Week 2 is complete and again, I'm pleasantly surprised at how well things are going. The main difference I noticed this week was work ethic. Maybe our students are just more ready for a college class. Or maybe we're better conveying and eliciting the amount of work necessary. It could be a combination. Either way, they are working hard. They're doing paper and MML homework as well as quizzes (in and out of class). They've remarked that the class takes a lot of time. We told them that on the first day, so I'm happy to see they've taken us seriously. Because a class doesn't take time unless you're really working on it. Most of my students in the fall said the class didn't take that much time. They also said at the end of the semester that they wished they had worked harder. And their results were fair, but not outstanding.
So far, we've done a little algebra, lots of numeracy, some proportional reasoning, and today began a look in functions. It's always something different, be it whole class vs. group work or the content. We mix it up regularly to maintain their attention and engagement. I overheard a student this week say, "this goes so fast!" That's an amazing comment since 1) it's a math class and 2) it's a 100 minute class period. But I'll take it.
I do a quiz every class to start the class. It's my way of checking in with them and keeping them accountable. Sometimes it's a MML problem. Sometimes it's a conceptual problem or something from homework. It varies. Today, I just wanted to see what they thought of the class so far and what they need to work on. The comments fell into two categories: "I like the class" and "I need to work more on fractions." Some examples:
"I was always struggling with math but this class and MML have given me better confidence in myself."
"This is probably the most exciting math class I've ever been in. I like how it's taught!"
Are some struggling and still asking for me to stand at the board the entire period working examples? Absolutely. It's not the majority but some want that familiar approach. Still, they're buying in. They see that a different approach can still be good. Plus, we do enough whole class and mini-lecture type work to appease those needs for direct instruction. I am very pleased to see that they're seeking out help. That alone will make a big difference.
We had a problem today that was very challenging. It dealt with units they're unfamiliar with and was very realistic and therefore, tough. But it was so fun to watch them break through the problem. At first they were frustrated and complaining, then "what about this?" and working, and finally I heard someone say they got it. And more followed. We talked about perseverance and how it's uncomfortable sometimes to learn but during that moment of discomfort is when the actual learning happens.
So, all in all, I'm pleased with the progression of the course. Certainly there are places for improvement and adjustment but it's taking shape into a course I hope to teach for many, many years. There's something incredibly satisfying about showing adults the power of mathematics in ways they haven't seen before.
Friday, January 27, 2012
Saturday, January 21, 2012
MLCS Round 2: Progress!
Note: The semester has started and so has blogging. I'm resuming my weekly blog updates and adding in other items as they occur.
Our second semester of Mathematical Literacy for College Students is underway and the differences are night and day. Heather and I have both been very pleasantly surprised at the attitudes, participation levels, and work ethics of our students. Being the lovers of math and statistics that we are, we want to know the source of the improvement. A lot can be attributed to it being the second time around and the improved confidence we're exhibiting. We know the goal of the course as well as each unit and can express that clearly. But we also know where they're going to struggle and have made very specific attempts to combat that.
First change: materials
The materials have come a long way, making the experience so much more enjoyable. We've applied our discovery about lesson framing to make each lesson have a flow that works well. No lesson starts in a way that students expect, which pulls them in, but they're well paced and developed so that students can progress with the content. We've yanked some lessons, written many new, reorganized all of them, and added many new features. The MyMathLab course has also improved in big ways. Overall, it's helped tremendously.
Second change: grading structure
We learned that the key component to this course upon which all success hinges is their willingness to put it in a lot of work with the various concepts and skills we're exploring. That's a new paradigm for students since they're used to "take notes, do 30 problems, test on ones similar." We don't operate under that model, so we've learned to show students how we will operate and build a grading scheme to elicit the behaviors we want. It's far too soon to see what will work and what will need tweaking, but I'm still optimistic. Students are already figuring out that the more work they do now, they less they'll need to do later. And since we have so few points in our course, every point counts.
Here's our scheme:
There are 10 points for each of the 4 units. That's it. Up to 4 points can be earned based on the test percentage (e.g., 85-100% on the test = 4 points). Up to 2 points are earned based on their MML average. Up to 2 points are earned based on their in-class work average. And the last 2 points are earned based on their group project grade. If they have perfect attendance, they earn 1 bonus point.
That's 40 points. The final exam is 100 points, making 140 for the course. They need 100 total points to get the lowest C. The premise is to reward work, to keep the points smaller so that each point is valued more, and to reward the idea of learning the content eventually. In real life, no one will ever ask you when you learned something, just have you learned it. So, we'll see. It may be a flop. If it is, we'll adjust and move forward. We built this approach using ideas from George Woodbury's use of gaming theory in the classroom.
Third change: the students
I've long enjoyed spring semesters more than fall semesters because you have students who usually have at least one semester of college under their belts. In the fall, we tend to get a lot of students who decide a few days before the semester starts that they want to go to college. That makes for a wide variety of preparation levels and commitment to education. We had a lot of great students in the fall who wanted to work hard and we had some who weren't ready yet to be in college. This time, we can already see in both sections that the majority of students are ready to go, happy to be in a class like this, and optimistic about trying something different. I'm sure we're selling it better and that helps. But it can't all just be us. We've been fortunate to get good classes already that want to work and learn. Will all of them be successful? Probably not. But I'm still incredibly hopeful that most will pass with a positive experience to boot.
Our second semester of Mathematical Literacy for College Students is underway and the differences are night and day. Heather and I have both been very pleasantly surprised at the attitudes, participation levels, and work ethics of our students. Being the lovers of math and statistics that we are, we want to know the source of the improvement. A lot can be attributed to it being the second time around and the improved confidence we're exhibiting. We know the goal of the course as well as each unit and can express that clearly. But we also know where they're going to struggle and have made very specific attempts to combat that.
First change: materials
The materials have come a long way, making the experience so much more enjoyable. We've applied our discovery about lesson framing to make each lesson have a flow that works well. No lesson starts in a way that students expect, which pulls them in, but they're well paced and developed so that students can progress with the content. We've yanked some lessons, written many new, reorganized all of them, and added many new features. The MyMathLab course has also improved in big ways. Overall, it's helped tremendously.
Second change: grading structure
We learned that the key component to this course upon which all success hinges is their willingness to put it in a lot of work with the various concepts and skills we're exploring. That's a new paradigm for students since they're used to "take notes, do 30 problems, test on ones similar." We don't operate under that model, so we've learned to show students how we will operate and build a grading scheme to elicit the behaviors we want. It's far too soon to see what will work and what will need tweaking, but I'm still optimistic. Students are already figuring out that the more work they do now, they less they'll need to do later. And since we have so few points in our course, every point counts.
Here's our scheme:
There are 10 points for each of the 4 units. That's it. Up to 4 points can be earned based on the test percentage (e.g., 85-100% on the test = 4 points). Up to 2 points are earned based on their MML average. Up to 2 points are earned based on their in-class work average. And the last 2 points are earned based on their group project grade. If they have perfect attendance, they earn 1 bonus point.
That's 40 points. The final exam is 100 points, making 140 for the course. They need 100 total points to get the lowest C. The premise is to reward work, to keep the points smaller so that each point is valued more, and to reward the idea of learning the content eventually. In real life, no one will ever ask you when you learned something, just have you learned it. So, we'll see. It may be a flop. If it is, we'll adjust and move forward. We built this approach using ideas from George Woodbury's use of gaming theory in the classroom.
Third change: the students
I've long enjoyed spring semesters more than fall semesters because you have students who usually have at least one semester of college under their belts. In the fall, we tend to get a lot of students who decide a few days before the semester starts that they want to go to college. That makes for a wide variety of preparation levels and commitment to education. We had a lot of great students in the fall who wanted to work hard and we had some who weren't ready yet to be in college. This time, we can already see in both sections that the majority of students are ready to go, happy to be in a class like this, and optimistic about trying something different. I'm sure we're selling it better and that helps. But it can't all just be us. We've been fortunate to get good classes already that want to work and learn. Will all of them be successful? Probably not. But I'm still incredibly hopeful that most will pass with a positive experience to boot.
Sunday, December 11, 2011
Pilot Recap, Week 16: Lessons Learned (Part 2)
Last week, I blogged about the lessons we learned on a large scale items (pedagogy, role of technology, metacognition, etc.). Today I'll add to our lessons learned but this time in terms of the course and structure.
We surveyed our students continually throughout the semester and also had informal check-ins with them to find out what was working and what wasn't. That helped us tweak as we went and also maker bigger improvements for next semester. During those surveys and chats, we started to inquire about what they could have done to make the experience better. Yes, we realize that we had a huge impact on the success of the course since it's brand new. But students are a part of this learning equation too. What they said was interesting.
1. MyMathLab homework matters and helps to develop skills but the paper homework matters more. Many of our students wanted to gloss over it because we didn't collect and grade each problem for correctness. This was the place where went "old school" and used the approach used by many countries who are successful with math eduction. That is, give students fewer but more involved and more meaningful problems and assign all of them. Some paper homework assignments may have only had 5 problems but they were 5 tough problems that would take some time to make sense of. And that sense-making process is where the learning happens.
2. Never, ever skip class. We had an attendance policy but it needs changing. Still, it did help to get students to class. But they found that they had to be there regardless of a policy or not. In a course like this, you can't just "get notes and do the homework." Much of the learning experience involved the students. In a typical lecture, the instruction happens through the instructor. But much of our instruction happened when students were working hard problems and talking to us and each other about them. Yes, we had notes and reference content on paper but nothing was boiled down to "here's a skill, here's 6 examples of it, and now there's 30 problems with multiple variations." What happened in class just couldn't be recreated outside of it. I don't think it necessarily can in a traditional course either. But that fact was glaring in this course.
3. Apathy will kill your grade. If they didn't care enough to show up, get help when things got tough, or even try the homework, they were sunk and quickly at that. Again, this is not all that different from any other math class. But where I see that most often is in my college level classes because the content is new and harder. In developmental classes, they've seen the content before. So they can ride on their memories from high school, help from their friends, MML, etc. We did topics that their friends had never seen either so they really needed to work on the content and get help ASAP.
4. Work more hours than you think you need to. We told them the college rule of 2 hours of work per week outside of class for every one hour in class. But they ignored us and tried to get by with less. And when we asked them if the time spent studying mattered, it was an unequivocal yes. They wished they had spent much more time each week.
Basically, the premise of this course is to take care of all their developmental math in one semester. Well, there is no free lunch in life. If you're going to do a year's worth of content in one semester, you're going to have to work at it. And no amount of us nagging or reminders about the obvious rewards (much less time and money in developmental math) mattered. In the end, it comes down to them. We had a lot of students who were successful in the course. And we had a fair number who withdrew or failed.
5. Points, even extra credit, were not strong motivators. This was such a disappointment to us. All our 'tricks' learned from years of teaching just did not work. We offered bonus points for various things and opportunities for extra credit with some special assignments. We had a points structure with lots of points for all the various things we did beyond tests. And in the end, few got any bonus points. They just didn't care enough to do what was needed to get them. I hated to see that but that again shows where they're just not quite college ready yet. We wanted them to learn the value of attending, working hard, and aiming higher. And some just wouldn't do those things. You can lead a horse to water...
Still, better learned now than in a college level class. That's the point of developmental courses: develop the content and student success skills to be successful in college. It's not just about math. So we're trying a new points structure in the spring based on a friend's approach with course contracts and a gaming principle. George Woodbury has been trying and refining his use of these approaches for a while. With his ideas and knowledge of our students and this course, we've developed a new structure that encourages work. Because honestly, that's what we needed them to do more than anything. It also is built on the concept of learning the material eventually. Yes, students need to pass each test but they also need to eventually make sense of the material by the end of the semester. We tried to encourage that this semester by letting them do test corrections on their exams and offering bonus points towards their final exam. Again, not that many actually did this. Frustrating but a recurring theme to this semester.
All of these lessons were hard but necessary if these students are going on to a college level course next semester. I don't hold my students' hands in my college level courses and neither do my colleagues. I hate to see a student not get these lessons until it's too late, but I can't make the learning happen for them. We learned a lot this semester, good and bad, and so did they.
We've got finals this week and then it's on to planning for next semester. I'm encouraged about it. One, because I'm an eternal optimist and two, because of what our students said on Friday of last week. "This is a great course." "Definitely keep offering it. We learned so much." "We really learned how to apply math." I know we're on to something good.
My blogs will continue with updates about materials and the course so please keep checking back. The first pilot is complete but the process to make this course come to life is not.
We surveyed our students continually throughout the semester and also had informal check-ins with them to find out what was working and what wasn't. That helped us tweak as we went and also maker bigger improvements for next semester. During those surveys and chats, we started to inquire about what they could have done to make the experience better. Yes, we realize that we had a huge impact on the success of the course since it's brand new. But students are a part of this learning equation too. What they said was interesting.
1. MyMathLab homework matters and helps to develop skills but the paper homework matters more. Many of our students wanted to gloss over it because we didn't collect and grade each problem for correctness. This was the place where went "old school" and used the approach used by many countries who are successful with math eduction. That is, give students fewer but more involved and more meaningful problems and assign all of them. Some paper homework assignments may have only had 5 problems but they were 5 tough problems that would take some time to make sense of. And that sense-making process is where the learning happens.
2. Never, ever skip class. We had an attendance policy but it needs changing. Still, it did help to get students to class. But they found that they had to be there regardless of a policy or not. In a course like this, you can't just "get notes and do the homework." Much of the learning experience involved the students. In a typical lecture, the instruction happens through the instructor. But much of our instruction happened when students were working hard problems and talking to us and each other about them. Yes, we had notes and reference content on paper but nothing was boiled down to "here's a skill, here's 6 examples of it, and now there's 30 problems with multiple variations." What happened in class just couldn't be recreated outside of it. I don't think it necessarily can in a traditional course either. But that fact was glaring in this course.
3. Apathy will kill your grade. If they didn't care enough to show up, get help when things got tough, or even try the homework, they were sunk and quickly at that. Again, this is not all that different from any other math class. But where I see that most often is in my college level classes because the content is new and harder. In developmental classes, they've seen the content before. So they can ride on their memories from high school, help from their friends, MML, etc. We did topics that their friends had never seen either so they really needed to work on the content and get help ASAP.
4. Work more hours than you think you need to. We told them the college rule of 2 hours of work per week outside of class for every one hour in class. But they ignored us and tried to get by with less. And when we asked them if the time spent studying mattered, it was an unequivocal yes. They wished they had spent much more time each week.
Basically, the premise of this course is to take care of all their developmental math in one semester. Well, there is no free lunch in life. If you're going to do a year's worth of content in one semester, you're going to have to work at it. And no amount of us nagging or reminders about the obvious rewards (much less time and money in developmental math) mattered. In the end, it comes down to them. We had a lot of students who were successful in the course. And we had a fair number who withdrew or failed.
5. Points, even extra credit, were not strong motivators. This was such a disappointment to us. All our 'tricks' learned from years of teaching just did not work. We offered bonus points for various things and opportunities for extra credit with some special assignments. We had a points structure with lots of points for all the various things we did beyond tests. And in the end, few got any bonus points. They just didn't care enough to do what was needed to get them. I hated to see that but that again shows where they're just not quite college ready yet. We wanted them to learn the value of attending, working hard, and aiming higher. And some just wouldn't do those things. You can lead a horse to water...
Still, better learned now than in a college level class. That's the point of developmental courses: develop the content and student success skills to be successful in college. It's not just about math. So we're trying a new points structure in the spring based on a friend's approach with course contracts and a gaming principle. George Woodbury has been trying and refining his use of these approaches for a while. With his ideas and knowledge of our students and this course, we've developed a new structure that encourages work. Because honestly, that's what we needed them to do more than anything. It also is built on the concept of learning the material eventually. Yes, students need to pass each test but they also need to eventually make sense of the material by the end of the semester. We tried to encourage that this semester by letting them do test corrections on their exams and offering bonus points towards their final exam. Again, not that many actually did this. Frustrating but a recurring theme to this semester.
All of these lessons were hard but necessary if these students are going on to a college level course next semester. I don't hold my students' hands in my college level courses and neither do my colleagues. I hate to see a student not get these lessons until it's too late, but I can't make the learning happen for them. We learned a lot this semester, good and bad, and so did they.
We've got finals this week and then it's on to planning for next semester. I'm encouraged about it. One, because I'm an eternal optimist and two, because of what our students said on Friday of last week. "This is a great course." "Definitely keep offering it. We learned so much." "We really learned how to apply math." I know we're on to something good.
My blogs will continue with updates about materials and the course so please keep checking back. The first pilot is complete but the process to make this course come to life is not.
Saturday, December 3, 2011
Pilot Recap, Week 15: Lessons Learned (Part 1)
This week was the last week of new content. We decided to spend next week (the last week of regular semester) to work on getting ready for the final exam. It's not a typical thing for either Heather or me to take a week to do that in any class but we thought it could help them do better on the final exam. They will work on MML and paper problems that recap the course and cover all the key content. And in the spirit of full disclosure, we're exhausted after this pilot so this idea for the last week was a welcome relief.
So what did we learn this semester?
There's not enough space to list it all so I'll be brief but still use two blog posts to cover it. In short, we learned a lot. Here's the first half:
1. As I've said numerous times on this blog, you can make a really hard, rigorous course without all the algebraic skills of a typical beginning and intermediate algebra course. We did that and then some. The course was a real challenge for students. We found ways to make it more accessible but the fact remains, it's quite hard to read and solve word problems all day, every day throughout the course. But it's a worthy challenge.
2. It can be really fun to do real mathematics with developmental students. Not canned problems, not rote skills, but real, rich mathematics. Problems that don't have a quick, pat answer. Situations that are fuzzy and ill formed. The discussions we had and the engagement of the students was really enjoyable. They were thinking and talking and learning about the power of mathematics. That's valuable regardless of passing or failing or what happens next semester.
3. Balance is everything. We finally got there but wow, was that a rough road. Finding just the right amount of MML vs. paper homework, lecture vs. group work, open-ended vs. single solution problems, skills vs. applications, the list never seems to end. Basically, this course turned our regular course approach upside down. So all the things we knew how to do well inside and out didn't work so well anymore. Finding ways to take students with us on this journey and make it work for all involved was hard but now I feel like we know what works. Or at least we're a whole lot closer to that point.
4. It's frightening to see how little numeracy and literacy skills our developmental students have. But I tend to not to focus on that. We get what we get and there's no point in getting upset over it. Instead, we consistently challenged them to read, research, and think in ways they hadn't. We stretched them. For that, I'm proud.
5. Developmental students really lack metacognitive skills. They don't know how they think or learn. We constantly asked them to take a problem that started out in words and translate it 3 more ways: numerically, graphically, and algebraically. But when we were done, another goal was to find out which way made sense to them. While we worked and worked on that, I think more work needs to occur there in an overt way. We focused so much on other student success skills, not knowing that metacognition would be a key one throughout. Usually student success is about attitude, test strategies, and time management. Those are included in our course but so are ideas about majors such as STEM fields, how to calculate and understand grading practices, and how to understand themselves and their learning processes.
6. Technology need not be that lightening rod of controversy it often is in mathematics education. Our approach was simple: use technology the people do in the workplace. That is, they use whatever they have or makes the most sense given a situation. So that's usually a calculator (scientific, could be graphing or not) and a computer but it could just be a pencil. We used Excel nonstop, and students really liked that. The graphing calculator was zero advantage to the students who had it. We're not doing a lot of "graph: y=3x + 2" so it's no leg up to have one. And the numeracy required is so consistent and involved that having a calculator didn't mean they had all the answers. Plus, our tests pushed them to explain calculations and delve deeper, beyond simple calculations. The calculator was just a tool, not a crutch.
7. My last lesson in this part is for all those instructors out there who are feeling disenfranchised by some of the approaches of redesign which seem to be replacing us with technology. Computers are just tools. The human element matters in learning. It always has and it always will. The role we had in the classroom was essential. We lectured some, not a lot, but were constantly questioning them, challenging them, and keeping them moving forward when they got stuck. We weren't guides on the side or sages on the stage. We were their teachers, in every sense of that word. Heather and I both walked around every inch of our classroom every class period, moving to where we needed to be and doing what needed to be done. Sometimes that's whole group, sometimes it's small group, sometimes it's with individuals. Whatever was necessary, we adapted.
I truly enjoyed it and feel re-energized towards teaching. I've also joked that I'm ruined on traditional classes. Now that I've had the opportunity to teach a course that every aspect is real and relevant, that's interesting and not contrived, and that students really enjoy, I can't go back to teaching traditional algebra face to face. I may continue teaching it online and will definitely continue teaching statistics, general education math, math for elementary teachers, and calculus face to face. I need to get college algebra using this approach but that will happen down the road. My goal is to take this approach to as many classes as I have the time and energy to do so. It's just too rewarding for them and me not to.
That's all for now. Next week, I'll recap the lessons we learned about the course structure like grading, advising, etc.
So what did we learn this semester?
There's not enough space to list it all so I'll be brief but still use two blog posts to cover it. In short, we learned a lot. Here's the first half:
1. As I've said numerous times on this blog, you can make a really hard, rigorous course without all the algebraic skills of a typical beginning and intermediate algebra course. We did that and then some. The course was a real challenge for students. We found ways to make it more accessible but the fact remains, it's quite hard to read and solve word problems all day, every day throughout the course. But it's a worthy challenge.
2. It can be really fun to do real mathematics with developmental students. Not canned problems, not rote skills, but real, rich mathematics. Problems that don't have a quick, pat answer. Situations that are fuzzy and ill formed. The discussions we had and the engagement of the students was really enjoyable. They were thinking and talking and learning about the power of mathematics. That's valuable regardless of passing or failing or what happens next semester.
3. Balance is everything. We finally got there but wow, was that a rough road. Finding just the right amount of MML vs. paper homework, lecture vs. group work, open-ended vs. single solution problems, skills vs. applications, the list never seems to end. Basically, this course turned our regular course approach upside down. So all the things we knew how to do well inside and out didn't work so well anymore. Finding ways to take students with us on this journey and make it work for all involved was hard but now I feel like we know what works. Or at least we're a whole lot closer to that point.
4. It's frightening to see how little numeracy and literacy skills our developmental students have. But I tend to not to focus on that. We get what we get and there's no point in getting upset over it. Instead, we consistently challenged them to read, research, and think in ways they hadn't. We stretched them. For that, I'm proud.
5. Developmental students really lack metacognitive skills. They don't know how they think or learn. We constantly asked them to take a problem that started out in words and translate it 3 more ways: numerically, graphically, and algebraically. But when we were done, another goal was to find out which way made sense to them. While we worked and worked on that, I think more work needs to occur there in an overt way. We focused so much on other student success skills, not knowing that metacognition would be a key one throughout. Usually student success is about attitude, test strategies, and time management. Those are included in our course but so are ideas about majors such as STEM fields, how to calculate and understand grading practices, and how to understand themselves and their learning processes.
6. Technology need not be that lightening rod of controversy it often is in mathematics education. Our approach was simple: use technology the people do in the workplace. That is, they use whatever they have or makes the most sense given a situation. So that's usually a calculator (scientific, could be graphing or not) and a computer but it could just be a pencil. We used Excel nonstop, and students really liked that. The graphing calculator was zero advantage to the students who had it. We're not doing a lot of "graph: y=3x + 2" so it's no leg up to have one. And the numeracy required is so consistent and involved that having a calculator didn't mean they had all the answers. Plus, our tests pushed them to explain calculations and delve deeper, beyond simple calculations. The calculator was just a tool, not a crutch.
7. My last lesson in this part is for all those instructors out there who are feeling disenfranchised by some of the approaches of redesign which seem to be replacing us with technology. Computers are just tools. The human element matters in learning. It always has and it always will. The role we had in the classroom was essential. We lectured some, not a lot, but were constantly questioning them, challenging them, and keeping them moving forward when they got stuck. We weren't guides on the side or sages on the stage. We were their teachers, in every sense of that word. Heather and I both walked around every inch of our classroom every class period, moving to where we needed to be and doing what needed to be done. Sometimes that's whole group, sometimes it's small group, sometimes it's with individuals. Whatever was necessary, we adapted.
I truly enjoyed it and feel re-energized towards teaching. I've also joked that I'm ruined on traditional classes. Now that I've had the opportunity to teach a course that every aspect is real and relevant, that's interesting and not contrived, and that students really enjoy, I can't go back to teaching traditional algebra face to face. I may continue teaching it online and will definitely continue teaching statistics, general education math, math for elementary teachers, and calculus face to face. I need to get college algebra using this approach but that will happen down the road. My goal is to take this approach to as many classes as I have the time and energy to do so. It's just too rewarding for them and me not to.
That's all for now. Next week, I'll recap the lessons we learned about the course structure like grading, advising, etc.
Friday, November 18, 2011
Pilot Recap, Week 13: Winding down
We're making our way toward the end of the course now. Next week we have our last unit test. After Thanksgiving, we plan to test a few additional lessons that hadn't made their way into the current units yet but will in the future. The last week, we have a big project planned to pull the entire course together. It will be an in-class, open-ended problem that students solve together as a group. They will also have an individual component to turn in to ensure accountability.
I was out of town for AMATYC last week and sick at the beginning of this week, so there's less to report. Still, it was a good week. We explored viral marketing with students, building exponential growth models and exploring social networking. The statistics are amazing in terms of how much time is spent worldwide on social sites. A few years ago, it was a fun past time. Now, it's a major means of marketing and sales for companies. Analyzing that was interesting mathematically and context-wise. Students definitely liked discussing it.
Today we talked about order of magnitude, pH, and the Richter scale. It was really interesting showing students how some contexts have really large and really small numbers in them simultaneously. Making sense of them and graphing them can be very difficult. Going to new scales based on order of magnitude makes the process accessible. It's interesting to show students the human side of mathematics, how we take numeric truths and use techniques to make them easier to deal with.
Heather and I can see the light at the end of the tunnel. A great deal of learning occurred this semester for our students and us. We've got lots of ideas for the spring to make things even better in terms of grading, testing, and helping them adapt to the level of work. The content and lessons have really worked well and those that haven't are in the process of revision. I believe we'll get this course to an even better place than it already is, which is pretty good so far.
I was out of town for AMATYC last week and sick at the beginning of this week, so there's less to report. Still, it was a good week. We explored viral marketing with students, building exponential growth models and exploring social networking. The statistics are amazing in terms of how much time is spent worldwide on social sites. A few years ago, it was a fun past time. Now, it's a major means of marketing and sales for companies. Analyzing that was interesting mathematically and context-wise. Students definitely liked discussing it.
Today we talked about order of magnitude, pH, and the Richter scale. It was really interesting showing students how some contexts have really large and really small numbers in them simultaneously. Making sense of them and graphing them can be very difficult. Going to new scales based on order of magnitude makes the process accessible. It's interesting to show students the human side of mathematics, how we take numeric truths and use techniques to make them easier to deal with.
Heather and I can see the light at the end of the tunnel. A great deal of learning occurred this semester for our students and us. We've got lots of ideas for the spring to make things even better in terms of grading, testing, and helping them adapt to the level of work. The content and lessons have really worked well and those that haven't are in the process of revision. I believe we'll get this course to an even better place than it already is, which is pretty good so far.
Tuesday, November 15, 2011
AMATYC Workshop Handouts
Below is the packet we used during our workshop on MLCS. It contains the course description as it is being used in Illinois, topics in each unit, implementation options, and a sample lesson. Based on your state or needs, some topics and lessons can be omitted without a negative impact. We are using a big version of this course (6 credit hours) but it is easily scaled down to a fewer objectives and credit hours.
One of the things we talked about during the workshop was the trouble Heather and I had when choosing a sample lesson. We can't pick just one lesson that encompasses all the great facets of this course. So this lesson does not contain theory that is being developed. It comes after a lesson with theory. But it does showcase the relevance, difficulty, and multiple approach process we use when developing the content. Also, the homework with the lesson looks brief. However, it isn't if the student works all the problems as intended. Also, there are other components to the homework not shown here such as online homework.
Keep in mind that the lessons are still being edited and are not in their final forms. But they still give you a taste of our approach. Looking at the presentation below will also give you more snapshots of how we approach the content.
MLCS AMATYC 2011 Workshop
One of the things we talked about during the workshop was the trouble Heather and I had when choosing a sample lesson. We can't pick just one lesson that encompasses all the great facets of this course. So this lesson does not contain theory that is being developed. It comes after a lesson with theory. But it does showcase the relevance, difficulty, and multiple approach process we use when developing the content. Also, the homework with the lesson looks brief. However, it isn't if the student works all the problems as intended. Also, there are other components to the homework not shown here such as online homework.
Keep in mind that the lessons are still being edited and are not in their final forms. But they still give you a taste of our approach. Looking at the presentation below will also give you more snapshots of how we approach the content.
MLCS AMATYC 2011 Workshop
Saturday, November 12, 2011
AMATYC Presentation
Below is a link to the slides used in the presentation. They're not the zooming variety since that takes a special app (pptPlex) in PowerPoint to see. But all content shown today is included below.
If you are interested in seeing more lessons and/or class testing, please email me.
AMATYC 2011 Presentation
For more information on the MLCS pilot, including video and weekly updates, please keep reading below.
If you are interested in seeing more lessons and/or class testing, please email me.
AMATYC 2011 Presentation
For more information on the MLCS pilot, including video and weekly updates, please keep reading below.
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