All about Orangamallows

Introducing the Orangamallow...

I was lucky enough to be able to attend Twitter Math Camp 2013 in Philly last week.  Part of TMC was a session called "My Favorite..."  This was a fantastic entry point for those who had a "small" idea to share that wasn't really enough for a full session (or, if you were too chicken (like me) to sign up to present a full session!)

Never have I been so nervous to get up in front of a room of teachers!  

So on to my favorite!  Imagine you have a store that sells only oranges and marshmallows.

Ask a volunteer to take a few of each and toss them in a bag.

Give the bag a good shake, and ask your volunteer "what's in the bag?".  Of course they will look at you like you are a little crazy, and in this case, say "3 oranges and 2 marshmallows."  Ponder this thoughtfully, and ask for another volunteer.

This time, tell them to pick up two sets of marshmallows and put them in the bag.

Shake it up, and ask again "what's in the bag?" In this case they will probably tell you "5 marshmallows".  Usually they don't look in the bag, so ask them to check and make sure.

This is where I like to look very confused...so if 3 oranges plus 2 marshmallows equalled 3 oranges plus 2 marshmallows, how did 3 marshmallows plus 2 marshmallows equal  5 marshmallows?

Using that reasoning, shouldn't 3 oranges plus 2 marshmallows equal 5 "orangamallows"?

So do this a few more times, and then ask what would happen if we put 2 "x"'s and 3 "x"'s in the bag?

Or 4 "x"'s and 3 "y"'s?

Somewhere in the conversation you can bring in vocabulary like "combining like terms", and model what the different algebraic expressions look like.

All year long, whenever someone makes a combining like terms error, you can hear a cry of "orangamallows" in the room!

Thanks, TMC and the general twitterbloggersphere for the forum to share!

Nicole

My Take on Standards Based Grading

During term 4 of this past school year, I tried out standards based grading.  I was alone in this endeavor (well, at my school anyway- lots of twitter/blog support and ideas!)  There are so many things that I loved about the experience (and several things I need to work out before we start back in August.)

Things I loved:

• being able to look at my online gradebook and see exactly where students were in their level of understanding of each concept.  I took extra time when grading to enter a comment about what types of misconceptions each student had on their assessment.  Each time they reassessed I updated the comment (often through cutting/pasting as many made the same types of errors, so it wasn't as time consuming as it may sound.)
• students being able to focus on what they really needed to work on, get help with, and having an interest in improving their grade by truly learning concepts they didn't fully understand.
• parents being able to see what their students understood (especially with the comments.  I also entered the grade as 75.1 or 60.2 to let me know how many times they had attempted a retest.  That way I could see right away who had/hadn't retested- only the grade prints out on my class grade sheet- comments show on individual grade sheets.
• advanced level questions-I felt like this really challenged my students and they had to use their problem solving strategies to answer some higher level quesions- my rubric was basically:  
• 50% (no understanding)- really , no understanding of concept
• 60% (limited understanding)- a start towards understanding
• 75% (basic understanding)- wide range in this grade- often I would have several variations of the concept...for example, for area of a circle, students needed to be able to calculate area given radius/diameter,  and calculate radius/diameter given area.  A student who couldn't work backwards from area to radius but was proficient in calculating the area earned a 75%.  In all cases students needed to show work to support their solutions.  A student could also have a 75% if they understood the concept but had calculation errors so they never arrived at the correct solution.
• 85% (understanding)- able to show understanding for all questions except the advanced.
• 100% (advanced understanding)- able to answer an advanced level question in a context that students weren't exposed to in class- definitely accessible to students who used problem solving skills in combination with their understanding of the concept.
• the grade truly reflected what students understood.  

I have always believed in reteaching and I truly wanted all of my students to reach understanding.  At the same time, I was always in the "I'm preparing my students for high school and real life" mindset.  I thought that students should study for the test (and I always had tutoring available before assessments), and that when the test was over, what they earned should be their grade.  I didn't think it was "fair" that students should get to retest and that they wouldn't study the first time if they were allowed to retest.  

The last two years my school has had a retesting policy for students who earned a D/F.  I had a hard time with a student who earned a D being able to improve their grade but those that earned a C/B/A couldn't. It was around this time that I discovered SBG (thanks to twitter and blogs- thanks to all who share successes and "needs revisions" so willingly!) I loved the idea and this year I talked to my (very supportive) principal about trying it out for 4th term. 

Why shouldn't I want students to learn every concept to the best of their ability before leaving my class?  If they understand it, why shouldn't they earn an A?  Some students get it right away, others need different strategies, or need to see how concepts connect with other (earlier or later) concepts before they really get it.  I had to get over the "I'm preparing them for high school where they won't get second chances" mindset.  They will still hit that, depending on their teachers, but they are going to leave my class with as much understanding of the concepts as possible!  And if earning a higher grade motivates them, fantastic! 

But really, in real life, there are second chances.   What if I got fired every time a lesson bombed wasn't fully successful?  I think that students need to learn that in real life they have to take responsibility when something isn't working and figure out how to make it work.  School (middle, high, college) should be a place where students should be able to take risks and learn from their mistakes, maybe even if the mistake was not studying for the test in the first place.   (I'm NOT judging those who aren't here yet- just sharing another point of view, and welcome any feedback (unless it's about my grammar, sorry!))

Things I need to work out:

• last year our schedule was 90 minutes one day and 45 the next.  Next year we are going to 47 minute classes daily, so I am losing a lot of instructional time.  It was really easy to build in extra reteaching/retesting opportunities in the 90 minute period.  Really have to think about how I am going to make it work in 47 min.  In addition, I'll have 5 classes of about 30 students rather than 4.  Need to make sure I can give them feedback in a useful time frame without giving up all of my time!
•  motivating students to want to learn the concept/improve their grade.  Students seemed to fall into one of these categories.
• absolutely wanted their grade to be 100% and worked to get it there.
• not happy with d/f  but satisfied once overall grade was improved to a C.
• worked really hard but despite numerous reteaching/retesting opportunities not able to improve grade beyond a C.
• did not show interest in changing their grade beyond original.  These students still had to participate in some mandatory reteaching but didn't show an interest in improving their grade.

• need to come up with a way to help students keep their assessments/reassessments organized in a way that they can use them, but that I can still have some sort of portfolio (department requirement)- maybe digital- anyone have a good way? 
• rethink how students can "qualify" for a retest- I don't want to waste their time or mine by having them take a retest on a concept they don't really understand yet.  During 4th term I had them make corrections to their original assessment.  With concepts that a large number of students had to retest, I created an extra practice sheet with a variety of types of problems, and posted an answer key.

I'm hoping that anyone who has any thoughts about SBG (whether you've tried it yet or not) will share!  We go back in about 5 weeks and especially with the move to Common Core and new schedule I've got a lot of planning to do :)