula in using the curser and a finger on the tract pad.  

I typed in the Pythagorean theorem using the ^ symbol for power and then clicked on it so the formula ended up in the work area and the edit formula area.  Once can also click on the text box in the work area, and then click and drag it to the dialog box at the top of the page and it shows up in all three areas.

The authors included an auto finish function in the program to help make suggestions based on the symbols or key words much like your phone does as you type text messages.  If the person is searching for a formula that is considered an entity, there is a corresponding card in the area below the work area.

this list of entities came up when I typed in the Pythagorean theorem.  If you hit the expand button, it gives you a definition from wikipedia or wiktionary.  These are all preloaded.  If on the other hand, you want to make a card for one of these formulas, you use the my cards section.  

At the bottom it keeps a list of what you've looked for and has several different keyboards beginning with common formulas and goes on to the Greek Alphabet, Relational, Binary, Delimiters, and Accents.

Rochester Institute of Technology has said they plan to work on improving it to better recognize handwriting, find equations in Pdf's and make the searching better. So they are not finished.  Head off to it and give it an exploration.  Let me know what you think, I'd love to hear.  Have a great day.

Alternative Grading

As a high school teacher, all the grades I put into the grade book are based on a part out of a whole number of points leading to a overall percent grade.  The percent determines the letter grade they end up with.  Some schools such as mine require I give a minimum grade even if they do not turn anything in.

I saw something on Twitter referring to someone who does not assign a grade the first time she corrects a paper.  She just highlights the mistake and expects the student to go back and make corrections.  Once the student makes corrections, she then assigns a grade because many students look at the grade and if it is one they can life with, they don't bother doing anything except putting it away.  By highlighting the mistake and requiring students to make corrections, the student is taking time to review their work.  I like that idea.

Another way of grading I've read about is the four point scale where very piece of work is graded between 1 and 4 as suggested by several including Marsano.  In one situation, the 0 means no work turned in, 1 represents below average, 2 is average, 3 is above average and 4 is exceptional while in another situation 1 represents a novice because they have just begun learning the material and have not met the objective.  2 means approaching because they are showing some mastery of the concepts but still have a ways to go.  3 is where they are considered proficient because they show mastery of the material while 4 is advanced understanding where they show mastery and show transference of the concept.  Marzano suggests that the 1 means

Then there is the idea that you do not grade every problem that the student does.  Before making the assignment, decide which problems embody the concept you are teaching and only grade those. The idea behind this is to really see if the students have mastered the concept itself.  In fact, it is suggested the teacher only grade assignments which advance student learning of the materials rather than grading everything.  When teachers grade everything, students get the idea they should only do work that counts towards their grades rather than doing things for the sake of learning.  Furthermore, it has been suggested that if a teacher grades homework, it should be done as a + or - indicating it was done or not done but does not effect the grades at all or a check mark with a plus or minus, the checkmark indicating it was turned in and the + or - showing it was superb or almost there.

A new one I just found is the narrative or holistic evaluation in which the teacher writes a brief essay to discuss the student progress in mastering the material.  This type of review focuses on the student's learning and offers feedback covering where they are in learning the material, their strengths and the areas they need to focus on to strengthen.  The reason for using a narrative evaluation is because many educators feel as if a single grade really does not provide enough information on a student's progress. This way of evaluating students is labor intensive but it also means the teacher gets to know the student better and it builds relationships.

I just saw one where they recommend that all work is graded using rubric for everything done in class.  For instance, for work that has been turned in the 5 means all the problems were done correctly, all the works is shown, the problems are neatly done with the answer circled while the 4 shows the work is mostly completed with the problems mostly showing work and most of the answers circled, down to 1 where the paper has little work done.  The numbers translate to a 5 = A, 4 = B, 3 = C, 2 = D and a 1 or 0 is an unsatisfactory.

In regard to the idea of giving a 0 when work is not turned in, I ran across a suggestion that the teacher use an incomplete for that assignment that can be changed to something higher when the student finally turns in the grade.  If the incomplete are not changed at the end, then a zero or minimum grade can be put in.

In everything I've read, it is strongly recommended that behavior is not include in anyway in the grade.  It is best to only evaluate the actual work turned in because teachers are looking at students mastering the material and behaviors are said to have nothing to do with that.  However, it is suggested people use a rubric with a grade for participation.  The highest one might require the student to participate in all discussions, help other students, and provides evidence they participated every day that week.  the second highest number might require a student managed to participate at least 4 days that week, the next one has the student participating 3 days that week and anything less than that is unacceptable and requires a conference with the teacher and possibly with the parents and teacher if participating does not improve.

Being able to use alternative forms of grading only works if your school allows it or if you can fit these things into the school requirements.  Let me know what you think, I'd love to hear.  Have a great day.

Warmup

Each almond tree produces 62 pounds of almonds, how many almond trees do you have if you harvested 1468 pounds of almonds?

Warmup

If there are about 460 almonds in a pound, how many pounds do you have if you have 17458 almonds?

6 Ways To Encourage Mathematical Conversation.

 We are always trying to find ways to encourage students to talk to each other rather than having students rely on us to get help.  By the time most of my students begin high school, they are so used to getting help directly from the teacher that they don't think about talking to each other.

There are six things a teacher can do to help encourage mathematical conversation among students.  One of the first things a teacher can do is to teach students to ask at least three other students for help before asking them.

This asking at least three other students has to be clarified because I've had students ask three students "Do you know how to do this?".... No and they will tell me they asked three other students.  We have to take time to teach them the specific questions to ask each other such as "Have you started # ____" or "How did you start the problem?" or "Why did you do it this way?".  The questions have to be ones that request information on solving the problem.  If the three people asked have not started the question, suggest students check with a few more to see if anyone has done the problem before asking the teacher for help.

Another thing is to ask students to work independently before they begin working in pairs or groups because most need a few minutes to process the problem and gather their thoughts.  This gives them time to determine what they know or don't know so they have a better idea of what to do during the mathematical discussion.  Once students gather into groups to discuss things, they should spend a bit of time comparing and contrasting approaches and solutions of everyone in the group.

It is also important for the teacher to pose questions to students which guide the discussion.  The questions might be open ended or designed to focus on certain processes, or justify their thinking, or explain their choice of processes or are designed to deepen their thinking.  Questions that have only one answer do not promote much dialogue but ones that ask students to justify, explain, compare and contrast do more towards deepening their thinking and understanding.

Furthermore, it is important to get students to understand that it is alright to make mistakes because we learn from mistakes.  Students need to understand that they will make mistakes as they explore new material or they are making conjectures.  In addition, making errors lead to better learning especially if students are asked to make corrections while taking time to explain where they made the mistake and why.  Analyzing mistakes is helping students learn to spot errors and it helps clarify their misunderstandings.

Then implement a variety of collaborative strategies such as think pair share or numbered heads so help boost student confidence because they can work in small groups to come up with an answer to share with the whole class.  If you haven't heard of numbered heads it is where each person in the group is given a number.  The people in the group know that anyone of them could be called on to share the answer so everyone needs to talk and be prepared to answer.

Finally, use strategies that allow all students to participate in class such as thumbs up/thumbs down, classroom response system or even corners as a quick way for teachers to assess student understanding quickly.  It takes a moment to check.

If you introduce these strategies to increase mathematical discussion, students will soon be talking about math with little to no guidance.  Let me know what you think, I'd love to hear.  Have a great day.

Connecting Math To Real Life.

One way to keep students engaged is to connect math to the real world.   Unfortunately, that isn't as easy was we would like because too many "real world" examples have no context and are no better than textbook problems.

One such problem I saw asked students to add several lengths of boards together to get a total.  Too many of my students see this as just another problem to do, rather than understanding why you might want to do this.

Why not give students a choice of several different wood building projects to calculate the amount of wood needed, total cost, and even the cost of the screws etc.  I brought up a set of plans for building a rustic bookcase which included a drawing, a supply list, and a cut list.  The supply listed things like one four foot 1 x 12 and two 8 foot 1 by 12's for a total of 20 feet of 1 x 12's.  This opens up a discussion in how lumber is labeled and sold.  What do they mean for a 1 x 12?  What lengths is it sold in?  Is the cost going to be per foot or for a whole length?  Using the cutting list, check to see how much left over there is once all the pieces are cut so students can calculate the amount of waste.  It is fairly easy to have students look prices up online for the various pieces of wood on the list.

In regard to recipes, most of the time the examples are asking students to figure out how to enlarge or reduce a simple recipe for 6 people.  Honestly, I know of very few people who actually sit down and turn a recipe for 6 into one to feed 18.  They just make three batches of whatever on the other hand, what about starting with a recipe made for 300 and cutting it down to feed 30.  On the other hand, when feeding larger groups of people, they usually calculate so much per person.  For instance when calculating portions for a large turkey dinner, they think about 1/2 to 3/4 cup of stuffing per person, or 1/3rd of a pound of raw potatoes per person.  Ask students to figure out the list of supplies needed to feed 300 or 450 people for a Thanksgiving meal and then calculate the cost of purchasing the supplies.  This site has a good breakdown for the amount of food needed per person.

I love having students design their dream bedroom and then calculate the amount of flooring, wall coverings, or ceiling needed to finish the room before having them calculate the cost.  In addition, I have them write up and turn in an estimate of the final cost of the room.  This exercise requires students to calculate square feet and depending on the product they might have to convert that to square yards for carpeting or leave it in square feet for flooring but they have to see what unit the wood flooring is sold in before they can determine how much they need to buy.  Furthermore, most cans of paint are labeled with the amount of area it covers so they have to keep that in mind.  I love this because it is real world math and they might look at the same types of things if they wanted to remodel their rooms.

A similar project to this is asking students to calculate the cost of remodeling their kitchen.  The remodel should include new cabinets, new appliances, new paint, and new flooring.  Again, they have to figure out how many cabinets they need and which ones they want assuming they are going with the commercial cabinets sold at Home Depot in order to find the cost.  Will they be painting or finishing those?  If so, they'll have to include the cost of the finish. What type of flooring will they use because that can add quite a bit of cost to the overall bill.

Another real world possibility is asking students to calculate the cost of outfitting a new office building with basic furniture of desks, file cabinets, and chairs.  This adds one more layer on the calculations and they will do it using a blueprint showing where everything is.  They can find costs for office equipment at Office Max or Staples.  Real life use of mathematics.

All these activities link math to the real world with context and depth.  The activities are not superficial but reflect possible real life activities someone might come into. Don't just find a worksheet on the internet, ask yourself how you can expand it so it relates to real life better.  Before I became a teacher, I had to prepare a quick cost sheet showing how much it was going to cost the company in overtime to have x number of workers come in on a Saturday to complete a project.  Let me know what you think, I'd love to hear.

Creating Your Own Notice and Wonders.

 It is often hard to find decent pictures to use for math on the internet.  I did a quick search and found several good pictures and videos to use in class but some of the pictures were nothing more than worksheets.

Anytime you use something for notice and wonder, it needs to be open ended so students do not go straight for the answer.  I saw one that is labeled a notice and wonder but it basically said that John spends 5 minutes setting up a game and has 7 games to set up.  This limits what can be noticed or wondered because there are numbers and most kids will automatically multiply the two numbers together to get 35 because they've been taught that.

On the other hand, the picture I put at the top has no numbers but it has lots of possibilities to notice things such as there are four different pizza boxes in a different size.  I also notice that three of the four boxes have a hole in the upper right hadn't corner.  I could wonder if the size increases the same amount from the smallest to the largest or I might wonder if the pizza inside is square or circular.

 This is another picture that has lots of possibilities.  Although it has lots of percents listed, it doesn't give any information to make it seem as if it is a problem.  I noticed that most of the percents end in zero and not five.  I also notice that the none of the numbers are done in the same color.  I could wonder if these are discounts or perhaps amounts you might put down for a car or house.  Maybe these are all the scores earned on the last test given in class.

Again, this picture offers possibilities rather than exact numbers.  There is no "right" answer and this one might be a good introduction to a unit on mark up or discounts.

I found both these photos on Pixabay.  All the photos on the site except for the top row are free to use and are not copyright protected.  I've found some awesome pictures there that could be used.  The photos do not have to appear to be math oriented but most are.  For instance, throw up a picture of a bridge that might have a parabola or a dining table set for lots of people.  The picture might show a kitchen or a road with a car.  If you make or find a video, know where to stop it so you can have students

Now if you don't have time, there are places you can find material that is put together but you just need to make a slight adjustment.  If you have a video, do not show the whole thing, show just enough of it to hook students when you have them do the "What do you notice?", "What do you wonder?"  Let students answer those questions and share their answers.

If you are using one of the three act activities, show the picture before you introduce the whole situation rather than going straight into the activity.  Math is visual has some really nice videos that you can show a little before stopping it so you can have students notice and wonder.  Once they've finished, continue with the video and the lesson.

Estimation 180 has some nice pictures with questions that ask students to make estimations of the situation.  To use it for notice and wonder, just show the picture without the question so students can think about it before they have to do a problem.

Think about using these a couple times a week to up the teaching in your classroom.  Let me know what you think, I'd love to hear. Have a great day.

Warmup

Your city is going to put on a fireworks show that costs $1785 per minute.  How much will it cost to put on a show that lasts for 1230 seconds?

Happy July 4th

July 4th and Math Possibilities

 Occasionally, I'd love to have math activities available to do in class when the  Social Studies teacher covers the Declaration of Independence but if you google July 4th math, you'll find a bunch of worksheets and that is not my idea of a cross curricular activity.

This is a good topic for several activities.  This site has lots of great information on July 4th that can easily be turned into an infographic.  In addition, there are pieces of information under "And the rockets red glare" that can be changed into percents.

This site features an infographic containing stats about July 4th that are not part of the previous site which students can use to interpret the information and write conclusions.  Within the infographic, there is a section on the amount of money Americans spend for food and that can easily be made into a pie graph showing the percent spent for each item.

If you want to include a reading activity, this site has some great information on hot dog eating contests, and history on the date itself.  Students can read the article and then create a summary and create an infographic to share the data.  This activity gives students a chance to take out the important information while ignoring the not so important things.

On the other hand, this site has some wonderful data including the population of the United States when the Declaration of Independence was signed and today's population, flags, fireworks, cookouts, and presidential last names.

If you wonder how many people traveled on July 4th, check this site as it breaks down the total into the number who traveled by car, airplane, or trains, boats, and railroad.  It has to be last year because the number of folks traveling this year is down due to the coronavirus.

This last site has stats on how many people hurt themselves with fireworks every year. There is both an infographic on the parts of the body most likely to be burned and the annual reports on injuries associated with fireworks from 2013 to 2019 from the United States product safety commission.  This site allows students to read and interpret data from official documents.  Students can also take the information to create their own infographics or even pie charts of the information.

When I began looking at the topic, I knew I didn't want regular worksheets because they really do not encourage students to practice reading, comprehension, writing, and interpreting data.  Most textbooks I deal with do not have any real data to interpret so these activities can help with that.  In addition, a couple of these infographics or parts of them could easily be used in a notice and wonder activity as an introduction.  One could even use the actual written data in the opening notice and wonder to perk their interest. Or maybe show three pictures, one of fireworks, one of hot dogs, and one of the flag and ask students what they notice and wonder.

I'll get back to notice and wonder possibilities on Monday but since tomorrow is July 4, I wanted to provide some possibilities to use in class once school starts.  Let me know what you think, I'd love to hear.  Have a great day.

Notice or Wonder in Math.

 I've been attending a series of webinars that focus on using "What do you notice?" and What do you wonder"? as a way to hook students and to get them to think.  The activity does not have any "right" answers but they open up the way to thinking.

One reason for using this routine regularly is because it helps students develop the persistence they need to solve problems.  If used to introduce a situation or concept, it allows students a chance to pique their curiosity and learn more about the context of the problem.

In addition, this routine gives them time to think about which strategy or strategies could be used to solve the problem while giving them the opportunity to see the whole picture.  Furthermore, it can help students build self confidence, reflection, and the realization that it is possible to solve the problem using a variety of ways.

One nice thing about using the notice and wonder routine is that it encourages students to brainstorm ideas which can help them get started because they are exploring the problem before they actually start.  It also helps students slow down to check out the details, and think about the actual problem rather than rushing through it.  Furthermore, it helps them see the math in a situation where the math may not be as visible as it might be in a problem.

The nice thing about the notice and wonder routine is that it can be used to open a lesson on a new concept, it could be used as a stand alone routine, or it can be spread over a couple of days so the routine begins on the first day and finishes up on the second or third day and can be used as the warmup.  When used regularly, it helps establish a safe environment.

To implement this routine, begin by showing students a situation, word problem with the question removed, a visual representation of a math concept, a set of data, or a graph and ask the students to write down thoughts on what they notice.  The next step is to ask students to share their observations but some students do not like sharing verbally. I have seen it suggested that this be done using a program that allows anonymity for the students so they can express their thoughts without fear or ask students to provide their answers on a slide, doc or post it note app.

Once they've shared their notices, ask them to think about what they wonder for a few minutes.  At the end, ask them to share their questions with each other, either aloud or via slides or a doc.  During this process, do not comment on anything in terms of correctness, do not ask for clarification, restating, or even praising them.  You only want to write down their thoughts and questions.  Use this information to determine where to go next in the lesson.

Next time, I'll be talking a bit more about using photos and such from the regular world where math may not be as visible for notice and wonder.  Let me know what you think, I'd love to hear.  Have a great day.