Math Based Game Faires.

 One year, I had my students create their own board games.  The idea was for them to choose a topic and create a board game complete with pieces and rules so younger students could play the games and learn something.

The hardest thing was to get students past trying to use the board games they were familiar with but without changing them.  With encouragement, they eventually began modifying some of the games to work with a topic such as adding or subtracting fractions, finding area, or other such topic.

Some of the areas students struggles with included creating a set of rules that made sense and explained everything the players needed to know.  I often read the rules and asked questions so students could revise them until one could play the game.  Once students decided they'd finished their game, I had another group of students try to play it, evaluate the weak spots while finding some good things about it.

Eventually, the students all had a playable game with rules that made sense and anyone could play.  Once they were ready, I made arrangements with several elementary teachers to have my students come in with their games for children to play.  I explained to my students that this is the Beta testing part of the processes to make sure the younger ones could play the games as designed.

The elementary students were asked to provide feedback.  If they were old enough, they provided it in written form and if they were younger, the teacher recorded their comments and students listened to their suggestions.  This often lead to revisions and when the games were as finished as possible, we invited parents in one night to play the student created games.  This event turned out to be quite popular with families.

Another year, I taught one class of high school students who'd missed so much school they were well below where they needed to be.  I happened across a huge book of math games for grades 1 to 5.  I had the students break up into groups of two and they had to look through the book to find a game they thought elementary kids would enjoy.

They had to make sure they had everything they needed for students to play the game.  They had to make sure they themselves understood all the rules and had to be able to explain the rules to the children.  I made them play their games several times through so they'd be ready.  I invited all the classes in grades 1 to 5 to the school library to try out the Math game faire.

It was successful.  The kids loved it and hated to go back to their classrooms.  Even the principal dropped by and joined in along with many of the paras and many hated to leave.  It was great because the older 4th and 5th grade students didn't mind trying some of the games geared for younger students.  They had fun.

Now, I admit, I don't know how successful this would be in today's world with all the mobile devices but I would still give it a try because most modern device based games have lost the human touch.  In another column, I'll talk about creating math based board games in more detail.  Let me know what you think, I'd love to hear.  Have a great day.

Teaching Math In The Middle Of Regionals

I work for a school district that covers quite a bit of territory and must fly students from one school to another so they can play.  Most of the students in this district are 1A while the school I teach at is 2A.  Every year 1A regionals move from school to school and this year, it is being held at my school.

This means for one solid week, there will be games running from early in the morning till fairly late in the evening.  Everyone will be helping out in some way and I'll end up volunteering to do books at various points throughout the tournament.

I struggled in the past on how to teach math to students while huge tournaments such as this were happening.  Most basketball players want to watch the games so they can observe those they will have to play against.  They'll want to look at plays, who throws the most 3 pointers, defensive formations etc.  So if I don't take them, they will take extremely long bathroom breaks or not even come to class at all.

I ended up developing a project for students to do during situations like this.  Before I take the students to the gym, I pass out a worksheet designed for them to select one player in the game they will be watching.  They have to mark down two point and three point attempts and completed ones.  They also have to keep track of steals, rebounds, etc so at the end of the week, they will go through and analyze all the data.  They will turn the data into a graphical representation.

Then they will select their favorite player in the NBA and compare the stats of the players they chose to the stats of the NBA player and determine if the student has the potential to be in the NBA.  They will have to select at least one player for the next part of the project.  Students will pretend they are offering potential players to be drafted by the NBA.

The student needs to take the stats, graphical representation of the stats, and create a sales pitch for their player.  They want the NBA to draft their player so the presentations must be good and they must meet certain criterial. The three main stats students must complete are field goal percentage for two and three pointers, effective field goal percentage and true shooting percentage because these do require math and are important.

Furthermore, they can compare the number of completed two and three point shots to the averages to see if they match up.  The average for shooting a 2 point basket is at 46 percent while the 3 point basket is around 37 percent. If the player is within 3 feet of the basket, the percent of baskets can be up around 74 percent.

I plan to sneak in some of the stats I'm required to do in this project because most of the stats do not fit with anything else in the course and this is a real life application of them.  It will make it much more interesting for the kids and they may not realize they are meeting standards.  I will let you know how it goes.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If it takes 22 pounds of olives to make one quart of olive oil and each tree produces 36 pounds of olives, how many gallons of olive oil will your orchard of 150 trees produce?

Warm-up

If one olive tree produces 20 kg of olives each year, how many trees do you need to produce a metric ton of olives?

The Importance of Spiral Review.

We've all heard of serial review.  Spiral review is where you have students practice key concepts and skill throughout the year on a regular basis rather than just when it is taught.

Spiral reviews have several advantages such as giving students multiple opportunities to maintain the skills they've already learned or strengthen any skills they are not yet proficient with.

Spiral reviews also give teachers a chance to assess where the student stands in his or her mastery of the concept or skill and can see how much progress the student has made.  Furthermore using spiral review helps increase student confidence and reduces time spent in prepping for state tests.

There are quite a few ways to use spiral reviews in class and many do not take much time to create.

1.  Use problems from previous sections during the warm-up so students regularly get to practice and review this material.  Look at previous skills and rotate through them on a regular basis adding new topics as needed and spreading the practice of mastered matured materials so they appear less frequently.

2.  Use 5 question quizzes at the end of class.  Make sure each week's worth of quiz problems are in the same format for each question.  For instance is the first question asks students to rewrite the standard form of a linear equation into the slope - intercept form, then every first question for the week should be that type of question.

3.  If you have stations in your classroom, one station should have review problems on previous material.  Let students work in pairs so they can help each other because the increases their learning when they have to explain it to others.  This is where you could use previous worksheets, problems, or activities you had to skip over earlier.

4.  Use math games to provide the spiral review.  Students love to play games and are willing to play them, even if they aren't fluent in the topic.  I've found students who are unwilling to try during the instructional part class will make an effort during games.  I often use games as the warm-up with material from previous classes.  My students love, love, love it.

5.  Create task cards that cover various standards and have broken down the standards into different levels.  The task cards should be different types rather than all the same kind. For instance, they might have to find an equation on one card, while they have to explain how to identify what the line looks like when it graphed to looking for patterns.  Get creative.  Add challenges to make each task card differentiated so the more advanced student is not bored.

6.  Throw in a review question in with the exit ticket at the end of the lesson. The review question focuses on previous material and is included with the question on the current material.

The nice thing about using spiral reviews is that this spaces practice out across time and this is a best practice.  It helps move the learning from short term memory to long term memory.  So if you are have not incorporated the spiral review in your classroom, give it a try.  Let me know what you think, I'd love to hear.  Have a great day.

One Important Reason For Students To Explain or Justify Their Work!

 I finally tripped over the answer to "Why students need to explain or justify their work?"  My students see no reason to do any explanations because they got an answer.  Unfortunately, it is not always the correct answer and my students cannot always explain how they got that answer.

What I read, makes so much sense because it is put into a context I can share with them.  In the future, many students will be working at jobs where they are given a problem to solve.

The solution may not be numerical as we get from solving mathematical equations but it will be a solution to the problem.  Usually two or three people will each work towards finding a solution, talking to each other, explaining their thinking, and eventually combining ideas into a solution.  Then one group or many groups will present their solutions to the boss and they have to convince him that their solution is the best.

When we have students draw pictures, or diagrams, it is preparing them to create multiple representations of their solution to a problem at work.  When people prepare a presentation for work, they usually include graphs, diagrams, illustrations, words,  mathematical equations, or tables to convey the information to an audience.  Furthermore, the idea behind these presentations is to convince the audience that the position of the presenter is the best one.  This is done through explanations and justifications of the method chosen with supporting data.

As we all know, more and more of the mathematical calculations are being done by machines via computer programs but people still need to interpret the results to know if the results indicate this choice is the best or if the person is arguing the other way, why it shouldn't be chosen.  Learning to justify or explain prepares people to support their position on the topic.

When the explanations are based on the mathematics, students who have gone through the process of developing mathematical communications are at an advantage over those who have not because they know how to formulate their ideas based on interpreting the results of mathematical calculations so they can argue one way or the other.

This is an important skill to develop.  Many industries rely on people who have excellent communications skills to develop new mines, new products, new ways of doing things.  For instance, when a mining company is looking at developing a new gold mine, they take samples, they do surveys, they determine if the amount of gold will be enough to build the mine, hire the people, pay taxes, and still make a profit.

In addition, many of these same businesses look at amortization tables to determine when a business will break even on the new project so they can account for inflation as part of the process and know if they can break even.  These are all important parts of communication. This is why we need to have students learn to explain and justify their work.  It teaches them an important skill for the future.  Let me know what you think, I'd love to hear.  Have a great day.

Suggestions For Improving Algebraic Knowledge

 Most of the time, we teach in ways that are not suited to help students improve their algebraic knowledge.  The current system is digitally based but it still has the examples set up so you click the screen and each step is shown in the proper order.  The students work their problems and are expected to learn but this method is not necessarily the best way to do it.

In 2015, The U.S. Department of Education made several suggestions designed to help students improve their algebraic knowledge.  At least one of these is contrary to what I learned when I was in my teachers education program but it makes a lot of sense.

1.  Start with a problem that has already been solved and shows all the steps.  You want students to analyze the problem, the process used to solve it and let them make connections among all the strategies and reasons they've learned.  You need to make sure the problem is one that focuses on the lesson's instructional goal.  You should include problems that show common errors so students become proficient at recognizing them.  Be sure to use a variety of methods such as small groups, whole groups, pairs, etc to discuss this.  This example could be pulled from the book, student work, or could be made by the teacher.

It is important to help students learn to analyze problems by having them describe the steps used to solve the problem, asking questions such as "Could it be solved in fewer steps?" or "Are there other ways to solve this problem?" or "Will these strategies work for other problems?  If so which ones?".  Furthermore, it is important to use more than one example and the examples should have different levels of complexity so they can see they cover the same concept.  By using several problems, students are able to see the steps are the same for all problems.

When having students analyze problems that were done incorrectly, let them verbalize why the error lead to a correct answer.  Another way is to have both the correct and incorrect problem next to each other so students can compare and contrast the steps to find the incorrect step.  It is important to ask probing questions such as "What advice would you give the student to help them understand why they did it incorrectly?"

2.  Encourage students to use algebraic representations by using language that promotes said mathematical structure. Teach students to use a type of self reflection questioning as they solve problems to help them see structure,  and help them see that the different types of algebraic representation can help them see different types of information.

Structure refers to the type and number of variables, operations, equality or inequality signs, and relationships among all of these.  It is important to use precise mathematical language so students develop the vocabulary and the connections between words and structure.  Furthermore, it is important to take time to teach students some questions they can use every time they solve a problem so they recognize structure.  The questions might be something like "What can I say about the form of the expression" or "What has happened in similar problems before".

It is important to teach students to compare and contrast different forms to what they focus on.  For instance the "Slope intercept form" makes it easy to graph starting with the y-intercept while the "Point slope form" begins at a specific point on the line.  Both forms have their uses depending on what you need to do and what you have to work with.

Furthermore, it is necessary to teach students to represent problems, especially word problems, using different methods.  Sometimes it helps to teach them to translate a word problem into a specific visual representation so they see what is going on.

3.  Take time to suggest students look for alternative ways to solve problems.  To do this, the teacher needs to help students learn to generate a list of possible ways to solve problems, look at the pros and cons for each method, and explain their reasoning for choosing a particular method.

One way to accomplish this is to show students different ways to solve the same problem including the standard algorithm that is usually taught.  By showing different ways of solving the same problem, students have the opportunity to see which ones might be more effective than others.  It is also important to let students come up with strategies on their own to try.  Furthermore, students should see how the same strategy can be applied to different problems so they see a connection.

Do not use all the alternate strategies at once or you might overwhelm the students. Introduce one or two at a time so they can practice them.  Teaching students a variety of strategies can help them become better at approaching new types of problems they have not seen before because they have tools to work with.

It is important to question students throughout the whole process to help them develop their self reflection and ability to try new problems.  Let me know what you think, I'd love to hear.  Have a great day.