Mathsational

Kelly Turner has this great site .  I can not find her on twitter, so if you know her personally, convince her to join.  Then tell me about it so I can follow her. She posts a graph with reflection questions every week during the school year.  I like to use these as warm-ups with my 9-12 students.  She asks students to look at a new, relevant, and interesting graph.  Students practice reading the graphs to answer questions like:  What is the topic of the graph? What do the axes represent? What observations can you make? What do you think will happen in the future? Reading graphs is always a frustrating topic for me to teach.  It seems like something that high school kids should be able to do, but  it turns out they can't.  I like to use this resource once a week to give my kids extra practice.  We also discuss misleading graphs and bias.

AOD is another site that I love. These usually take the entire period to get through so they may not be just a warm-up. I could certainly see starting the activity at the beginning of a unit and then asking students to draw a conclusion. When they indicate that they don't know how to justify their position, it creates a need for the unit that you are starting. Then you can come back to this activity again at the end of the unit and do the math to support or dispute their original claim. Tim McCaffrey, the creator of this site has asked engaging questions that require 3-acts to reach their conclusion.  The 3-acts typically involve posing a problem, giving more information, and finding a solution.  Other tweeps have their own 3-act databases that are awesome too.  I'll write about those in a later post.  For now, enjoy these.  This is a good place to get started with 3-act math because it is not too overwhelming.  

Graphing stories are probably one of my favorite ways to start class.  The kids love it too.  I use it for all of my 9-12 students.  I don't match the graphs to the type of function we are studying, we just have at it.  Something about the videos is just very engaging for students. Here is how I use the site. 1)  Give students this handout . 2)  Play the first part of the video pausing as the y-axis is labeled so that students can write their title and labels. 3)  Play the full speed and half speed part of the video. 4)  Pause the video and ask the students to sketch the graph. 5)  Ask if anyone wants to see the video again (sometimes they do, sometimes they don't) 6)  Ask students to compare their graph with an elbow partner and discuss any differences. 7)  Take a pic and project one student's answer (I use Doceri on iPad) 8)  Ask the student to explain what is happening in their graph and how it matche...

The next resource that I like to use to start the class period is visual patterns .  I use these about once a week with my 9-12 students.  My ninth graders start the year not knowing anything (or remembering) about linear equations so they are really just trying to make a table of values and look for a pattern.  After we learn (review) how to write equations of lines we discuss how we can use that new knowledge to make our visual patterns easier to find.  Some of the patterns are quadratic or even exponential, so you will want to discuss this with students.  They should check to see if their pattern really is linear before beginning. The quadratic and exponential patterns are good for my algebra 2 kids, you just need to look through the list to find them.  The creator of the site, Fawn, will send you an answer key if you want a quick reference to tell what type of function each pattern is.   On this page , you can find several worksheets that ca...

My Second MTBoS favorite is Would You Rather .  This is another resource that I like to use to start my 9-12 classes.  Some of the questions are quick enough to use as a warm-up while others are long enough that you could spend an entire class period researching, calculating, and arguing.  I like these activities because they are interesting to students and require a low level of math knowledge to get started.  Of course, students can get very in depth with some of their answers.  I especially like to use these at the beginning of a unit before students have the skill to answer the questions.  An example of this might be using this probability task before learning about compound probability.  In this case the students might try to solve the problem with the brute force method, creating a sample space.  Then I can share with them the short cut and they would have a better appreciation for it.  The most important thing about these tasks i...

One of the reasons that I wanted to start a blog is that I had been an MTBoS consumer for about a year.  It all started last summer at a conference when I was encouraged to live tweet during the event.  I thought the idea was a little silly and I was not really interested in keeping up with the Kardashians.  However, I did learn something that I considered to be tweet worthy.  So I joined and tweeted.  After a few months, I had found about 50 math teachers from around the world that had great ideas.  These teachers were sharing their resources at no cost.  Twitter became my go-to lesson planning resource. Eventually I started to notice questions on twitter for which I felt I could contribute to the solution.  I tried to reply with 140 characters, but I often wanted to share links.  So, I decided to start a blog.  So far I've blogged about standards based grading and hybrid learning.  This next series of posts will be about my...

The process of planning for a hybrid classroom is not drastically different form planning from a traditional classroom.  You will need to consider that students will be progressing through the stations in different orders so you will need to be careful not to assign something at one station that can not be done without completing another station first.  You also want to be careful about over planning for the direct station.  The direct station should be different for all three groups.  It should be based on the questions that students have when they come to you.  If you find yourself doing the exact same thing all three times, you are probably doing something wrong.  To help you get started, here are some of my favorite resources. Direct station: I start off by preparing a traditional lesson.  This way if students do not ask questions, I have a variety of practice problems available to get them started.  Once we do one or two problems toge...

As with any teaching and learning strategy, teachers need to make it their own to get the most out if it.  In this post I’ll describe some of the modifications that I have tried as well as some that I know other teachers have tried. My classroom during year 1:  I am a rule follower.  When I learned about hybrid learning, I knew that the people who developed it spend tons of time trying different variations.  I understood that the training sessions that I was attending were based on what worked best out of thousands or trials.  Therefore, I tried to do everything by the rules. So, during the first year, students rotated through all three stations each day.  The problem with this was that I was teaching on a traditional schedule.  I had just enough time to run three 15 minute stations each day.  I had no time for warm-ups or closure.  This really bothered me.  I missed these opportunities to whole class pre- and post- asses...

Accountability is another important piece of hybrid learning.  I teach high school, so maybe my view of students is a little jaded.  Most of my students do not like school, do not like math, and only come to school so that they can see their friends.  There is very little intrinsic motivation.  Even my honors students are motivated purely by grades.  They almost never see that value of productive struggle.  They do not get a sense of satisfaction after solving a challenging problem.  This is a whole other concern that I do not have an answer to, but I am always looking for possible solutions.  In the meantime, since my students do not buy into learning for the joy of learning, I need to include accountability at each station every day.  This is easy at the direct station.  With so few kids in each group, it is impossible for them to hide or not participate at the direct station.  The other stations can be a little trickier. ...

The biggest challenge with teaching in a hybrid classroom is that students have much more freedom than they have ever had before.  This means they will need a lot of modeling and direct instruction on how to work at each of the stations. Here is a secondary example of what a hybrid classroom should look like. Here is what my typical first week of school looks like: Day 1:  Welcome students to the class, introduce myself, begin to learn student names/faces, begin work of a review packet covering material from the previous math course, explain hybrid learning Day 2:  Practice direct station, do this by learning about objectives based grading and continuing review, model classroom routines like signing out, use of electronic devices, turning in assignments, etc. Days 3 & 4:  Practice independent station, do this by getting all students registered for all computer programs that we will use such as Edmodo, edpuzzle, manga high, etc.  Give...

 In this post I’ll discuss what a typical hybrid classroom looks like.  I’ve made some modifications to make it work in my classroom and I know of other changes that other teachers have made that I will discuss in a later post. In general, hybrid learning works best on a block schedule and with a co-teacher or teacher’s aide.  I have neither of these for every period that I teach so it can certainly work if you do not have these things.  There are 3 stations direct, independent, and collaborative.  The teacher starts by creating a lesson plan for these three stations and then assigns students to each of the three stations.  Students then rotate through all three stations. One benefit is that the stations help to reach all preferences for learning.  The direct station is for small group instruction.  It often appears to look like a traditional classroom.  However the teacher should not be repeating the exact same lesson three times ...

In addition to standards based grading, hybrid learning is the other main thing that sets me apart from most of my peers.  The majority of the teachers in my department teach math in a very traditional way.  A typical class for them might look like this: warm-up, check homework, notes, guided practice, and exit ticket.  This process would repeat basically every day with the exception being test days then the entire period would just be spent taking the exam.  This method works well for teaching kids to solve routine algorithmic problems with fluency. However, our demographic is changing.  Practicing algorithms is not as important as it used to be.   No human has a future in performing algorithms .    This video is cool and scary.  It makes me rethink my future as a teacher.  Even if it were possible to make a living running algorithms, not all of our students can retain what they learn this way.  This is where hybrid learni...

One important part of standards based grading for me is student responsibility.  I require students to track their progress.  I also track their progress in the gradebook of course, but I like my students to do this as well. For my own tracking, I just grade the weekly quizzes and replace higher grades for lower ones.  I don't keep track of progress over time, just the best performance.  I mentioned in my last post that students individualize there quizzes on their own by choosing which questions to answer and which questions to skip.   Here is an example of a page from a student tracking sheet.   This past year I had students give themselves one sticker when they reached the mastery level M and a second sticker when they reached the mastery level E.  I wrote about the mastery levels here.  One change that I am considering for next year is the possibility of using colored pencils instead of stickers and having ...

 One of the most common questions that I get about standards based grading is how I do individualized assessments.  What I do is give each kid the same really long assessment and then they individualize it on their own by choosing which questions to answer and which ones to skip.  My next post will be about how my students and I track their progress, but basically the kids know which objectives they have and have not mastered so they answer only the quiz questions that they have not mastered yet.  This method saves me the overwhelming amount of work it would be to create 150 individualized quizzes every week on my own. So here is what I do in more detail.  In an earlier post I wrote about how to create your objectives list .  I make a test bank in a separate document for every objective.  In each bank, I write 10-20 questions that measure the particular objective.  I make odd numbered items easier and even numbered items harder.  ...