Are you interested in developing MLCS at your school? If you have questions or would like to see a sample of a unit or would like a training workshop, please contact me.

View more PowerPoint from kathleenalmy

- 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

Below is a recent presentation on MLCS given at ICTCM and IMACC. It is related to but different from the workshops I've been giving since November.

Are you interested in developing MLCS at your school? If you have questions or would like to see a sample of a unit or would like a training workshop, please contact me.

Are you interested in developing MLCS at your school? If you have questions or would like to see a sample of a unit or would like a training workshop, please contact me.

View more PowerPoint from kathleenalmy

This past week we taught a lesson that begins with a hands-on component. The video excerpt will show some of the whole class parts of the lesson. Here is a run-down of the lesson:

Lesson: Shortest Distance

Objective: Develop and apply the distance formula

*This lesson appears late in unit two. This unit focuses on understanding numbers and operations. To that end, we work with many situations that allow us to explore how numbers behave and introduce algebraic ideas at the same time. By the time we see this lesson, students have learned signed numbers and their operations, number properties, order of operations, exponent rules, Pythagorean Theorem, and slope.*

To begin the lesson, we measure the classroom and make a scale drawing of it using a scale of 1 unit on a grid = 1 foot in the room. We then decide to place objects from the classroom on the drawing by establishing an origin and axis system based on that origin. This process of setting an origin and determining locations based on it emulates a simplistic version of what surveyors do.

This leads to a good discussion on where in the room the origin should be and what would make it easiest to work with. Eventually students settle on the back left corner of the classroom (from their perspective) since that makes the classroom the 1st quadrant. This choice creates all positive ordered pairs.

Since the measuring tapes are only 25 feet, measuring becomes an interesting challenge. Discussion quickly ensues on logistics and the role of accuracy. We try to measure with the tape on the floor, but are careful to keep the tape taut if measuring off the ground. Students then find ordered pairs for objects in the room they choose. We pick up the lesson at this point being taught by Heather Foes:

*NOTE: This is not a professional quality video.*

The lesson continues, moving between whole group discussion and small groups with students practicing tasks and digging deeper into the ideas of the lesson. I've described below what occurred but was not shown on the video.

After finding a few specific distances, we generalize the process using Pythagorean Theorem with generic ordered pairs. Students need to really understand the order of operations to use the formula accurately.

Students practice using the formula. As a class, we discuss how a graph can be used to avoid using the distance formula but there are limitations to that method as well. Lastly, we connect this idea to slope. Both slope and Pythagorean Theorem can be used on or off a grid. We want students to see how the formulas look with a grid and without as well as the pros and cons of each method. The goal is not just apply the distance formula to two random points. Instead, the goal is to see how the formula can come about and why it is necessary.

A discussion always arises about what can be measured and what cannot. We also discuss the pros and cons of physical measurement vs. math on paper. Students usually surprise us by liking the idea of working on paper. Measuring doesn't require much math, but it is challenging to do it accurately. Also, it requires them to move and they don't always enjoy that element.

This lesson illustrates the depth of the lessons in the MLCS course. The algebra or an algorithm are not the only goals of the lesson. It's the process and discussion of getting there that elicits the most learning and improvement of students' conceptual understanding. Students quickly see that real life problems are almost always much more complicated than traditional textbook problems. But those same real life problems are also very rich and interesting. They are worth the effort necessary to solve them.

Lesson: Shortest Distance

Objective: Develop and apply the distance formula

To begin the lesson, we measure the classroom and make a scale drawing of it using a scale of 1 unit on a grid = 1 foot in the room. We then decide to place objects from the classroom on the drawing by establishing an origin and axis system based on that origin. This process of setting an origin and determining locations based on it emulates a simplistic version of what surveyors do.

This leads to a good discussion on where in the room the origin should be and what would make it easiest to work with. Eventually students settle on the back left corner of the classroom (from their perspective) since that makes the classroom the 1st quadrant. This choice creates all positive ordered pairs.

Since the measuring tapes are only 25 feet, measuring becomes an interesting challenge. Discussion quickly ensues on logistics and the role of accuracy. We try to measure with the tape on the floor, but are careful to keep the tape taut if measuring off the ground. Students then find ordered pairs for objects in the room they choose. We pick up the lesson at this point being taught by Heather Foes:

The lesson continues, moving between whole group discussion and small groups with students practicing tasks and digging deeper into the ideas of the lesson. I've described below what occurred but was not shown on the video.

After finding a few specific distances, we generalize the process using Pythagorean Theorem with generic ordered pairs. Students need to really understand the order of operations to use the formula accurately.

Students practice using the formula. As a class, we discuss how a graph can be used to avoid using the distance formula but there are limitations to that method as well. Lastly, we connect this idea to slope. Both slope and Pythagorean Theorem can be used on or off a grid. We want students to see how the formulas look with a grid and without as well as the pros and cons of each method. The goal is not just apply the distance formula to two random points. Instead, the goal is to see how the formula can come about and why it is necessary.

A discussion always arises about what can be measured and what cannot. We also discuss the pros and cons of physical measurement vs. math on paper. Students usually surprise us by liking the idea of working on paper. Measuring doesn't require much math, but it is challenging to do it accurately. Also, it requires them to move and they don't always enjoy that element.

This lesson illustrates the depth of the lessons in the MLCS course. The algebra or an algorithm are not the only goals of the lesson. It's the process and discussion of getting there that elicits the most learning and improvement of students' conceptual understanding. Students quickly see that real life problems are almost always much more complicated than traditional textbook problems. But those same real life problems are also very rich and interesting. They are worth the effort necessary to solve them.

Non-STEM courses like Quantway, Statway/Statpath, and MLCS are taking flight across the country and with that comes a lot of questions. Because we've been working on a course and implementation for over a year, we've learned some things to help make it work. Here are some tips for course development:

**1. Identify your goal.**

We wanted appropriate preparation for the student heading to liberal arts math or statistics. Sometimes the goal is acceleration. While that wasn't our first goal per se, we are certainly happy for that to be a by-product of the course.

Knowing your goals defines your next step.

**2. Determine the course content.**

Look forward to where students will go and see what they need when they get there. For us, that was statistics, liberal arts math, or intermediate algebra. While we have many intermediate algebra topics in our course, they are covered in a conceptual, applied way that uses modeling. So yes, we look at rational functions but no, we don't add rational expressions. If a student will eventually take college algebra or precalculus, they'll need those algebraic manipulation skills. We wanted them to be able to go into an intermediate algebra (IA) course without issue. Our IA course has factoring in it, as most do. So we were comfortable with exposing students to the concept of factoring in the MLCS course and doing one very useful type: GCF. Again, they can get the rest of the factoring techniques in an IA course.

Using IA as our bridge forced us to add in a few more objectives on polynomials. It was funny; at first we didn't like that because it felt contrived. It seemed like we were only adding them for a next course that many wouldn't take and therefore felt disconnected from the content. But as we taught the course in the fall, there were times where polynomials came up and I needed to be able to say "degree" or "binomial" and students know what I mean. They were necessary topics to our end goal. That was great! So we embedded them in the second unit of our course to ensure students have that basis for later material. It also further prepares them for the bridge course. In so doing, we solved two problems.

How much content you have affects the next step.

**3. Determine the number of credit hours.**

It was very important to us that this course not be like all the other developmental math courses we teach: rushed. This learner needs time to discuss and think and learn. We need that time too and we wanted it in the classroom with them. Plus, our state has a lot of requirements to make this course something that can be articulated. Add that up and we have 6 credit hours. It's unlikely that schools outside of Illinois will need anywhere near that many. The mode for this course as it's being developed around the country is 4 credits.

Also consider if you want a lab hour embedded within the credit hours or in addition to them. We use MyMathLab and have considered having an hour with students in a lab while they're working on skills. We haven't needed to go to that yet but it's something to think about. Doing this is kind of a hybrid of a self-paced emporium model and a pathways model.

**4. Write a course outline.**

Now comes the fun part: goals and objectives. State succinctly but clearly the course description, goals, objectives, and content. Here is our course outline that went to the college curriculum committee if you'd like to see an example. You can download it as a Word document so that it's editable.

**5. Choose materials.**

In our course outline, you'll read that we have a MLCS course packet and MyMathLab. The course packet is the book that we're writing for this course that isn't yet in print. If you're interested in seeing a unit, please email me. I can request a copy be sent to you from the publisher, Pearson. It is available for testing this fall if you want to pilot MLCS and will be officially in print in summer 2013.

We started writing because we wanted materials to match the content and goals of this course. Because this course is new, they did not exist. You can piecemeal books together but it will be awkward for the teacher and student. You can also write lessons, but that is a time-consuming undertaking. Open source materials will be available eventually but that content doesn't cover all the objectives in our course or state. Plus, we wanted MML. It was an important requirement with any materials we used. Lastly, we wanted materials that addressed every possible need for any instructor. So we have written and designed many tools for instructors in the book.

**6. Plan the execution of the course.**

This is the step where you think about how many sections you will offer, when they'll be offered, who will teach them, and how they'll be taught. If possible, plan schedules so that teachers can get to each other's classes and observe occasionally. Heather and I did this throughout the fall semester and it was invaluable. It has improved the materials greatly and educated us on ways to make the class experience even better. You see things in the back of the room that aren't obvious from the front. So consider this step.

If this step isn't possible (or even if it is), plan how the instructors teaching the course can converse after lessons to debrief and improve them. We meet after our classes and talk. If you can't do that, set up a discussion board. But this step is so important that it shouldn't be skipped over. This is not an algebra course. It's new for everyone. Having the security of people to talk to helps everyone entering into the course for the first time. And it helps the course get better and better over time. This technique is like a Japanese lesson study. Not identical, but it emulates their philosophy of teaching a lesson and refining it with other instructors over time.

**7. Training**

You may want training before you begin your pilot to understand better what a class feels like, how to make groups function well, what kinds of pitfalls there are to be aware of, etc. I've been helping schools who are developing the course and will continue to do so. Experiencing a lesson is so important so that you can see what the classroom will feel like and what you need to prepare for. I can say without question that teaching in this way has made it very hard to go back to my 100% lecture, traditional courses. Students are engaged and discussions are rich. I truly enjoy what we do in the classroom in a way I never have. And I've always loved teaching so that's saying something. Yes, it's an adjustment but one that's made quickly for everyone.

I'm also thinking about creating a training workshop that would allow several schools to come to one location so that I can work with them. If this is of interest to you, please email me. If there is sufficient interest, I can try to work out the logistics of making it happen.

My main goal with this post is to let you know you're not alone. I've been working with schools on various redesign initiatives for years. I will continue to do that with this course as well. Having someone to ask questions of and bounce ideas with really helps everyone involved have more confidence in the process.

We wanted appropriate preparation for the student heading to liberal arts math or statistics. Sometimes the goal is acceleration. While that wasn't our first goal per se, we are certainly happy for that to be a by-product of the course.

Knowing your goals defines your next step.

Look forward to where students will go and see what they need when they get there. For us, that was statistics, liberal arts math, or intermediate algebra. While we have many intermediate algebra topics in our course, they are covered in a conceptual, applied way that uses modeling. So yes, we look at rational functions but no, we don't add rational expressions. If a student will eventually take college algebra or precalculus, they'll need those algebraic manipulation skills. We wanted them to be able to go into an intermediate algebra (IA) course without issue. Our IA course has factoring in it, as most do. So we were comfortable with exposing students to the concept of factoring in the MLCS course and doing one very useful type: GCF. Again, they can get the rest of the factoring techniques in an IA course.

Using IA as our bridge forced us to add in a few more objectives on polynomials. It was funny; at first we didn't like that because it felt contrived. It seemed like we were only adding them for a next course that many wouldn't take and therefore felt disconnected from the content. But as we taught the course in the fall, there were times where polynomials came up and I needed to be able to say "degree" or "binomial" and students know what I mean. They were necessary topics to our end goal. That was great! So we embedded them in the second unit of our course to ensure students have that basis for later material. It also further prepares them for the bridge course. In so doing, we solved two problems.

How much content you have affects the next step.

It was very important to us that this course not be like all the other developmental math courses we teach: rushed. This learner needs time to discuss and think and learn. We need that time too and we wanted it in the classroom with them. Plus, our state has a lot of requirements to make this course something that can be articulated. Add that up and we have 6 credit hours. It's unlikely that schools outside of Illinois will need anywhere near that many. The mode for this course as it's being developed around the country is 4 credits.

Also consider if you want a lab hour embedded within the credit hours or in addition to them. We use MyMathLab and have considered having an hour with students in a lab while they're working on skills. We haven't needed to go to that yet but it's something to think about. Doing this is kind of a hybrid of a self-paced emporium model and a pathways model.

Now comes the fun part: goals and objectives. State succinctly but clearly the course description, goals, objectives, and content. Here is our course outline that went to the college curriculum committee if you'd like to see an example. You can download it as a Word document so that it's editable.

In our course outline, you'll read that we have a MLCS course packet and MyMathLab. The course packet is the book that we're writing for this course that isn't yet in print. If you're interested in seeing a unit, please email me. I can request a copy be sent to you from the publisher, Pearson. It is available for testing this fall if you want to pilot MLCS and will be officially in print in summer 2013.

We started writing because we wanted materials to match the content and goals of this course. Because this course is new, they did not exist. You can piecemeal books together but it will be awkward for the teacher and student. You can also write lessons, but that is a time-consuming undertaking. Open source materials will be available eventually but that content doesn't cover all the objectives in our course or state. Plus, we wanted MML. It was an important requirement with any materials we used. Lastly, we wanted materials that addressed every possible need for any instructor. So we have written and designed many tools for instructors in the book.

This is the step where you think about how many sections you will offer, when they'll be offered, who will teach them, and how they'll be taught. If possible, plan schedules so that teachers can get to each other's classes and observe occasionally. Heather and I did this throughout the fall semester and it was invaluable. It has improved the materials greatly and educated us on ways to make the class experience even better. You see things in the back of the room that aren't obvious from the front. So consider this step.

If this step isn't possible (or even if it is), plan how the instructors teaching the course can converse after lessons to debrief and improve them. We meet after our classes and talk. If you can't do that, set up a discussion board. But this step is so important that it shouldn't be skipped over. This is not an algebra course. It's new for everyone. Having the security of people to talk to helps everyone entering into the course for the first time. And it helps the course get better and better over time. This technique is like a Japanese lesson study. Not identical, but it emulates their philosophy of teaching a lesson and refining it with other instructors over time.

You may want training before you begin your pilot to understand better what a class feels like, how to make groups function well, what kinds of pitfalls there are to be aware of, etc. I've been helping schools who are developing the course and will continue to do so. Experiencing a lesson is so important so that you can see what the classroom will feel like and what you need to prepare for. I can say without question that teaching in this way has made it very hard to go back to my 100% lecture, traditional courses. Students are engaged and discussions are rich. I truly enjoy what we do in the classroom in a way I never have. And I've always loved teaching so that's saying something. Yes, it's an adjustment but one that's made quickly for everyone.

I'm also thinking about creating a training workshop that would allow several schools to come to one location so that I can work with them. If this is of interest to you, please email me. If there is sufficient interest, I can try to work out the logistics of making it happen.

My main goal with this post is to let you know you're not alone. I've been working with schools on various redesign initiatives for years. I will continue to do that with this course as well. Having someone to ask questions of and bounce ideas with really helps everyone involved have more confidence in the process.

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