At the end of each chapter we spend a day making a study guide and then playing some sort of review game. In the past this games have included BINGO (fill in laminated cards with answers, then if you solve the problem you get to cross out the square), "the points game" (jar full of cards that say +5, +10, -5, -10 and x2, correct answer means you get to pull a card to determine your points) and a simple game of solving problems in teams to see which team can solve the most before the end of class. This year I have played these, and added in a few more thanks to the wealth of ideas on twitter. Last week we played basketball in my fundamentals class (solve some problems on a half sheet, if they're correct crumple and take a shot at the recycling bin, bonus point if you make it in! However- if you get one wrong you have to shoot from the far line, so there's an incentive to check your work).
Today, we finally played Taboo. I'd been hearing about the great reasons to play Taboo from lots of people, but hadn't wanted to make the cards. Last night I sat down to do it and it wasn't actually as hard as I'd expected. In fact, the worst part was fighting with Word to get the table to stay the way I wanted. I started with this set (google docs link) and then added my own to get this:
Taboo Ch 1-3
It's roughly in order of how I teach them so it should be easy to add more pages as the year goes on and play again. And I definitely will play again! This kids were really engaged, they said they learned from it and the most telling moment was when a couple kids were hesitant to take the talking role since they knew they didn't know the words well enough. Those two will definitely be doing some studying! (And they did eventually take turns in the role of describer.)
These are the rules we played by:
Taboo Rules
I assume I'm not the only high school teacher whose students have selective hearing, so you do need to go around and 'buzz' kids until they start monitoring each other. One group was just reading the words on the card! I was impressed that they knew all the vocabulary words, but it wasn't very challenging for the describer. They had a good laugh once they learned they were doing the exact opposite of the rules.
We didn't do a great job of forming teams but rather just grouped into clusters. That actually worked out fine since everyone was playing an active role (describing, checking or guessing), but I think next time if we want to have opposing teams they should sit A, B, A, B, A, B in a circle so there's no need to have kids switching seats between rounds. Finally, I didn't have enough timers for each group to have their own, so I just yelled out "Start" then when the time on my phone went off announced "Stop! Tally up your score and switch." And repeated until there was just enough time left in class to fix the desks. Overall I think it was a great activity to get students talking about math, using vocabulary and stretching themselves to do something other than recite a definition they memorized. I would highly recommend playing Taboo with your class. Especially if you want to make cards for the next few chapters in Geometry! Kidding, although I'd love to hear feedback on the taboo words I chose and other words to add to our deck.
Monday, November 21, 2011
Monday, November 14, 2011
I don't share well
A post on how I fail at co-teaching.
My school does an awesome job of supporting students with learning disabilities by offering courses co-taught by a content teacher and a special education teacher. This year I have 2 co-taught Geometry courses and I have the same co-teacher for both of those. I also have an "Algebra 1" (in quotes because we're not exactly at that level) course for students with moderate to severe learning disabilities. That course has 2 special education teachers so we've split it into 2 groups with 1 teacher (plus several paraprofessionals) in each class and me jumping between them.
The title of this post is actually true in a far more general sense than just co-teaching. I like to do things my way, I'm quite stubborn when I get my mind set on something and most of the time I'm rather independent. I do enjoy collaborating and I love the support of having another teacher in the room, but I'm still stuck in the mindset of considering my co-teachers support as opposed to equal level players.
I'd love to hear some ideas on how people have found a good balance in a shared classroom.
Some issues that have come up recently:
Grades were due last week so my Geometry co-teacher offered to do some of the grading. Problem was, I like grading those classes better than my others since they go fast (smaller class size and my other class is working on proofs- so glad I'm not an English teacher!) so I'd already graded almost everything. She later shared that she'd really like to do some of the grading since she wants to have a better sense of how everyone is doing. This struck me as totally obvious yet I'd never realized it - I'd been hoarding the grading since I want to see how the kids are doing, but she should get to share those insights! So now we're going to split it so that one of us does tests and the other does test corrections, then we both get to see. (I know, poor me, I have to give away some of my grading.)
I talked to one teacher for "Algebra 1" and shared what I thought the kids were ready to do next. She said that she was happy to put together a worksheet since I would be working with the other group the following class. When I talked to some people who had been in that class later she had gone and done something totally different than what we discussed. I was really frustrated that she didn't follow the plan that we had made, but I realized that most of the time I leave her in the dark and just show up with something to do that day. In my head I have an arc that I'm following and it all flows, but this probably isn't clear to her (especially since math isn't her area of expertise). I'm going to really try to work on communicating my goals and hope that she will offer me the courtesy of doing the same so when changes need to be made they aren't a surprise to either of us.
A success:
I've been using dropbox with the other teacher for "Algebra 1" so she gets real time updates as I create worksheets, write to-do lists and formulate plans. She did her practicum in middle school math and studied computer science, so she can see the underlying structures I'm putting in place when random files pop up on her computer. (I'm also using dropbox with some of the teachers in the math department to share everything I'm doing in my current courses and some projects I've used in the past that may apply to the courses we don't have in common. I do at least share resources well!)
I know that part of the problem I'm having is a lack of time to sit down and discuss everything with my co-teachers. We need to make that a priority in the future. Otherwise, I'm having a hard time not making all the decisions and monopolizing the small amount of teacher-centered time there is in my our classroom. Advice? Personal anecdotes? Articles I can share to get the conversation rolling?
Thursday, November 10, 2011
A Variety of Variables
This year I am teaching a course for students with moderate to severe learning disabilities. We are supposed to be studying Algebra and so we are working on the concept of a variable. I've found that many students have a really hard time understanding variables and their purpose.
I can think of three different ways to interpret variables so far, and so I'm trying to provide situations that promote comprehension of variables in each context.
1. A variable can be used to generalize, in this case it is a representation of any and all numbers. For this situation we did number tricks:
Pick a number. Add 6. Multiply by two. Subtract 4. Divide by two. Subtract your original number.
Students quickly realize that they keep getting 4, but in order to know it always works, they need something to hold the place of their original number. I talk about using a variable instead of spending the rest of your life checking numbers since you can put any number in the place of the variable and it will still work.
(Side note: this is a great way to introduce proof in Geometry since they actually see why they would want to prove something- it seems clear but they don't know why it works.)
2. A variable can be a number that changes. It could be something that varies over time, or that is different for different people. I came across this example rather circuitously. I found a worksheet translating verbal expressions into algebraic ones, but I also wanted students to substitute and evaluate the expressions. Problem was, the original author did a really awesome job of choosing different letters, so much so I didn't feel like writing in values for every variable. Then it dawned on me, there's an easy way to assign a number to each letter- a cipher! My non-math major friends in college all took cryptology which meant that I got to learn along with them and I've been surprised how often I've used ideas from that class in new situations. Using a cipher to decide the numbers to substitute did a few things- first it was a cool mini history lesson on codes, second it allowed me to easily change the values and show that we could make the same expression simplify to different things depending on the "key of the day."
**Edit- read the awesome comments below, I'm leaving #3 in its original form so you know what the comments are in reference to, but I'm no longer counting this as a valid category.
3. A variable can represent a specific number that we don't know. This is the case for most equations that we have students solve. We know the value of the variable, their goal is to find it. To introduce this concept we started by solving really simple word problems (Chris has 5 apples, Josh has 3, how many do they have together?) by writing an expression equal to a variable (5+3=A). The word problems have increased in difficulty but the idea is the same, that letter represents some specific value we are trying to determine.
I have no idea if this is a standard way of dividing up the roles variables can play, it's definitely something I'm still trying to figure out. But my goal is for students to see many different ways to approach solving problems using variables. And then, somehow, we need to merge all of these ideas into one concept of symbol represents number(s).
Finally, I'm hoping they will understand that all of these methods apply in any situation. Just because you have a number to substitute for your variable doesn't mean that substituting is the best first step. Frequently simplifying and solving before substituting can show structure (just like delayed evaluation when you only have numbers). Conversely, even if a variable is representing a particular number you need to find, guessing random numbers isn't a bad way to start out. For students who have no idea how to approach a problem having them try their favorite number will usually give some insight on the steps to solve a problem (which they can eventually generalize to an equation using a variable).
What misconceptions do you see when students are using variables? What other situations can I introduce that use variables in a different way?
"Just a darn minute! Yesterday you said x equals two!"
I can think of three different ways to interpret variables so far, and so I'm trying to provide situations that promote comprehension of variables in each context.
1. A variable can be used to generalize, in this case it is a representation of any and all numbers. For this situation we did number tricks:
Pick a number. Add 6. Multiply by two. Subtract 4. Divide by two. Subtract your original number.
Students quickly realize that they keep getting 4, but in order to know it always works, they need something to hold the place of their original number. I talk about using a variable instead of spending the rest of your life checking numbers since you can put any number in the place of the variable and it will still work.
(Side note: this is a great way to introduce proof in Geometry since they actually see why they would want to prove something- it seems clear but they don't know why it works.)
2. A variable can be a number that changes. It could be something that varies over time, or that is different for different people. I came across this example rather circuitously. I found a worksheet translating verbal expressions into algebraic ones, but I also wanted students to substitute and evaluate the expressions. Problem was, the original author did a really awesome job of choosing different letters, so much so I didn't feel like writing in values for every variable. Then it dawned on me, there's an easy way to assign a number to each letter- a cipher! My non-math major friends in college all took cryptology which meant that I got to learn along with them and I've been surprised how often I've used ideas from that class in new situations. Using a cipher to decide the numbers to substitute did a few things- first it was a cool mini history lesson on codes, second it allowed me to easily change the values and show that we could make the same expression simplify to different things depending on the "key of the day."
**Edit- read the awesome comments below, I'm leaving #3 in its original form so you know what the comments are in reference to, but I'm no longer counting this as a valid category.
3. A variable can represent a specific number that we don't know. This is the case for most equations that we have students solve. We know the value of the variable, their goal is to find it. To introduce this concept we started by solving really simple word problems (Chris has 5 apples, Josh has 3, how many do they have together?) by writing an expression equal to a variable (5+3=A). The word problems have increased in difficulty but the idea is the same, that letter represents some specific value we are trying to determine.
I have no idea if this is a standard way of dividing up the roles variables can play, it's definitely something I'm still trying to figure out. But my goal is for students to see many different ways to approach solving problems using variables. And then, somehow, we need to merge all of these ideas into one concept of symbol represents number(s).
Finally, I'm hoping they will understand that all of these methods apply in any situation. Just because you have a number to substitute for your variable doesn't mean that substituting is the best first step. Frequently simplifying and solving before substituting can show structure (just like delayed evaluation when you only have numbers). Conversely, even if a variable is representing a particular number you need to find, guessing random numbers isn't a bad way to start out. For students who have no idea how to approach a problem having them try their favorite number will usually give some insight on the steps to solve a problem (which they can eventually generalize to an equation using a variable).
What misconceptions do you see when students are using variables? What other situations can I introduce that use variables in a different way?
Monday, November 07, 2011
How to Study for Math
Last week I gave a test on proofs. It went poorly. As I graded them I felt badly for rushing the test to get it in before the end of the quarter. When I returned them, I apologized for giving the test before everyone was ready but made sure to say that I was sharing the blame, they needed to take responsibility too and tell me when they didn't understand what we were doing. I've had a better sense of what everyone knows from regular quizzes this year, but I try to make those 3 short questions while the test has multi-step and cumulative problems, which is where everyone got stuck.
All this was fine, until I started reading their test corrections. The first question on the page asks "How did you study for the test?" Page after page had answers such as "I didn't" or "I read my notes" or "I flipped through notes right before the test." Now I know that most high schoolers don't know how to study for math, so from the beginning of the year I talk about how to organize notes into two columns with vocab on one side and definitions on the other so they can easily skim and quiz themselves. We make a study guide together the class before the test (which gives them 2 nights to study thanks to block scheduling). I make them write out the study guide even if they have nice notes because I know (and share) that the act of writing helps implant information in the brain. I talk to them about active vs. passive methods of studying. I specifically assign the practice test in the book. But, after all of this I get "I looked over my notes" as the sole method of studying. I no longer felt guilty for rushing the test, but frustrated with my students for not taking responsibility by preparing for the test.
So, I decided I must not be enough of an expert- I'd need something more official or more flashy to convince them. So today I provided just that. First I took this article (direct link to pdf: How to Study Math by Paul Dawkins) and broke it into 4 sections. We did a jigsaw where each kid was assigned a page to read and annotate (underline things you currently do, circle things you could do for the next test) and compared notes with people who read the same page. Then, they got into groups of four and shared out. This activity made me want to be an English teacher - they read, made notes and talked to each other! All of English must be so easy! Then I came back to my senses, I don't envy English teachers at all, but it was fun to read and discuss something.
How to Study Math
After students shared a few of the most interesting parts of their page with the whole class I showed them this diagram:
I hope that the quote and the percentages really hit home. Maybe now they'll start practicing vocabulary words as soon as they get them? And do actual practice problems since the best way to learn is by doing? Maybe?
At the very least it was a productive 30 minutes of students reflecting on how they study and being exposed to some other options from sources other than me (who they have to listen to every day). I'll let you know how the next test goes!
All this was fine, until I started reading their test corrections. The first question on the page asks "How did you study for the test?" Page after page had answers such as "I didn't" or "I read my notes" or "I flipped through notes right before the test." Now I know that most high schoolers don't know how to study for math, so from the beginning of the year I talk about how to organize notes into two columns with vocab on one side and definitions on the other so they can easily skim and quiz themselves. We make a study guide together the class before the test (which gives them 2 nights to study thanks to block scheduling). I make them write out the study guide even if they have nice notes because I know (and share) that the act of writing helps implant information in the brain. I talk to them about active vs. passive methods of studying. I specifically assign the practice test in the book. But, after all of this I get "I looked over my notes" as the sole method of studying. I no longer felt guilty for rushing the test, but frustrated with my students for not taking responsibility by preparing for the test.
So, I decided I must not be enough of an expert- I'd need something more official or more flashy to convince them. So today I provided just that. First I took this article (direct link to pdf: How to Study Math by Paul Dawkins) and broke it into 4 sections. We did a jigsaw where each kid was assigned a page to read and annotate (underline things you currently do, circle things you could do for the next test) and compared notes with people who read the same page. Then, they got into groups of four and shared out. This activity made me want to be an English teacher - they read, made notes and talked to each other! All of English must be so easy! Then I came back to my senses, I don't envy English teachers at all, but it was fun to read and discuss something.
How to Study Math
After students shared a few of the most interesting parts of their page with the whole class I showed them this diagram:
I hope that the quote and the percentages really hit home. Maybe now they'll start practicing vocabulary words as soon as they get them? And do actual practice problems since the best way to learn is by doing? Maybe?
At the very least it was a productive 30 minutes of students reflecting on how they study and being exposed to some other options from sources other than me (who they have to listen to every day). I'll let you know how the next test goes!
Monday, October 24, 2011
Illogical Logic Units
Last year when I introduced the unit on logic I quickly realized that students were experiencing a ton of vocabulary with no context, and there was no way they would be able to "mind their p's and q's" just working with the textbook definitions. I tried to backpedal but we'd already reached the "we're never going to need to know this" and "this isn't math" frustration level so it was only marginally successful.
This year I did things differently. As students walked in I asked them to write a couple true sentences that fit the form "If ______, then _______." Then we got started with this worksheet:
Conditional
It went much better than last year's introduction, but I need to rewrite the questions on the second page since I ended up doing most of those with the class (there were too many questions to answer individually). Even so, they realized that a) and d) were always true, which translates to "if a conditional statement is true, so is the contrapositive." And most quickly saw the repeated structure once I explained exactly what I was talking about. Best of all, only one student asked why we were studying sentences in math; she asked it genuinely and was happy with the answer I gave about precise definitions and careful explanations. When reading the journal entries about this class period there were students who said this was fun! Such a difference from last year!
After we went over the general form for a) through d) I gave them the names (conditional, converse, inverse, contrapositive). Vocabulary goes over so much better when they already have a context to apply it to. The next class we talked about biconditional statements and I used some of the examples that students had made up, which is always more fun than creating my own.
On a slightly less successful note, we're still struggling with counterexamples. At the beginning of the year we did an activity I call "True, False, Fix" (a simplification of Prove or Disprove and Salvage if Possible from PROMYS) where students read a statement, decide if it's true or false and fix the false ones. They keep wanting to fix when I ask for a counterexample. We've quizzed on it twice and I hand it back with "counterexample?" and re-explain, but they still keep fixing and explaining without providing examples. I hate to mark off for accurate statements, but they aren't answering the question I asked.
So, advice on re-wording the 2nd page of the activity? And/or how to convince my students that counterexamples are actually examples that prove the statement is false? Thanks!
This year I did things differently. As students walked in I asked them to write a couple true sentences that fit the form "If ______, then _______." Then we got started with this worksheet:
Conditional
It went much better than last year's introduction, but I need to rewrite the questions on the second page since I ended up doing most of those with the class (there were too many questions to answer individually). Even so, they realized that a) and d) were always true, which translates to "if a conditional statement is true, so is the contrapositive." And most quickly saw the repeated structure once I explained exactly what I was talking about. Best of all, only one student asked why we were studying sentences in math; she asked it genuinely and was happy with the answer I gave about precise definitions and careful explanations. When reading the journal entries about this class period there were students who said this was fun! Such a difference from last year!
After we went over the general form for a) through d) I gave them the names (conditional, converse, inverse, contrapositive). Vocabulary goes over so much better when they already have a context to apply it to. The next class we talked about biconditional statements and I used some of the examples that students had made up, which is always more fun than creating my own.
On a slightly less successful note, we're still struggling with counterexamples. At the beginning of the year we did an activity I call "True, False, Fix" (a simplification of Prove or Disprove and Salvage if Possible from PROMYS) where students read a statement, decide if it's true or false and fix the false ones. They keep wanting to fix when I ask for a counterexample. We've quizzed on it twice and I hand it back with "counterexample?" and re-explain, but they still keep fixing and explaining without providing examples. I hate to mark off for accurate statements, but they aren't answering the question I asked.
So, advice on re-wording the 2nd page of the activity? And/or how to convince my students that counterexamples are actually examples that prove the statement is false? Thanks!
Sunday, October 16, 2011
Organization System
It's Sunday evening and I don't feel like grading, so instead I'll tell you about how all of my piles of work are neatly organized. Since it's systemized, when I do get some motivation I can get right to work without spending time figuring out where everything is. That means I have extra procrastination time, great right?
In my classroom I have a magazine holder (cheap plastic thing from target that google can't find a photo of) with a bunch of folders. It lives on a table filled with other supplies kids might need (extra paper, pencils, stapler, hole punch and sharpener) and the goal is to have students become self sufficient. Not only do I expect them to think (and use logic! what??), but I want them to get their own supplies rather than ask me "Can I borrow ___?" or "Do you have any more ___?" every day.
First folders: Extra Copies. I have two levels of geometry and each one has a labeled manila folder filled with extra copies of anything I hand out. If kids were absent or lose a paper, they are learning to head to the folder to get one. When students come in and ask what they missed, I send them to the folder. If they lost the homework, I send them to the folder. If they totally destroyed something, I send them to the folder. I don't like to waste paper so I don't make many extra copies, but I know my Fundamentals class has plenty of kids who can't hold on to a single piece of paper for an entire chapter (I photocopy the review page and they do a section each night for homework- books stay in school).
Next folders: Papers to Hand In. This is a set of manila folders with the letter of the block (A Block is first period at my school) written on the tab. Anything kids want to hand in must go into this folder. I won't accept papers handed to me, but merely point at the folder. For a class when I know I'm collecting something I will pick out the correct folder and lay it on the table ahead of time. To reduce chaos of everyone up and crowding at the table at once we pass papers down and the kids sitting near the table put them into the folder. If a student is handing in something late, or a correction, they find the correct folder and place the work inside.
Last folders: Papers to Hand Back. These are color coded pocket folders (one thing I kept from last year) with red for both fundamentals classes (matte for A and gloss for H) and blue/purple for CP classes. Eventually I'd like to take this responsibility off of myself as well, but for now when there are papers to hand back I grab that folder and distribute them or ask for volunteers. I like handing back papers while kids are working because it makes sure that I am moving all over the room in a rather random pattern, so I really do see what everyone is working on. I also use it like Sarcasymptote's Ukelele Time- I tell everyone I won't answer questions about what I'm returning or the work they're doing until I'm done, so they'll have to ask their partner or look up the answer. It's not much time, but it's a start of forcing them to talk to each other rather than come running to me. Maybe next quarter I'll at least assign someone to look in the folders and remind me if they're full of stuff to return.
On my desk I have boxes of things everyone needs- journals, test corrections, quiz corrections and quarter sheets of scrap paper for quizzes (and every random thing I want to remind myself of).
Last year I had everything on my desk, which meant kids were in that area all the time. When students wanted to hand work in I had them put it on my chair because I didn't trust that it would land in the right spot otherwise. It was definitely chaotic and messy. Now when I feel motivated to grade I just grab the manila folder of the class coming up (or really, the one filled with something easy to grade), grade and transfer to the corresponding color pocket folder. Then I reset and I'm ready to go! Now if only I could get started...
Sunday, October 02, 2011
Reflection and Self Assessment
This year's school-wide focus is writing. Many math teachers groan or cringe or opt out of the reading/writing initiatives, but I've always had kids do a minimum of daily journaling; sometimes up to entire stories or paragraphs explaining projects. Last year's school-wide focus was rubrics. It was our NEASC evaluation and so we were supposed to all use the same rubrics so kids had continuity. I would argue that students are more intelligent than we give them credit for and don't need that much continuity, but the idea behind the rubrics was okay and I was able to reformat them into something I find kid-friendly. The result of these two foci is an ellipse (math joke!), okay, actually it's a double sided weekly reflection sheet.
Journal and CW Rubric
We operate on a block schedule, so if I collect these every Friday that's 5 days (barring schedule changes, which happen approximately daily, okay not really, but I do plan to count how many of the two week periods I get all 5 days filled in). I used to carry around a clipboard all class and mark down any time a student was off task. This, combined with attendance/tardies made up their classwork grade. I'm still making occasional notes on my clipboard, and of course still taking attendance, but most kids are pretty honest when they fill in the rubric. The original plan was to have them out on desks all class so every time a student was off task or doing a good job at one of the sections I (or my co-teacher) would mark that down on the rubric. This turned out to be totally unrealistic. If a kid is off task I don't want them to find their rubric for me to write on, I want them to get to work! And several of them relate to behaviors when I am standing at the board. Instead, I'm trying to use the language on the rubric when I reprimand or congratulate students on the behavior, and making a few notes so if my memory completely fails me for some reason they won't get an unreasonable grade.
The journal side looks boring now, but that's because the questions will be on the board. Every day they will be asked "How did you meet the objective(s)?" and if they didn't to explain why. There's also a second question that varies. Some examples: to make a connection, to predict, to reflect (what are your goals for 2nd quarter? how should you study for the test?). I expect a minimum of two sentences and they don't get credit otherwise. The first week of past years I'd get quite a few "writing in math class?!?" exclamations, but this year there weren't so many. It's a quiet way to close class and students will remind me that it's journal time if I get too caught up with a lesson. The goal is to get students thinking about what they did in the hope that more of it will stick until next class (2-4 days away thanks to block scheduling). The first question has changed year to year, sometimes asking what math they learned and other times about the objective. I'm hoping that they will be more precise if they have to justify how they met the objective, although I'll miss the occasional comment about how someone did some really cool math in science class.
Journal and CW Rubric
We operate on a block schedule, so if I collect these every Friday that's 5 days (barring schedule changes, which happen approximately daily, okay not really, but I do plan to count how many of the two week periods I get all 5 days filled in). I used to carry around a clipboard all class and mark down any time a student was off task. This, combined with attendance/tardies made up their classwork grade. I'm still making occasional notes on my clipboard, and of course still taking attendance, but most kids are pretty honest when they fill in the rubric. The original plan was to have them out on desks all class so every time a student was off task or doing a good job at one of the sections I (or my co-teacher) would mark that down on the rubric. This turned out to be totally unrealistic. If a kid is off task I don't want them to find their rubric for me to write on, I want them to get to work! And several of them relate to behaviors when I am standing at the board. Instead, I'm trying to use the language on the rubric when I reprimand or congratulate students on the behavior, and making a few notes so if my memory completely fails me for some reason they won't get an unreasonable grade.
The journal side looks boring now, but that's because the questions will be on the board. Every day they will be asked "How did you meet the objective(s)?" and if they didn't to explain why. There's also a second question that varies. Some examples: to make a connection, to predict, to reflect (what are your goals for 2nd quarter? how should you study for the test?). I expect a minimum of two sentences and they don't get credit otherwise. The first week of past years I'd get quite a few "writing in math class?!?" exclamations, but this year there weren't so many. It's a quiet way to close class and students will remind me that it's journal time if I get too caught up with a lesson. The goal is to get students thinking about what they did in the hope that more of it will stick until next class (2-4 days away thanks to block scheduling). The first question has changed year to year, sometimes asking what math they learned and other times about the objective. I'm hoping that they will be more precise if they have to justify how they met the objective, although I'll miss the occasional comment about how someone did some really cool math in science class.
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