My SBG Letter

This may or may not be of any interest to you, but this is what I hand out to my students along with their syllabus to discuss my version of Standards Based Grading.

Standards Based Assessment

Philosophy

            This class will be graded on a system known as “standards based assessment.”  Grades will be assigned for content knowledge based on understanding of the main standards needed in the course.  Thus, the grade for the class will accurately reflect the student’s understanding of the material from the class.

            This system has many positives for the student, teacher, and the student’s family.  Grades will be posted based on the concepts.  Seeing a 74% on the Chapter 4 test in the gradebook is not informative to any of the participating parties.  The student may have a wonderful grasp of three quarters of the material while missing only a single key concept or he could barely have a working knowledge of the entire chapter’s material.  On the other hand, an 80% on Trig Graphs is much more informative to all the stakeholders to show where the student may need to improve his understanding.

            The main goal of the class is to teach students the mathematical material for the course.  Thus, a student’s grade should reflect his knowledge and understanding of that material without being clouded by completion or participation grades, extra credit for material not related to concepts from class, or behavioral issues.  Any behavioral issues, nonparticipation, or incomplete homework will certainly be addressed, but will not be directly reflected in the grade for the class.

            Since mathematics often requires a good understanding of a topic before being able to work well with the following topic and because I wish for all students to understand all of the topics from class, I will give students the opportunity to retake assessments over concepts covered in class.  No graded assignment will be dismissed since every assignment is given for a purpose.  Retaking an assessment can help students more accurately show their understanding of the material and helps students to learn the material before getting too far ahead in the curriculum.  If a student has a bad day or does not fully understand the topic on the day of the quiz, he will have the opportunity to show his improved understanding at a later time.  I care less about when the material is fully grasped than the idea that it actually is understood at some point.  That being said, grades and understanding of concepts can be time sensitive, so students will need to complete all retakes in a timely manner.

            The new grade will completely replace the original grade.  Thus, students should never give up on the class, no matter how low his grade gets.  As long as he is keeping up with the material in class and working on reassessing the material for which his understanding has improved, an F in the class can quickly become an A as zeroes are replaced with better scores.  The grade is constantly in flux and should be viewed as such.  Until the final grading period, parents should concentrate on the individual grades to see what their child should work to improve rather than the overall grade for the course.

Policies

• Students may retake only ONE section per day.
• Students must retake the entire section (even if it is more than one question)
• Students may retake each section two times (in addition to the original)
• To have the retake ready for the following day, students must sign up before 8pm (according to Google’s clock).
• Students should be able to show proof of work done to improve understanding since the original assessment to merit a retake
• Students may take it in during encore or before or after school.
• The new grade replaces the old grade entirely (whether it’s better or worse) to reflect the current understanding.
• Retake questions will assess the same concept, but may be drastically different in format or more difficult than the original.  Students should be prepared to demonstrate mastery of the topic, not just hope for an easier question.
• Students must take all the retakes for this semester before the date to be announced.

Procedure

The procedure for signing up for retakes will be done online.  Students should look at the teacher’s website for detailed instructions.

Our Little Baby All Grows Up

I lived for 11 years in Music City, Nashville, Tennessee.  I found myself putting music in a bunch of holes I found in my life (after breaking up a 5 year relationship, after leaving school, etc.).  Being there, when I was, I found a number of outlets to consume local, indie music.  In the early to mid 2000s, enjoying indie music was even cool, so there was the weird thing of being part of a popular movement whose whole point was to enjoy things that were not mainstream.

I feel like this is where we are with our online community of math teachers, affectionately known as the mathtwitterblogosphere (or MTBos).  We're the rising indie band who is a couple steps away from having Sony call to offer us a contract.  It's a little bit of a scary place.

Many of the things that define this community are directly related to the smallish size and "grass-roots" popularity that we enjoy.  Will we "sell out" if our little group grows too big?

On the one hand, we want our ideas and the group itself to be open to anyone and everyone who feels moved to join.  After all, what we do is for the kids.

On the other hand, it feels like we will lose a lot of the things I love about the group if it grows too big.

I was trying to tell my wife about my confliction with my vision of the future of this group.  Sarah asked if I wanted TMC to just be a little get together of my friends.  It hurt when she said it, because it sounds bad and exclusive, but I'll admit that I selfishly kind of do want that.   I have found some people that I would consider friends for life through this community and I am continuing to find more here and there, so I guess I shouldn't be worried about that part.  Whatever happens to the community at large, I can hope that people I really want/need to interact with will still be there for/with me.

Sam posted about the close-knit community we have.  How can we maintain that while growing much larger?  Will we split into groups (#geomchat, #algchat, #statschat, Northeast, West, Central, early adopters, newcomers, etc.)?  What happens when we're bigger than physical space will allow us to get together during the summer?  Would corporate sponsors at meetings help or hurt?

I guess what I'm saying is that change is hard.

Phrases that Annoy Me

There are a couple phrases that students use that really annoy me in lessons.

"So, is it just...?"

and

"So, do you always...?"

The main reasons they annoy me is because I can tell students are just looking for an algorithm rather than learning the background reasoning.  They want a formula they can plug into.  They don't want to think about it.

I mean, I get it if they're looking for a generalization and if they truly understand what is happening and are putting the pieces together to make a formula, then I'm all for it. 

The worst thing about the phrases, though, is that they shut out learning.  I will try to turn the questions back around and ask them, "You tell me.  Is it always...?"  Then they get frustrated that I didn't answer their "simple question" and solidify their, "Well, I guess I'm just going to fail this quiz" mentality.  If I answer, even if I follow it up with, "Yes, but here's WHY it works (or doesn't)," they shut off their brains after I say, "Yes." 

Perks of SBG

This deserves a longer post, but this post made me think I should post now.

There are at least 2 times where Standards Based Grading saves my butt with no real work.

1. Talking to parents.  So much responsibility goes to the students for this type of grading.  They have no reason to fail.  Help is always available  There are opportunities out the Wazoo for them to succeed.  So parents who try to point a finger have to just turn back around and look at their own kid.

2. Final exams.  As a teacher I get so sick of students talking about how in their chem class they can turn in a blank exam and still get a B.  They take the last 2 weeks of school to just be bodies in seats and not work at anything.  With SBG, the kids have to prove their knowledge on this final assessment and their grade can jump up or die fast with their performance on it.  So, even my A+ students who might be able to get a decent grade with half the exam blank in a traditional system know that they have to still put in the effort to show me that they understand the material and deserve the grade they are shooting for.

Precal Problems

I'm having fun writing some problems for my precal exam and review, so I thought I'd share some of what I've got so far.  Feel free to use.  Where necessary, numbers were researched and are accurate:

1. (Law of Sines/Cosines) You Quantum Leap into the body of an artist who works on building furniture from reclaimed wood.  Ziggy and Al agree that you have a 98% change of moving on if you create a triangular table top from the three pieces of wood that remain from your wife's crib.  The pieces measure 3 feet, 2.5 feet, and 4 feet.  Without cutting any of the pieces, at what angles should you attach the ends of the pieces to one another to create this amazing table?  (Find all three angles and pray that this one will be the leap home!)

2. (Right Triangle Trig) You are marching your army towards "The Wall" away from the White Walkers towards the 7 Kingdoms.  You know this wall is 700 feet tall, but need to figure out how far away you are to know how much food you need to take from Craster's stores.  One of your scouts runs ahead 4 miles and from there sights the top of the wall at 1º from his position.  How far is your camp from the Wall? (Answer in miles. 5280 feet = 1 mile).

3.  (Right Triangle Trig)  It's 1895 and you are emigrating to the United States!  To prove your worth to your new country so they will let you in, you decide to do some quick calculations while on the boat ride to Ellis Island.  From some distance away, you initially sight the top of the Statue of Liberty at an angle of elevation of 3º.  Based on the ship's speed you calculate that you travel 1460 feet closer right when the angle of elevation becomes 4º.  To the nearest foot, how tall is the Statue of Liberty?  Your future citizenship may depend on it!

4. (Angular Motion) The Curiosity Mars rover has a weird pattern on its wheels that includes the morse code for ``JPL'' (Jet Propulsion Lab, the arm of NASA driving the rover).  This helps the scientists figure out how far the rover has traveled by seeing the pattern in the tracks left behind while driving.  The wheels have a 50 cm diameter.  How many copies of JPL are left in the ground when the rover has traveled 5km?  If it takes the rover 3 days to travel this distance, what is its average speed in kilometers per hour?

5. (Angular Motion) A "45" was a vinyl record with a single on each side.  It was called that because it would spin at 45 revolutions per minute.  The standard size is a 7 inch diameter.
(a.) A fat ant wants to slim down his exoskeleton by running along the edge of the outer edge of the record while it plays the entirety of The Monkees' ``I'm a Believer'' (2 minutes 47 seconds long).  How far will it have run by the end of the song?
(b.) The ant's friend wants to keep her company, but doesn't really need as rigorous of a workout.  So, she's going to run around the hole which only has a 1.5 inch diameter.  By the end of the same song, how far will this ant have run?

6. (Angular Motion) Your car came with 17 inch diameter wheels.
(a.) How many times will a wheel rotate in one mile? (1 mile = 5280 feet.  1 foot = 12 inches.)
(b.) You want to pimp your ride up to 22 inch rims.  How far will you have actually gone in the new rims when they rotate the same amount as the answer from part (a)? (Answer in miles.)
(c.) If you don't recalibrate the sensors in your car, your spedometer may say you are going 60 mph on the interstate, but how fast are you actually going in the new wheels? (Does your answer make sense?  Should it be faster or slower than the car says? This has happened to me!)

7. (Right Triangle Trig) After the Mars Curiosity rover landed, it needed to assess where it was in relation to one of its goals, Aeolis Mons (aka Mount Sharp).  NASA knows that the mountain is supposed to be 18,000 feet tall (about the same size as Mount McKinley, the tallest mountain in North America).  Initial pictures show that the angle to the top of the mountain from Curiosity's current position was 18.71º.  What is the horizontal distance from the rover to the mountain (round to the tens place)?

8. (Law of Sines/Cosines) You wake up in a daze in the middle of a forest.  You've been kidnapped!  Fortunately, your captors left your school bag with you and (oddly) a map.  From the map you can tell that if you walk at a bearing of 53º, you'll find your way to civilization.  In your bag you also have a ruler and calculator.  You find two straight sticks and measure them to be 8 inches and 5 inches.  If you put two ends of the sticks together, you should be able to form a 53º angle and find your way.  How far apart (in inches to three decimal places) should the other ends of the sticks be to create a 53º?