I'm writing early this week because I'll be leaving soon to present at Pearson's Course Redesign conference in Orlando, Florida. Instead of giving our students the day off on Friday, we've provided them with the classroom and time to complete their second open-ended problem. I can't take credit for that idea; it's all Heather's. We're not at the point where we can have subs yet, so that solution makes use of the time and teaches students a valuable lesson in time management. Beyond content, one of our primary goals in the course is to help students understand what college level expectations and work look like. The better we do at that, the better prepared they are in the spring when they head to a college level math class.

Now back to this week.

There has been a prevailing theme for a few lessons now: our balance is off. We see how much students enjoy being given challenging but accessible problems to solve with their groups. But we have to have some mini-lectures to teach new skills. We started the course with more of a block approach: they work together for a period of time, then we work as a class for a little while, then they go back to their group to apply knowledge. Now we're doing more back and forth (whole class/small group) after every few problems and it's just not as effective. They get antsy to keep working together and I feel like we're drawing things out too much, interrupting the flow. Luckily, my co-author is the queen of logistics and efficiency. She can easily see how to regroup certain problems and streamline others to make the class time better. It's funny that neither of us noticed this when we were writing but that's what the classroom does: it shines a spotlight on all the weaknesses of any print materials. We joked that if this were a traditional class with someone else's book, we'd be saying, "What were they thinking? Good bones but needs some reorganization." Unfortunately, those people are us. Hindsight's 20/20 for sure.

Are they learning? Absolutely. I'm continually amazed and pleased with what they can do with the challenges we present. The rigor is there but the packaging is different. We just feel that the pace of the class is dragging some which causes another problem: overconfidence. When students feel that everything is simple and/or they've seen any of the content in previous classes, they will jump to the conclusion of knowing it all. When we challenge them with extensions, connections, and explanations, they sometimes swing to other extreme of frustration. That comes from being overconfident and not listening as closely to the somewhat familiar content (even with a new twist of going deeper and focusing on understanding). We've been working on that for a little while and already see improvement. Again, it's an issue of balance. We have to have enough challenging problems to lure them into wanting to know more, but not get so challenging that they give up. We're diligently working on productive struggle and persistence.

I'm pleased that both sets of students are real troopers. They do what we ask and stay positive in the process. They realize that the course is a work in process and for that I'm grateful.

Really, this course is like writing a proof in graduate school. You're posed with a problem that looks insurmountable at the beginning. You try this and that and slowly see you might be getting somewhere. Add some time, sweat, perseverance, lots of erasing and rewriting, and before long, you can see the finish line and a path to reach it. I'm seeing a way to the finish line and I like what I see.

On to Florida. Let's redesign!

## Math Lit Toolbox

- 2017 Webinar Math Lit 5 Years Later
- Math Lit Forum
- MLCS Book: Math Lit
- 2014 Math Literacy webinar (Youtube)
- Math Literacy Training
- 2013 MLCS Presentation: What is Math Literacy? (Youtube webinar)
- MLCS syllabi (objectives and outcomes)
- 4 Credit Hour Math Literacy Course Syllabi
- A Typical Day: Math Lit classroom videos
- Math Lit instructor support
- Math Lit FAQ's
- Implementing Math Lit Presentation (Youtube webinar, PPTs, & handouts)
- Implementation blog series

## Wednesday, September 21, 2011

## Sunday, September 18, 2011

### Pilot Recap, Week 4: Busy, busy

In week 4, we tested, debriefed the first open-ended problem, conducted a unit 1 survey, and debriefed the whole unit. Both Heather and I were interested in finding out what students liked and didn't. A brief summary:

Active learning

Content is interesting and real-life

They're not bored

Getting to use MML

Working in groups to talk about problems

All the word problems

Long class period

Not being able to make up assignments

Heather and I are unapologetically strict on attendance and class participation. The course necessitates us to be so. We meet for a long class period and go through a lot. That experience cannot be duplicated at home since it's usually very active, has some kind of exploration, always has discussion, and relies on working as a whole group and small group to go through the content. Students like that dynamic because it's interesting. But missing class has consequences. Since developmental students can be their own worst enemies sometimes, we want them to learn the importance of doing work on time and attending every class. We're not unreasonable about either but our expectations are high and there are consequences to missing.

The first tests were not great nor terrible. They are learning to read the problems closer and study more. We spent time working on them afterwards and I believe there will be a better outcome on the next unit.

Since our class periods are 100 minutes each, that was just one day. The rest of week we began a new unit with a new focus. One of my favorite parts of this second unit is the incorporation of manipulatives. We're constantly noting things that could be improved and one is more hands-on learning in the first unit. They are eager to dig in and participate so we've got to integrate more of that into the course earlier on.

We investigated the idea of center using shapes, physical situations, and numbers. It was interesting to look at the concept of the mean in so many different perspectives. As with almost every activity we do, it starts out looking deceptively simplistic but always goes deeper than students anticipate, challenging them.

We closed the week on a somewhat frustrating note. It's always aggravating to test a lesson and find it's just not there yet. But that's the pilot process for you. My notes from that day are covered in annotations and post-its about all the ways to make it work better. It wasn't a complete loss as students got to explore something they can do usually (multiply fractions) but have little understanding of the procedures involved. This is not a course in arithmetic; that's the prerequisite. But we know this student is usually very weak on fraction and percent understanding. So we've incorporated those concepts within other lessons to strengthen their abilities whenever possible.

I almost forgot: we closed with a very short lesson that incorporated logistics by looking at an academic department's flowchart. Again, seemingly simple, it wasn't. There are lots of little details to read and understand to answer the questions. I always like the activities that incorporate a student success element into the math. Student success courses that are disconnected from content don't always have much punch. It means more to discuss ideas related to student success when they directly relate to the content or point in the course. We're trying to capitalize on that approach and timing whenever possible.

Next up: integers.

**What they liked:**Active learning

Content is interesting and real-life

They're not bored

Getting to use MML

Working in groups to talk about problems

**What they disliked:**All the word problems

Long class period

Not being able to make up assignments

Heather and I are unapologetically strict on attendance and class participation. The course necessitates us to be so. We meet for a long class period and go through a lot. That experience cannot be duplicated at home since it's usually very active, has some kind of exploration, always has discussion, and relies on working as a whole group and small group to go through the content. Students like that dynamic because it's interesting. But missing class has consequences. Since developmental students can be their own worst enemies sometimes, we want them to learn the importance of doing work on time and attending every class. We're not unreasonable about either but our expectations are high and there are consequences to missing.

The first tests were not great nor terrible. They are learning to read the problems closer and study more. We spent time working on them afterwards and I believe there will be a better outcome on the next unit.

Since our class periods are 100 minutes each, that was just one day. The rest of week we began a new unit with a new focus. One of my favorite parts of this second unit is the incorporation of manipulatives. We're constantly noting things that could be improved and one is more hands-on learning in the first unit. They are eager to dig in and participate so we've got to integrate more of that into the course earlier on.

We investigated the idea of center using shapes, physical situations, and numbers. It was interesting to look at the concept of the mean in so many different perspectives. As with almost every activity we do, it starts out looking deceptively simplistic but always goes deeper than students anticipate, challenging them.

We closed the week on a somewhat frustrating note. It's always aggravating to test a lesson and find it's just not there yet. But that's the pilot process for you. My notes from that day are covered in annotations and post-its about all the ways to make it work better. It wasn't a complete loss as students got to explore something they can do usually (multiply fractions) but have little understanding of the procedures involved. This is not a course in arithmetic; that's the prerequisite. But we know this student is usually very weak on fraction and percent understanding. So we've incorporated those concepts within other lessons to strengthen their abilities whenever possible.

I almost forgot: we closed with a very short lesson that incorporated logistics by looking at an academic department's flowchart. Again, seemingly simple, it wasn't. There are lots of little details to read and understand to answer the questions. I always like the activities that incorporate a student success element into the math. Student success courses that are disconnected from content don't always have much punch. It means more to discuss ideas related to student success when they directly relate to the content or point in the course. We're trying to capitalize on that approach and timing whenever possible.

Next up: integers.

## Sunday, September 11, 2011

### Quantway and the Complete College initiative

Complete College America is challenging and supporting states in efforts to improve completion rates. Recently, they awarded ten $1 million grants to ten states. The grants will help fund initiatives that should allow students to move forward through college towards degrees and ultimately, careers. One common theme amongst the states who received grants: initiatives to improve and accelerate the developmental math sequence. We know that it is often a bog for students and can prevent students from ever getting to college math and therefore, a degree.

Most colleges looking at ways to accelerate the process through developmental math are considering modular models based on the emporium concept of self paced, lab based learning.

But another option, Quantway, could potentially be faster for students and simpler for colleges to implement since it is only one course.

One of the main reasons we wanted to develop the Quantway course Mathematical Literacy for College Students at our college was the overwhelming number of Associate of Arts degrees awarded each year. Students need a statistics or general education math class to satisfy the majority of AA degrees. We saw time and again that when students had a high enough ACT or placement score, they could start in one of these courses and usually complete them. Both courses have a pass rate of around 70-75%, regardless of instructor, day pattern, or time of day. If we can get students into these classes, they usually pass and can complete the math requirement for their degrees.

The problem was so many students are just shy of meeting the requirement for entry. Enter a lengthy developmental math sequence emulating high school math with courses like intermediate algebra that can be more rigorous than the college level courses it feeds into. There lies the bog. At our school, we worked very hard to get them over that hump only to get into a class like statistics or general education math that is more accessible and does not depend on the prerequisite skills they worked so hard to get.

Yes, emporium models can accelerate the process. But they are costly initially (and potentially long term if they are not successful) in terms of both time and human investment. For the student headed to statistics, they still don't address the skills that student needs to be successful in the course or in their career.

Quantway's MLCS course is not proven yet to work since the pilots are still just beginning. But as we've already seen, something good can come of this approach. If it is successful, and that is a big if, schools can have a viable option to redesign that only involves the investment of teachers learning about the course and its pedagogy. Part of our pilot is to develop all the resources an instructor would need to be successful, not just the materials for a student. As someone who looked at option after option to try in a large scope redesign that would not be grant funded, it was always encouraging to find ideas that weren't costly and had real potential. We've already seen that with our combined algebra course. In one semester, a student can take beginning and intermediate algebra (if they place high enough) and go into college level math the following semester. We hope that MLCS will do the same for our program, but this time serving a different population with different goals.

Most colleges looking at ways to accelerate the process through developmental math are considering modular models based on the emporium concept of self paced, lab based learning.

But another option, Quantway, could potentially be faster for students and simpler for colleges to implement since it is only one course.

One of the main reasons we wanted to develop the Quantway course Mathematical Literacy for College Students at our college was the overwhelming number of Associate of Arts degrees awarded each year. Students need a statistics or general education math class to satisfy the majority of AA degrees. We saw time and again that when students had a high enough ACT or placement score, they could start in one of these courses and usually complete them. Both courses have a pass rate of around 70-75%, regardless of instructor, day pattern, or time of day. If we can get students into these classes, they usually pass and can complete the math requirement for their degrees.

The problem was so many students are just shy of meeting the requirement for entry. Enter a lengthy developmental math sequence emulating high school math with courses like intermediate algebra that can be more rigorous than the college level courses it feeds into. There lies the bog. At our school, we worked very hard to get them over that hump only to get into a class like statistics or general education math that is more accessible and does not depend on the prerequisite skills they worked so hard to get.

Yes, emporium models can accelerate the process. But they are costly initially (and potentially long term if they are not successful) in terms of both time and human investment. For the student headed to statistics, they still don't address the skills that student needs to be successful in the course or in their career.

Quantway's MLCS course is not proven yet to work since the pilots are still just beginning. But as we've already seen, something good can come of this approach. If it is successful, and that is a big if, schools can have a viable option to redesign that only involves the investment of teachers learning about the course and its pedagogy. Part of our pilot is to develop all the resources an instructor would need to be successful, not just the materials for a student. As someone who looked at option after option to try in a large scope redesign that would not be grant funded, it was always encouraging to find ideas that weren't costly and had real potential. We've already seen that with our combined algebra course. In one semester, a student can take beginning and intermediate algebra (if they place high enough) and go into college level math the following semester. We hope that MLCS will do the same for our program, but this time serving a different population with different goals.

## Saturday, September 10, 2011

### Pilot Recap, Week 3: Real, encouraging signs

Throughout this first unit of the Quantway MLCS course, Heather and I have both had lots of moments of questioning whether or not students were benefiting from the approach. They like most of the lessons and are engaged but still have that somewhat skeptical reaction to the course approach. It's just so different from what they are used to that the adjustment is real.

But yesterday, something wonderful happened. We graded the first set of open-ended problems they were asked to solve as a group.

Part of our idea in approaching this course is that we want to develop real problem solving skills as well as critical thinking. As anyone who's held a job knows, problems don't come boiled down, well organized, or well defined. Part of the problem with problems is just figuring out where to start. Plus, you have to figure out what you know, what you don't, what's relevant, and what's extraneous.

Traditional developmental math word problems are very nicely presented to students. They're short usually, 1-3 sentences, and full of key words. Often, they follow a "type" that students can recognize. Once they know how to deal with that type, they can solve the problem.

This sounds like the problems are easy. But anyone who has taught word problems knows that even with all these nice facets, students often seize up when presented with one and have little success with them.

One perk to this course is that like a statistics course, every problem is presented in a word problem format. The catch is they don't look like it. So students get used to reading the scenario presented and are willing to attempt them. They're not always successful but at least the willingness level is higher.

Every lesson is filled with problems to solve based on a scenario. But nearly all the problems have a unique solution. This is so we're not so out of the box that students resist entirely. They like solving a problem and checking their answers. The problems are realistic and difficult but they can find out if they're right or not.

That's all well and good but we do want them to see what real problems look like. Enter our once per unit open-ended problem.

On day 1 of the unit, students are presented with a large paragraph that explains the scenario and problem. Students have 3 weeks to work with a group to solve it. We intentionally help them through this by having regular revisits to the problem, each time with specific tasks for the group to complete. The first time through, we have them identify what they know, what they don't, what terminology they need help with, etc. The second time around, we have them develop a list of tasks for the group members as well as a timeline for completing them. They're also challenged with starting their rough draft. The third time has them looking at the rough draft with the group, refining it and making a plan for the final solution. They submit, we grade, and we debrief the whole thing the fourth time in class. We show them a strong solution, talk about the problem, and make notes for the next one so that they can do better when facing another problem at this level.

It's an interesting approach and we had our fingers crossed the whole time hoping they could do it. Every time they worked together, they went into the typical mode students do when they're confused. "We're lost. We don't get it. Can you help us?" Usually we swoop in as teachers and hold their hand. Heather and I both made an agreement: we will not do that or else they will never be able to do these problems. Instead, we ask questions and answer questions with questions in an attempt to get them talking. This helps them from getting too frustrated, but also keeps them in charge of figuring out their solution.

When they submitted the solutions, more than one student said they had done some research on their own, talking to people who might have been in the situation in the problem.

Grading them, we were even more surprised and pleased. In short, they rose to the occasion. The grades were much better than we ever expected, some C's but mostly A's and B's. No perfect papers but that was to be expected. They followed the expectations, and we could see that they finally got to the other side with the problem. In class, so often they were struggling to get started but at some point, they dug in and solved it. We had them do an individual assessment of their work and the group's after submitting their solution. Repeatedly, we read that students liked working with the group and enjoyed the process. We didn't ask them "do you like your group? Do you like this approach?" We just asked them to give a percentage to the level of work each person did and comment on anything if they wanted to. If someone wasn't pulling their weight, this was a private chance to tell us. What they volunteered was unexpected yet great to read.

All in all, it was a very positive way to close out the unit. Monday is the first test. My fingers are going to cramp from all the crossing but I do hope they can do well and rise to our expectations again. We've prepared them; the ball's in their court now.

But yesterday, something wonderful happened. We graded the first set of open-ended problems they were asked to solve as a group.

Part of our idea in approaching this course is that we want to develop real problem solving skills as well as critical thinking. As anyone who's held a job knows, problems don't come boiled down, well organized, or well defined. Part of the problem with problems is just figuring out where to start. Plus, you have to figure out what you know, what you don't, what's relevant, and what's extraneous.

Traditional developmental math word problems are very nicely presented to students. They're short usually, 1-3 sentences, and full of key words. Often, they follow a "type" that students can recognize. Once they know how to deal with that type, they can solve the problem.

This sounds like the problems are easy. But anyone who has taught word problems knows that even with all these nice facets, students often seize up when presented with one and have little success with them.

One perk to this course is that like a statistics course, every problem is presented in a word problem format. The catch is they don't look like it. So students get used to reading the scenario presented and are willing to attempt them. They're not always successful but at least the willingness level is higher.

Every lesson is filled with problems to solve based on a scenario. But nearly all the problems have a unique solution. This is so we're not so out of the box that students resist entirely. They like solving a problem and checking their answers. The problems are realistic and difficult but they can find out if they're right or not.

That's all well and good but we do want them to see what real problems look like. Enter our once per unit open-ended problem.

On day 1 of the unit, students are presented with a large paragraph that explains the scenario and problem. Students have 3 weeks to work with a group to solve it. We intentionally help them through this by having regular revisits to the problem, each time with specific tasks for the group to complete. The first time through, we have them identify what they know, what they don't, what terminology they need help with, etc. The second time around, we have them develop a list of tasks for the group members as well as a timeline for completing them. They're also challenged with starting their rough draft. The third time has them looking at the rough draft with the group, refining it and making a plan for the final solution. They submit, we grade, and we debrief the whole thing the fourth time in class. We show them a strong solution, talk about the problem, and make notes for the next one so that they can do better when facing another problem at this level.

It's an interesting approach and we had our fingers crossed the whole time hoping they could do it. Every time they worked together, they went into the typical mode students do when they're confused. "We're lost. We don't get it. Can you help us?" Usually we swoop in as teachers and hold their hand. Heather and I both made an agreement: we will not do that or else they will never be able to do these problems. Instead, we ask questions and answer questions with questions in an attempt to get them talking. This helps them from getting too frustrated, but also keeps them in charge of figuring out their solution.

When they submitted the solutions, more than one student said they had done some research on their own, talking to people who might have been in the situation in the problem.

*They were talking and thinking about math outside of class*and not just in the "what's the answer?" way they usually do. We were very pleasantly surprised.Grading them, we were even more surprised and pleased. In short, they rose to the occasion. The grades were much better than we ever expected, some C's but mostly A's and B's. No perfect papers but that was to be expected. They followed the expectations, and we could see that they finally got to the other side with the problem. In class, so often they were struggling to get started but at some point, they dug in and solved it. We had them do an individual assessment of their work and the group's after submitting their solution. Repeatedly, we read that students liked working with the group and enjoyed the process. We didn't ask them "do you like your group? Do you like this approach?" We just asked them to give a percentage to the level of work each person did and comment on anything if they wanted to. If someone wasn't pulling their weight, this was a private chance to tell us. What they volunteered was unexpected yet great to read.

All in all, it was a very positive way to close out the unit. Monday is the first test. My fingers are going to cramp from all the crossing but I do hope they can do well and rise to our expectations again. We've prepared them; the ball's in their court now.

## Monday, September 5, 2011

### Pilot Recap, Week 2: Does a Quantway approach dumb down standards?

I get many comments and questions about the new course Mathematical Literacy for College Students (MLCS), which is in the Quantway model. One that I don't get directly but I hear of often is "won't you be dumbing down the content and standards by using this approach?"

It's a valid concern because we are changing the focus off traditional algebra. Whenever that happens, educators worry that we'll be expecting less of students. I cannot say strongly enough that this concern is not an issue whatsoever. Actually, quite the opposite is the reality.

Students in a beginning or intermediate algebra class see content that's very prescriptive. And while they may not understand it, they can often get by with mimicking and memorization. As good intentioned as we all are to bring in conceptual understanding, applications, and understanding of the processes going on, the bulk of the content is rote use of skills that usually can be classified by a "type": one step equations, "work" problems, mixture problems, etc. A student who doesn't really know what they're doing can find ways to pass tests despite their lack of understanding.

In this class, the skills are not the focus. They exist and are plentiful but they're just one cog in a much bigger machine. The approach is something like this:

In the U.S., we have a well-defined view of what a math classroom should look like. It may or may not be the best view for employers or jobs but it's one we know and understand. Many instructors and from what we've seen, many students, believe that to do math, it must look something like this:

Solve: -3(2 - x) = 4- 2x

Certainly that is in the spectrum of mathematics, albeit in the skill band. But this is mathematics too:

There are two pay structures, a 5% raise or a 3% raise with a $1000 bonus. For whom is each option best?

Because these students are so new to a large problem like this, we're walking them through it and taking the opportunity to show graphs, tables, patterns, the role of variables, and develop numeracy whenever possible. But at the end of the day, solving that problem requires solving this equation (that they wrote): 1.05S = 1.03S + 1000. So we still get to equations of all sorts just as you would in an algebra class. This is simpler equation that they'll solve in the course. The large ones are seen as well.

The reality is when you do the skills

We're not going to walk away with a 90% pass rate so worries of this being an easy course to make students feel good that puts them in college level math for which they're unprepared are unfounded. The ones who succeed will be excellently prepared.

I hope that we will work our way through this journey this semester, over the hills and valleys, and come out on the other side with the great majority of the students with us and better for having the experience. My Pollyanna ways just expect that to happen. But we have to wait and see.

Enough with the metaphors and referencing of old movies. It's time to get back to work.

It's a valid concern because we are changing the focus off traditional algebra. Whenever that happens, educators worry that we'll be expecting less of students. I cannot say strongly enough that this concern is not an issue whatsoever. Actually, quite the opposite is the reality.

Students in a beginning or intermediate algebra class see content that's very prescriptive. And while they may not understand it, they can often get by with mimicking and memorization. As good intentioned as we all are to bring in conceptual understanding, applications, and understanding of the processes going on, the bulk of the content is rote use of skills that usually can be classified by a "type": one step equations, "work" problems, mixture problems, etc. A student who doesn't really know what they're doing can find ways to pass tests despite their lack of understanding.

In this class, the skills are not the focus. They exist and are plentiful but they're just one cog in a much bigger machine. The approach is something like this:

- Rich situation initially explored
- Skills identified that need development
- Development of skills
- Application of the new skill in the original context
- Further exploration of the situation in a deeper way while making connections

In the U.S., we have a well-defined view of what a math classroom should look like. It may or may not be the best view for employers or jobs but it's one we know and understand. Many instructors and from what we've seen, many students, believe that to do math, it must look something like this:

Solve: -3(2 - x) = 4- 2x

Certainly that is in the spectrum of mathematics, albeit in the skill band. But this is mathematics too:

There are two pay structures, a 5% raise or a 3% raise with a $1000 bonus. For whom is each option best?

Because these students are so new to a large problem like this, we're walking them through it and taking the opportunity to show graphs, tables, patterns, the role of variables, and develop numeracy whenever possible. But at the end of the day, solving that problem requires solving this equation (that they wrote): 1.05S = 1.03S + 1000. So we still get to equations of all sorts just as you would in an algebra class. This is simpler equation that they'll solve in the course. The large ones are seen as well.

The reality is when you do the skills

*and*the concepts*and*make connections*and*apply every skill developed in multiple contexts, you get a hard course. It's an interesting course, but it's hard nonetheless. We're watching closely to see how students fare in the pilot and studying the methods we use such as sequencing and pacing of topics to ensure they'll understand them. But regardless, this is a tough approach for students. They can't fake it or mimic anything and that can be frustrating, because that's a technique they may have come to trust in times of struggle. The ones who are successful will do well in a college level course, that we're confident of. At this point, we're just hoping that most can be successful at this course and make it to the college level course.We're not going to walk away with a 90% pass rate so worries of this being an easy course to make students feel good that puts them in college level math for which they're unprepared are unfounded. The ones who succeed will be excellently prepared.

I hope that we will work our way through this journey this semester, over the hills and valleys, and come out on the other side with the great majority of the students with us and better for having the experience. My Pollyanna ways just expect that to happen. But we have to wait and see.

Enough with the metaphors and referencing of old movies. It's time to get back to work.

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