Students writing in math class

I started this towards the end of the year, and it's something I'll definitely continue next year.  I would create an assignment on Edmodo that asked my students to write explanations, rules, real-world examples, etc. about a particular topic we had been working on in class.  I used Edmodo because it allowed me the ability to quickly and easily provide students feedback so they could refine and improve their response.  Below are some examples of the following assignment: Write an explanation of how to solve systems of equations. How many ways do you know? Explain how to find the solution to both equations? How do you know your solution is correct? Consider these questions when typing your response. This assignment is not due until next Friday, May 31. Click TURN IN to enter your response. Do NOT submit the assignment as a comment under this post.

1. Graphing 
Solve both equations for y to change them to y=mx+b form. Then graph both lines and the solution is the point where both lines meet. 
2. Elimination 
If needed multiply one or both of the equations by a certain number until you can eliminate or cancel out one of the variables by adding the equations. Then solve for the remaining variable. When you have solved for one variable plug it into one of the original equations and solve for the other variable. 
3. Substitution 
In one of the equations solve for either variable. Then plug that solution into the other in the place of the variable you solved for. Then using the new equation solve for the variable that is left. Once you solve for that variable plug the number into the original equation and solve for the remaining variable. 

On all three methods you can plug in your answers and if they make both equations true, you have the right answer.

Here are the three ways I know how to solve systems of equation: 
1.Graphing 
First, you make sure that the equations are in y=mx+b form. If they are not, you have to rearrange the equations so they are. After that, you use the y-intercept and plot the first point on a graph. Then, you use the slope to plot the next point. Once you have done that, you do the same thing for the second equation. Finally, you find the x and y coordinates of the point where the lines cross through each other. That is your answer. 

2. Elimination 
First, you combine the two equations. You add/subtract the x's and the y's and the numbers. If you have one variable and one number then you plug that variable into one of the equations and solve for the other variable. If you have two variables when you combine the equations, then you must rearrange the equation so one of the variables is on a side by itself (y=number+x).Then, you plug that equation into one of the original equations that you combined. If you have y=number+x then wherever the "y" is in the original equation you put "number+x" in instead and solve the equation like that. Once you find out what the variable is, you plug it into the equation from when you combined and rearranged the two equations (y=number+x). You can then find the other variable. It does not matter if you rearrange the equation to find x or y. You end up with the same answer in the end. 

3.Substitution 
First, make sure that there is one variable on a side by itself in one of the equations. If not, rearrange the equation so there is. After that, you take the equation with the variable on the side by itself and plug it in to the other equation for that variable. You should end up with two of the same variables in the equation(x and x or y and y), then solve it. Once you solve it, you take the variable that you just solved for and plug it in to the second equation that you have not solved yet. Once you solve that equation, you take the x answer from one equation and the y answer from the other and that is your answer. 

You can check your answer when solving systems of equations by plugging the x and y coordinates back in to either of the equations and see if the equation is equal. You can also solve the equations using the opposite equation you used the last time. Whatever equation you started with, start with the other equation. 

Here is another example of an assignment where my students were required to write in order to demonstrate understanding. In response to this assignment, type out the rules for exponents. When can you add the exponents, subtract the exponents, multiply the exponents? Use proper grammar, capitalize, and punctuate properly please. It is part of your grade. You may submit this assignment whenever you are ready. If you don't submit the assignment today, I will assume that you are still working on EXPONENT RULES. You have until May 31 to complete the assignment.

I found that by requiring students to write out "math", which is at times a difficult skill, they developed a deeper understanding.  I began to get comments like "I'll never forget this Mr. Oldfield", which is what I had intended in the first place.  

Continuing Blended Learning Over the Summer

In the last couple weeks of school, I traded classes with the 7th grade math teacher and signed all of her students up for Khan Academy and created an Edmodo account and entered them all into the class "Summer 2013."  All of these students are ones I will have in my classes next year as 8th graders.  My plan was to sign them up, give me the teacher a couple weeks to experiment with Khan Academy in conjunction with Edmodo.  Long story short, I use Edmodo as a means to allow my students and I communication.  Communication about what's happening in the classroom and communication about what's happening on Khan Academy.  It also serves as a great platform for posting assignments, new exercises to try, new videos to watch, etc.  So I started by posting a list of 12-15 exercises appropriate for early 8th grade.  Things we'd begin the year with like adding/subtracting negative numbers, combining like terms, operations with variables, etc.  I spoke to the students about using Khan Academy throughout the summer and the advantages it could offer them when returning to school in August.  I gave them brief introductions in navigating the system for videos, using the hints, exploring exercises, etc.  I have even created screencasts with more in depth explanations of KA and it's purpose in my classroom.  In the first couple weeks, I had a ton of activity on Khan Academy and a bunch of questions, comments, requests on Edmodo.  Many students breezed through the exercises I gave them to start with and asked for more.  Keep in mind that I was not/am not seeing these students in class.  Their learning is entirely self-directed.  It will remain that way throughout the summer.  So I'm curious as to how engaged and motivated I can keep them through communication that is done entirely online.  So far so good.  Stay tuned for more updates.

"How do you use Khan Academy to get ahead in class?" Student responses.

I created an optional assignment on Edmodo recently.  My students had the opportunity to respond to this simple question: "How have you used Khan Academy?"  I explained to them that several of my students have been able to work ahead in class.  They've been able to learn new topics and skills without any instruction from a teacher.  Some of the responses I received were quite interesting.

Student A: I do different things depending on what the skill is. Normally, I watch whatever video there is on it. Sometimes I watch the whole thing and sometimes I just watch part of it. Then, I start on the practice. If I need to I use the hints. For some skills, I skip the video and just use the hints. However, I think that some of the hints just make it more confusing. And if after all of that I still don't understand how to do it, I ask whatever adult I'm with.

Student B: If it was hard and I didn't understand it I used the hint for the first problem. I either worked along with it, or I wrote down the steps they used and tried to understand it. Although other times I asked a friend who had already finished the skill to explain it to me.I found the first and third methods worked the best.

Student C: One time before a quiz, I was using Khan Academy to help study for a test. The test was really important and I needed to bring my grade up. I reviewed everything that would be on the test and I saw something that went with the topic so I decided to do it. Even though the certain problems were not on the test, but they were on a bonus question. I got the question right so it helped me. 

Student D: One way I worked ahead to work on 'Units' watched the Videos and read the comments. After still not having a 100% understanding, I logged out and clicked all the hints and read them through. I then tried the problem until I understood how to do it. Then I logged back in and worked ahead. For other problems, like area, I looked up the formulas online.

As you can see, each student has formed a different strategy for learning new material on their own.  I have enjoyed reading these responses after my students have had a full year's experience with Khan Academy.  Often unmeasured, the skill of learning how to teach yourself is a critical one in our society today.  

Student persistence!

These are screenshots highlighting the activity of a specific student of mine over the last couple days.  This student has demonstrated inconsistent glimpses of this effort and hard work all year.  Her grades in my class are D and F.  Unfortunately, I'm not able to assign grades based on Khan Academy.  Khan Academy should have a significant affect on a student's grades, but it cannot overcome the affect that the home has on a student's grades.  Regrettably, I feel like I'm sometimes fighting a losing battle, because I cannot control what happens when students get home.  Here is a student that obviously shows persistence and hard work, the motivation to push onward and master skills.  But I'm afraid the home situation prevents any consistency.  It's heartbreaking to think of the potential in this student.  I hope that her experience in my class can give her a foundation strong enough to carry her to success in high school.

Teachers vs Coaches

I'm reading through Sal Khan's book The One World School House, and my mind won't shut down this evening.  Sal presents an immaculate argument for the advantages a self-paced curriculum where students do not move to the "next grade" until they have demonstrated mastery of a particular set of skills.  The most recent portion of the book I have read contains an accurate comparison of a teacher and a coach.  Sal asks the reader why some students loathe and hate their teachers, but love and admire their coaches.  He suggests that both teacher and coach are there to support students, teach students, and  motivate students.  "Both ask students to push themselves to do difficult things- not infrequently, things that kids claim they really hate to do such as deriving equations or running wind sprints."  He also suggests a noticeable difference being that coaches represent something students choose to do while teachers represent something students have to do.  Teachers are adversarial, while attitudes towards coaches are cooperative and enthusiastic.  Why do students accept criticism from coaches but not so easily from teachers?
Sal reiterates the problem facing teachers is that public school students are put in positions that lead them straight to eventual failure and embarrassment.  Students that pass to the next grade before demonstrating mastery of the previous skills and concepts are headed straight to frustration, failure, and embarrassment.  This repeating system pits teacher and students as adversaries, not allies.  Even the most sincere of teachers are facing insurmountable odds inside an educational system focused on test scores, educational jargon, state standards, and the latest fads-everything except the students.  Until we accept that 70% is NOT passing, we'll continue to lead students down the road to failure.  The swiss cheese approach to public education is leaving us stuck centuries behind where we could be.

Daily Activity/Students accessing Khan Academy on their own

This is a screenshot of just a section of my students who had any activity during the day January 7, 2013.  I included this screenshot because this displays how active the students have been, even on days where I do NOT take them to the lab.  We did not go to the lab today, but I've still got several students who were active during school!  They are accessing khan academy during their free time in other classes.  This is tremendous because it proves students are taking some responsibility for their progress in class.
Holding the mouse over any one of these bars, will reveal the name of the skills each student has been working on during their time on the site.  I will typically go to a few students' focus charts just to get a more detailed look at the skills they were working on, whether they demonstrated proficiency, or whether they are struggling, etc.

Focus Charts

I added two screenshots to show an example of a focus chart.  These are some of the most useful charts/graphs provided to me as a coach for my students.  The top chart is a list of all the skills that particular student accessed during a 30-day period.  Any of the skills with a star beside them are ones that he/she has mastered.  The data on that chart includes skills completed in class and skills completed from home.  On the bottom chart, you can see some of the data I can see if I hold the mouse over top a piece of the chart.  That particular student was in one of my classes that were working on solving inequalities at the time and she was having a difficult time with compound inequalities.  As you see she eventually demonstrated that she had mastered that skill, given enough time and practice.