Things I have been working on…

Math Recorded

This semester I have beScreen Shot 2013-05-24 at 3.17.41 PMen trying to encourage other teachers to start recording themselves teach.  I brought this idea to my assistant principal (who liked the idea), and he started randomly picking teachers to record.   Teachers were terrified and hated to get picked.  Which I get, it is scary to have your peers watch you teach.  We also ran into the issue of what do we use to record with?  Then, once we got something recorded, we never had time to watch the entire1-hour video. So what I am going to try this semester is start out by just recording myself and then sharing it with other teachers using this site.  Instead of recording or uploading the entire video, I am just going to put up small clips of different parts of the lesson.   That way, if a teacher wants to see how other teachers open their classes or how they facilitate a discussion, they can watch just clips of those videos. (Also, it is much easier to upload a 10 minute video then a 60 minute video.) Teachers can simply filter the Google Spreadsheet for whatever they want to see.

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Later on in the semester, I would like to have teacher start feeling more comfortable with recording themselves and then upload those videos to the website.   I think watching these clips could lead to great discussions at our PD meetings and could lead to teacher being real reflective about their teaching.   To record the videos I bought a small tripod to hold my iPhone.   I then simply edit the clip and upload the video to Vimeo.   I change the privacy settings to require a password to view in order to protect the privacy of our students.

Vertical Non-Permantent Surfaces

After seeing the slides from Peter Liljedahl’s presentation on whiteboards, I was intrgued on how to best hang my large whiteboards that I made out of panel boards.  I came up with drilling holes in the corner of the whiteboard and then using grommets to make sure the holes last.  Here is a picture of my room with all of my whiteboards hung up.

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And here is an up close picture of the corner.

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Quadratic Toolbelt

This year when I was teaching students about quadratic functions I wore a tool belt and told students we were going to learn how to use some tools in order to work with quadratics.  So, for example, when I taught students how to complete the square, I would say something like, “this “tool” is used for putting a quadratic function into vertex form.”   Or, “Sometimes we can use the “factoring tool” for solving quadratics equations, but if that tool doesn’t work, we can always get out the power tool, “the quadratic formula” and he will do the job.”   Then, I would belt out a Tim Allen grunt. Using the tool belt analogy helped students realize what all these things (completing square, factoring, quadratic formula, ect.) are best used for. When we were working on more open ended problems, I would hear students say things such as, “Let’s try a different tool.” or, “Isn’t the completing square tool good for finding the vertex?”    I am going to continue using this analogy when we look at other functions and see if it has the same effect.

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Advanced Teaching Metrics

I have been teaching for 5 years and every year I feel like my principles and district people get more and more into data. We all give the same assessments and EOCAs so they can look at the data and make decision.  The worst part is most of these people have taken the single statistic class that is required to get their masters and don’t understand much about data.  (funny side note: At a meeting one time, our principle was showing predictive data.  The data said our students were predicted to do 4% better on our high-stakes test this year.  My principal asked the following question to the staff, “Do you guys know why we want to get this percent higher?  Because the margin of error is ALWAYS +/- 5% and we want to be out of the margin of error.”)  Regardless, because our bosses value the data from these assessments, these affect the way teacher teach.  This is no new secret, bad high-stakes tests and bad summative assessments can lead to bad teaching.  What is interesting, is that this is not limited to teaching.  The NBA for years used statistics that did a bad job at assessing the effectiveness of a player.  Michael Lewis wrote an article in 2009 about the NBA player Shane Battier titled, The No-Stat All-Star.  The gist of the article is that Battier doesn’t accumulate a lot of the standard statistics (points, rebounds, assists, ect.), but because of his unselfish play, he is as effective as some of the more well known NBA all-stars such as Carmelo Anthony or Vince Carter (This is 2009 Vince Carter).  Here is a quote from the article, where Daryl Morey (The GM of the Houston Rockets, the team Battier played for in 2009) discusses how they do a better job at measuring the effectiveness of players:

“…the big challenge on any basketball court is to measure the right things. The five players on any basketball team are far more than the sum of their parts; the Rockets devote a lot of energy to untangling subtle interactions among the team’s elements. To get at this they need something that basketball hasn’t historically supplied: meaningful statistics. For most of its history basketball has measured not so much what is important as what is easy to measure — points, rebounds, assists, steals, blocked shots — and these measurements have warped perceptions of the game. (“Someone created the box score,” Morey says, “and he should be shot.”) How many points a player scores, for example, is no true indication of how much he has helped his team. Another example: if you want to know a player’s value as a ­rebounder, you need to know not whether he got a rebound but the likelihood of the team getting the rebound when a missed shot enters that player’s zone.”

Morey goes on to show other instances of how standard statistics create selfish players.

“Taking a bad shot when you don’t need to is only the most obvious example. A point guard might selfishly give up an open shot for an assist. You can see it happen every night, when he’s racing down court for an open layup, and instead of taking it, he passes it back to a trailing teammate. The teammate usually finishes with some sensational dunk, but the likelihood of scoring nevertheless declined. “The marginal assist is worth more money to the point guard than the marginal point,” Morey says. Blocked shots — they look great, but unless you secure the ball afterward, you haven’t helped your team all that much. Players love the spectacle of a ball being swatted into the fifth row, and it becomes a matter of personal indifference that the other team still gets the ball back.”

I feel this same problem occurs in education.  When we value simple statistics, such as test scores, we create selfish teachers.  We say things such as, “Don’t worry about that, its not on the test”, or “The best way to get the answer is to just plug in the 4 multiple choice answers.”  Maybe the more detrimental part of selfish teaching is it limits the types of tasks we do in our class.  For example, a teacher might say,  “I am not going to do that Mathalicious lesson because it doesn’t exactly go over the problems that are on our district created tests.”  or, “I am not going to do Estimation 180 because my students don’t need to estimate on the AIMS test. I am going to work on adding/subtractice integers instead.”   When we value simple statistics like test scores, we reward teachers for selfish teaching.  The NBA has become better at finding effective, less-selfish players by developing advanced metrics to measure the effectiveness of players like Shane Battier.   Here are some examples of new NBA advanced statistics:

Opponent Field Goal Percentage at the Rim (Opp FGP at Rim): This stat measures an opponent field goal percentage at the rim when you are defending them.  If there is a low percentage, that means you defend well at the rim.  If there is a high percentage, it means you do not defend well at the rim.   The lowest percentages for Opp FGP at Rim is Bismack Biyombo at 38%.  Biyombo rates 21st in blocks which is usually the statistic we use to measure great rim protectors.  On the other hand, DeAndre Jordan who is second in blocks, rates 36th in Opp FGP at Rim.  To the casual fan, we think of Jordan as a better rim protector because of his high number of blocks, but really, it is  Biyomo.

Another method NBA teams have taken to better evaluate players is by installing SportVu cameras in all of the NBA arenas.  These cameras track all of the player’s movements.  Teams can use this for multiple purposes such as seeing how teams defend pick and rolls or how much distance a player travels in a game.  SportVu cameras also allow teams to see how fast a player is moving at all times.  This information can tell them how often a player is sprinting, jogging, walking, ect. which can factor into a player’s effort.
So, let’s say we were able to record every single math class and chart the data, what are the advanced metrics that we would want to collect?  Here are some of my ideas and I would love to hear some of yours.
1. TQ (Teacher Questions): Number of questions a teacher asks per 60 minute class period.
2. SQ (Student Questions): Number of questions students ask per 60 minute class period.
3. CQPTNQ (Challegeing Questions per Total Number of Questions) Number of challenging questions a teacher asks in comparison to the total number of questions they ask.
4. Helping: Number of times a teacher gives students the answer per 60 minute class period.
5. Estimations: Percentage of times a teacher requires a student to make an estimation prior to starting a problem.
6. Less Helpfuls: Percentage of times a teacher answers a students question with another questions.
7. LP (Lecturing Percentage): Percentage of time a teacher is talking.
8. SSDP (Student to Student Discussion Percentage): Percentage of time on topic student to student discussion occurs.
9.  TeacherVu: Track the movement of a teacher.  For example, how much time is a teacher spending with struggling students. Is a teacher standing in front of the room or at their desk.
10. DOK average: Percentage of problems used in class that are DOK levels 1, 2, or 3.
11. Leinwands:   Number of times per 60 minute class period a teacher asks questions of the type, “Why?”, “Can you explain?”, “How do you know?”
12. Feedback Length: Length of feedback on a assessments (By letter count).
We are probably never going to get to the point of collecting this type of data, but if we did, would it change change anything?  Does an NBA player knowing he is being measured by Opp FGP at Rim instead of blocks change the way he plays defense?  Maybe. Shane Battier was making all of the same unselfish plays before he got to the Rockets.  Just like Fawn Nguyen is doing all of the right things in her classroom without advanced metrics guiding her instruction.  But the truth is, not all NBA players or Teachers, are playing unselfish.  The advanced metrics have had an affect on the play of other NBA players.  For example, the Houston Rockets believe the best shots to take on a NBA court are 3 points and layups.  These are the shots they tell their players that they value.  They believe that long 2-point jump shots are not valuable.   This year the Rockets took the fewest shot from 15-19 ft.
This is important because it shows when you let your employees know that you take certain statistics seriously, you can change their behavior.  If a school decided to make other statistics more important than test scores, teachers would change their behaviors and try to meet the new statistics.
The counter argument to advanced metrics in the NBA is that it doesn’t give you a complete picture of a player’s value.  You cannot measure the competitive spirit that Jokim Noah plays with.  You cannot measure the mentoring a veteran player does with a young player.   With teaching, there are so many things that matter that can’t be measured by statistics.  For instance, the personal connections that teachers make with students. Or, the guidance a veteran teacher provides to a new teacher.   While there are definitely limits to statistics, advanced metrics paint a better picture of what is going on in a teachers classroom.   And with the right advanced metrics, you can positively change what happens in a teachers classroom.
I feel like for the most part math teachers are happier with the Math CCSS than with our previous state created standards.   However, we are all waiting to see the PARCC and Smarter Balance assessments to see if they will actually assess the CCSS.  If they do, the belief is that teachers will have to change the way we teach.  But if this were true, then NBA teams like the Rockets, could have just used wins and loses to motivate their players to play in an unselfish way.  Some teachers need good advanced metrics, that measure specific things, in order to change the teaching that occurs in their classroom. If we don’t have these advanced metrics in teaching, then I believe no statistics are better than simple ones.

 

 

Math Intervention

We are piloting a new math intervention program next year.   Currently, if a student is placed in our math intervention class, they have 2 consecutive hours of math every day.  The class is split up into 3 – 40 minute rotations.  1st rotation is with the teacher where they are taught new content.  The 2nd rotation is with a Teacher Assistant or co-teacher where they usually work on a review worksheet.  The last rotation is on computers where students are working on ALEKS.  We  have been using this model for the last 5 years and haven’t seen any success with our students.  I think there is a lot of issues with this model.  First, placing all of the lower students in the same class sets the bar of expectation really low.  Students know that they are in a class with other low students and they start to develop the mindset that “we all are just not good at math”.  The second issue with this model, and probably the most important, is the lack of student engagement in each of the rotations.   Students are not engaged when they are working on ALEKS.  Students are not engaged doing a review worksheet for 40 minutes. Then, when the students are finally with the lead teacher learning the new content, it is usually just guided notes because the teacher is limited due to the fact there are 2 other rotations going on in the room.   We are expecting these students, who generally have never liked math, to stay engaged with probably the 3 most boring things we can do in math, worksheets, guided notes, and computer programs like ALEKS, for 2 hours straight everyday.  It is needless to say, this isn’t working and we need to change things up.

At my school,  we are going to be trying something different that hopefully produces better results.  The basic goal is to increase student engagement in these classes.  The first major change is to place all students in a traditional Algebra 1 class.  This will hopefully raise expectations.  Also, it should allow students to be part of more engaging lessons that are not limited by the structure of the class.  Putting all students in a traditional math class will also eliminate the need for students to have 2 consecutive hours of math.  Now, just putting these students in a traditional math class is obivisouly not enough, students need extra time to close the gap.  So we are giving these  students a second hour of math (it will just not be a consecutive hour of math.)  The big questions then is, how do we make that second hour of math engaging?  What we are trying is peer tutoring.  We are taking our advanced juniors and seniors and training them to be tutors.  The goal is to have 2-3 students per tutor. Our thought is with this ratio, students will innately be more engaged.  For instance, if a students doesn’t understand something, they don’t have to wait for a teacher to help them, they will instead have a tutor sitting next to them that can answer their question. It will be easier for the teacher to differentiate instruction because of the small group sizes.  Management issues, which usually plagues these classes, will be minimized because of the smaller groups and more engagement.  Better management will also occur because the teacher’s job is simply to facilitate the class.  The teacher doesn’t have their own group of students to look over, they are simply are their to provide the different materials to the different students and take behavior issues that arise.  Now, just having smart students tutor struggling students, even with the small ratio, isn’t necessarily going to work.  The key to the success of this program is how well we can train our tutors.  Our plan is to bring all of the student tutors in before the school starts and train them.  Also, we are going to be training them throughout the year.   The other key for this program to be successful is what we have the tutors do in this time.   It can’t just be working on a review worksheet or doing the students math homework.  This is boring with or without tutors.  Fortunately, my principle has given me the freedom to try new things in this class.  At this point in time, I am not exactly sure what we will be doing, and even when I figure it out, I will probably change it up through out the year. But as of now, my goal is to change student’s mindset on mathematics and I plan on doing this by doing interesting mathematics.   I believe that if I can make these students better thinkers and develop their problem solving skills, they will innately become better at mathematics. Thus, I don’t want to use this time just doing worksheets on adding and subtracting integers.  Some of things that I plan on doing in this class are Math Talks.   I would have the students explain their reasoning and thought process to each of the tutors.   Counting Circles also sounds intriguing.   I also like Michael Pershan‘s idea of catching students up by preparing them for upcoming lessons.  For example, if students are about to learn how to graph exponential function, we could practice substituting values into equations and plotting points.  This way when students are taught by their other math instructor,they will not get hung up on prerequisite skills.   Part of the class will include practicing the skills they did in class, but I want to make sure that big portion of the class is doing interesting mathematics that students have success with.   Another thing we will be doing in class is keeping a log of what students did that day and how well they performed.  Both the students and tutors will be keeping a log.   I want students to reflect everyday on what they did.   I am not really sure how a grade will be awarded in this class.  The students will just receive an elective credit so I have a lot of freedom on what I can count as a grade.   I have thought about making the grade primarily based on participation.  I have thought about coming up with a standards based grading system, but I am not sure how this would work.   I have thought about making part of the grade based on their actual math class.   Anyways, this is where I am at right now and I have a lot to figure out this summer, but I am excited to try something new with these students that hopefully changes their mindset about mathematics.

Make a Guess Calculator

A common issue teachers face in Algebra 1 and Geometry classes are student’s weak arithmetic skills.  Students tend to struggle with the simple rules of adding, subtracting, multiplying, and dividing integers. The teachers of these students are put in a difficult situation.   Do you spend class time practicing these basic skills before you go on to more advanced mathematical topics?  What if this takes weeks or months?   What if it is only half of your students who are struggling with the basic arithmetic?  How can students solve for x is they don’t know if 2 – 9 is positive, negative, 7, or 11?   Students get so many rules jumbled in their head that they will miss something as basic as 5 – 2.  One solution is to allow these students to use a calculator.  Which in my opinion, is a good way to allow weak students to attempt more advanced mathematics.  Now, as you probably know, there are a lot of people who don’t feel the same way.  I am not here to say which is the right solution, but rather, I have an idea that people on both sides of the calculator debate might find useful.

I created an calculator app for iOS devices.  It’s called Make a Guess a Calculator.   The basic idea is that it requires students to make a guess before they are given the answer. Here is how it works.

A student enters an expression into the calculator.  (I made it so students could see the entire expression that they entered.)

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When they push the “=” button, a screen comes up asking students to make a guess. (The more I think about the question, “What is your guess?”, the less I like it. I almost feel like “What’s your answer?” or “What did you get?” might be better.) IMG_0927If a student has the right answer, then the calculator let’s them know they got it right.

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If a student has the wrong answer, then the calculator gives the student a choice; they can choose to Try Again? or they can choose Give me the Answer.IMG_0928

If a student chooses Give me the Answer, they have to wait 3 seconds before the answer appears.  IMG_0929

The idea of the calculator is that students are trying the basic arithmetic on their own and the calculator is simply checking their work.   This calculator, in a way, hits both sides of the calculator debate.  Students can do more advanced topics because they have a calculator, but at the same time, they are practicing their basic arithmetic.    Now, I don’t think this is a perfect solution for students who struggle with basic arithmetic,  but I do feel it could be a better solution than what we do now.   I also think the calculator would help give students feedback with just basic arithmetic practice.  For example, if students were just using doing a worksheet with basic arithmetic they could check their answer as they go.

If you have ideas that you feel would make this calculator better, or ideas for students who struggle with arithmetic, I would love to hear them in the comments.

Here are some possible tweaks I am already thinking about.

1.  Have no timer.  For example, have students enter an expression, make guess, and then give them the answer.  I worry student will take advantage of this and not try the problem on their own first.

2.  Make the timer increase.   As a student get consecutive problems incorrect the timer would increase.  Now, the way around this would be to every time you get a problem wrong, just do a simple arithmetic problem such as 1+1 to reset the timer.

3.  Remove the timer and only give students the answer if they get it correct.

Screen Shot 2014-01-03 at 3.54.41 PM*There are a few quirks with the calculator.  The biggest issue has to do with fractions.   When you enter a fraction like 3/5, the answer is not 0.6, but rather, 0.   The reason is because of the way it is coded.   You are dividing an integer by an integer so your answer needs to be an integer.   If you enter 3.0/5 instead, then the calculator will give you 0.6.  My thoughts about this are I don’t really want the calculator to give the decimal answer anyways.   I feel more teacher would rather have the students find the reduced fraction answer.   For example, if a students enters 6/10 the correct answer that the calculator would check would be 3/5. This also makes more sense for fractions like 2/6.   If a student did 2/6 on the calculator, it is only going to tell them they are correct if they put the right number of 3s in their answer.   Now, I am not sure how hard this is to code and it probably brings in other issues,(For example, what is the answer if a student enters 2.4 + (1/2)?  Is it is 2.9 or 29/10?) but I do feel it would make more sense for this calculator.

Tangram Wall

This is the first summer that I have not taught summer school, taken college classes, or worked a second job and I am starting to find out that I have too much spare time.  While my girlfriend is at work and the hot Arizona sun prevents me from leaving my apartment, I spend my days getting caught up on the first 4.5 seasons of Breaking Bad and working on school stuff for the upcoming year. I am at the point where I am creating things that I think are cool, but not really sure how I am going to incorporate into a high school math class.    Recently, I thought it would be cool to create a Tangram wall (Again, I don’t know what I am going to have my students do with it, but I think it will be cool). I have an extra whiteboard in my room that is magnetic.  I bought some colorful magnet sheets (I used two 8.5×11 sheets per Tangram).  Then cut out two different Tangrams sets using an Exacto knife (part of the fun was figuring out how to make the Tangram correctly on two separate sheets of magnets).

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Now I just need to figure out how to incorporate these into my class.  One thought is to print out a bunch (like 100s) of puzzles.  Then put them on the wall by the whiteboard with the Tangrams.   Then, as students complete the different puzzles, they can write their name next to the puzzle they completed.   My only problem with this is, when are students going to have time to be messing around with Tangrams? After school?  Before school? At the end of class?  Any ideas would be greatly appreciated.

Gamifying My Classroom

One of the more interesting talks that I attended at NCTM13 this spring was by Alex Sarlin and David Dockterman called The Gamification of Math: Research, Game Theory, and Math Instruction.  They talked a about different ways to use game theory to increase student motivation in your classroom.  A similar talk by Sarlin about game theory can be found here.  Sarlin gave a few guidelines on how to implement game theory in your classroom.  Here is a list of some of them.

  1. Build increased difficulty over time.
  2. Reward skill, time, effort, and progress.
  3. Destigmatize failure by creating activities that demand multiple failure cycles.
  4. Reward behaviors, not results.
  5. Offer rewards for going beyond expectations, not meeting them.
  6. Rewards should be granted at the moment of accomplishment.
  7. Rewards should be given objectively for meeting a predetermined goal.
  8. Rewards should be byproducts of work, not goals in themselves.
  9. Rewards should reflect both short-term and long-term goals.

Another interesting video interesting video on game theory is Seth Priebatsch’s Ted Talk about the The Game Layer on Top of the World.

After listening to these talks I wanted to come up with a way that I could integrate game theory into my classroom.  The challenges that I saw in front of me were:

  • How do I award students points for completing tasks , as well as, keep track of these points without using too much of class time?
  • Creating tasks that meet the criteria that Alex Sarlin laid out.
  • How do I get high school sophomores and juniors to buy into this “game” when they know there is no tangible reward at the end?

To address the first concern I created a word doc that I would give each student.  This document is the place where students keep track of all the points they have accumulated through out the semester.

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The basic idea is that every time a student competes a tasks, I either stamp or initial one of the circles.  Then, every week or so, the students turn in their game logs and my TA will total up their scores and keep track of it.  I will also have a leader board in my classroom where I will list the top 5 students in each of my classes.  I don’t want to put my students actual names on the leaderboard, thus each student will create their own Avatar Name.  Also, I only want to list the top 5 students because I don’t want students who haven’t scored a lot of points to be embarrassed or to give recognition to the students who have no interest in the games or think its silly.

The next struggle was creating tasks that met the criteria that Sarlin and  Priebatsch talked about.  I am going to go through each part of the game log explain the rational for it.

First the Status Bar.

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The point of this is to incorporate both the influence and status dynamic, as well as, the progression dynamic.  Students will gain a new “title” the more points they acquire throughout the semester.  Also, the amount of points it takes to go from once level to the next increases.  For example, to go from Scholar to Mathematician it takes 700 points, but to go from Mathematician to Gaussian it takes 1000 points.  This plays on Sarlin’s idea of increasing the difficulty over time.

Next, are some of the tasks or goals I created for my students.

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Again, I am trying to increase the difficulty over time.  The first task is simply to get one 5 on a concept. (I am using Dan Meyer’s SBG system.  So a  5 is a getting two perfect scores on a concept on two different concept quizzes. I am a little skeptical about this task because it is related to the student’s grade.  I don’t want this to be a game that only the A and B students can be good at.  I want this game to be equal for all levels of students.  The reason I kept it as a task is because students can retake concepts as many times as they like, so I am hoping that it encourages students to retake more concepts which in the end will reward effort; not just ability.)  That is something that every student should be able to do.  I want students to have success early and then have the next tasks to be a little bit more difficult each time.  If you think about the game Temple Run, the first time you play you get an award from running only 500 meters and collecting 100 coins.  Then the next time, the objective is a little harder, run 500m collecting no coins.  That is what I am trying to accomplish here.

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The next set of objectives are all about effort.  I want to reward students who continually do their homework.  I don’t care if the homework is right or wrong, just that they continually do it.  And Again, the tasks get incrementally harder to complete.  (In my classroom, since I am doing SBG, homework is not part of the student’s grade.)

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The next set of objectives are things that students can do as many times as they would like.  These are tasks that require students to go beyond what is expected of them.  For example, students don’t have to do quiz corrections, but if they do, they get 40 points!

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The next section is called Bonus Points.  My idea here is that through the year I come up with things for students to do that I usually assign extra credit to.   For example, I might say something like, “I will give 40 points to whoever can find a picture of a set of stairs with the steepest or shallowest slope.”  or if I am doing a review game instead of giving extra credit to the winning team, I will give Bonus Points.  The nice thing about these is that I can stamp the students paper the moment of accomplishment. 

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The next section is for students who attempt a challenging question during class.  This is to encourage students to attempt things they don’t necessarily feel comfortable doing. (This one I am a little skeptical about because what constitutes a “challenging questions”?  The reason I kept this is because I wanted to try different things the first time around see what works and doesn’t work.)  Again, I am rewarding students the moment they complete the task.

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The last part is to encourage students to come in for tutoring.  I will write the date the students came in for tutoring in the box.  Again, students get ten points for coming to just one tutoring session.  However, it takes 3 more tutoring session before they get more points.

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Now, the last concern that I have is whether or not my students are going to buy into this game if there is no tangible reward at the end.  Is simply getting points, moving up the status bar, achieving new “titles”, and having a ranking board posted in the classroom enough?  I don’t know.  But, it is enough for the game Temple Run and many others.  Now I just hope my classroom is as fun as running through a jungle being chased by gorillas!

Here is the Word doc as well as the PDF.  I used the font Pretendo.

The Next Step in Math Blogging?

Dan Meyer‘s recent post on how to deliver a “3-Act” lesson really got me thinking that more teachers should be posting videos of themselves teaching.  The main point about having a math blog is to become a better teacher.  Right now, the way the we achieve this is through sharing ideas, giving and receiving feedback from other bloggers, and reflecting on our practice.  Is it possible to go further by recording yourself, and then getting feedback on the actual delivery of the lesson?  I feel that I continually create lessons that I have such high hopes for, but rarely ever live up to the amount of time and effort I put into creating them.  I think being able to receive feedback on lessons you taught, as well as, seeing how other “expert” teachers deliver a lesson, would be so helpful.   It’s one thing to create the perplexing lesson, and I feel like this is getting easier since joining the math blogosphere, but it is entirely different thing to implement it.  Steve Leinwand proposed an idea at NCTM 13 of recording teachers every month and then at the professional development meetings, randomly watch one of the videos as a department.  I think this would be a great idea, but I also think it would take the right department, and a good department chair to lead the discussion so that it is productive.   That is why I think putting the videos online would be much more productive.  First, the audience is much more motivated to give sincere and meaningful feedback. Second, it is easier to give and take feedback when it is written down because you have time to process it.  If this is already going on, someone please tell me where and how I can join, but I think this is the next place the math blogosphere can go.  Is this something other teachers would feel comfortable doing?  Is this something that teachers would even want to do?  And if it is, what would be the best way to do it?  Let me know what your thoughts are on this.