Sunday, December 1, 2013

Tuesday, November 26, 2013

Math Lit FAQ: Is there enough algebra in Math Lit for students to be successful in intermediate algebra?

Answer:  Yes!

Math Lit was designed to have a substantial amount of algebra so that students have multiple options after the course, including intermediate algebra.  Most of our students do not head that way, but those who do are successful.  Math Lit has almost all of the beginning algebra skills except for trinomial factoring and solving/graphing linear inequalities.  Even though most MLCS students take general education math or statistics after the course, they can transition to intermediate algebra if they so desire.  They do not have to go back to beginning algebra.

Because some states have stringent intermediate algebra requirements, more algebra topics were incorporated into our book to allow schools to include the topics they need.  Systems, rational functions, radical functions, quadratic functions, and exponential functions are included.  The approach to all of these topics that are at the intermediate algebra level is one of modeling and application, not symbolic manipulation.  Students who go to a traditional intermediate algebra class after MLCS have seen all of these ideas at a deeper level and just get the additional manipulation skills necessary for STEM courses.

Sunday, November 17, 2013

Math Lit FAQ: How is MLCS different than Quantway, Statway, and the New Mathways Project?

Pathways courses:
  • include Math Literacy for College Students (MLCS), Quantway, Statway, and the New Mathways Project.
  • create alternative routes to or through college-level math courses, especially non-STEM courses.
  • look forward to college needs instead of backward to high school deficiencies.
  • emphasize critical thinking and problem solving.
  • integrate college knowledge and student success into the course.
  • use online homework for skill development and paper homework for concept development.
  • use authentic problems and contextualized learning.

Where the differences lie are the execution and philosophy.

Quantway and Statway are part of the Carnegie Foundation's pathways initiative.  The New Mathways Project (NMP) from University of Texas-Austin's Dana Center is a pathways initiative that includes a Foundations course at the developmental level as well as college level courses in both STEM and non-STEM.  Each foundation has its own policies and protocols for member schools.  Membership sometimes has a monetary cost associated with it, which can be substantial for a college.  Other times, a member school is asked to contribute lessons, data, feedback, etc.  Membership requirements for schools depend on the foundation and the level at which a school wants to work with a foundation.  Options are available to provide flexibility for schools.  Additionally, member colleges become part of a network that allows faculty to talk to one another through collaboratories.  Training is also included.

MLCS is part of AMATYC's New Life initiative, which initially worked with both the Carnegie Foundation and the Dana Center.  So the objectives of Quantway, the NMP's Foundations course, and MLCS are very similar.  However, MLCS does not require a school to sign a contract or commit to a timeline.  Instead, they have independence.  But with that independence comes some additional tasks.  They must find their own materials and training, if desired.  They do not become a member of collaboratory.  So they will need to establish a network within their school or with other piloting schools if they wish to have faculty communicating with each other.  Because there are so many schools teaching MLCS, this is not difficult to do as it might have been a year or two ago.

MLCS is highly adaptable, ranging from 3 to 6 credit hours and replacing beginning algebra or beginning and intermediate algebra with the option of geometry as well.  We chose this course because we believed in the concept of pathways but needed to adapt the course to our state's requirements.  To secure a pilot and get state-level approval, we had to be able to modify the objectives and content.  Also, an intermediate algebra requirement exists in many states and can heavily affect articulation.  Since the MLCS objectives and curriculum were built by faculty from various states, its course outline can flex to address that requirement.  Other pathways courses have a defined curriculum and credit hour requirement.

The philosophies are different too.  MLCS is about taking a developmental student to college level throughout a semester.  When it begins, the content is at the low beginning algebra level but progresses as high as a school wants, potentially to the high intermediate algebra difficulty level if desired.  Other pathways courses feel like a college level quantitative literacy or statistics course with just-in-time remediation on algebra topics as needed.  We make algebra a focus in MLCS for a couple of reasons.  Many students in the course haven't seen much algebra.  Those who have taken it often have large holes in their understanding.  But beyond both of those concerns, students need options after the course.  MLCS students have the option of quantitative literacy, liberal arts math, or statistics after the course.  Including a significant amount of algebra allows a student to move to intermediate algebra if they want to bridge over to a STEM track.  Without that algebra, they would have to go back to beginning algebra if they change their mind, as is the case with Quantway and Statway.

Pathways courses usually include student success facets with the content in some way, but the execution varies.  The NMP Foundations course includes student success aspects but is also recommended to be paired with a student success course.  Doing so requires students to take two courses simultaneously.  We integrated the student success component into MLCS content for many reasons but a big one was logistics.  Pairing courses is a logistical challenge, to say the least.  It requires more advising and has more issues with scheduling faculty to teach them and registering students. Keeping all that content within the MLCS course simplifies things considerably.  It also gives the student success content more meaning because the content is not separate.  It's developed along with mathematical content, allowing students to use math to analyze various aspects of college success.

That idea of practical logistics is a key difference with MLCS and other pathways courses.  MLCS was developed by the faculty who were teaching it.  Every lesson we have in our book, Math Lit, has been tested repeatedly by us in our classrooms and with many class testers around the country.  You learn so much when you teach something yourself.  Our materials are the only ones on the market taught by all the authors.  There are many materials packages becoming available now written by very talented people who are not in the classrooms where the material is taught.  Occasionally, an instructor is also an author but it is not the norm.  That makes a big difference.  We know the developmental student because we teach them every day.  We also know issues that colleges have with articulation, scheduling, adjuncts, resources, and the like.  So we wrote materials with those issues in mind.  Additionally, it's not necessary to have a Ph.D. in educational theory to use our materials and teach the course successfully.  Our intent was that major amounts of training and collaboration would not be necessary.  Yes, they are helpful but they are also hard to come by when working with large numbers of adjuncts, something that is typical of most college math departments.

The work and research that foundations do is valuable and necessary for success with this initiative.  But foundations are just one necessary facet of a monumental change like this one.  It also takes the practitioners from all around the country to make a course work outside of an educational lab and inside a college classroom.  It takes the major publishers getting on board to create materials that faculty can use in ways they are accustomed to, such as having MyMathLab for online homework.  To my knowledge, there has yet to be a grant-based or foundation-based initiative that scaled on its own.  The statistics reform movement has had the most success for an initiative scaling but it too was supported by all the major publishers, not just grants or organizations.  Similarly, the Common Core is starting to take off because commercial materials to support its implementation are available.

All of these components (foundations, grants, publishers, and practitioners) are working together to create lift off for the pathways movement.  No one person, organization, or method is enough.  And no one execution will work for all schools or states.  Options are a good thing.  Regardless of the approach, we are working for a common objective.  How we do that differs but ultimately we are all committed to same goal:  meaningful and sustainable change in developmental mathematics education.

Tuesday, November 12, 2013

FAQ: Do you offer training for MLCS using Math Lit?

Answer:  Yes!

Heather and I provide numerous ways to train faculty to teach a Math Literacy course using Math Lit.  We wrote the book and supporting materials so that training is not a requirement for using the materials successfully.  Several schools using the book have done so without training.  To see all of the instructor supports available, check out this blog post from August.  At the time of that post, the information was "coming soon," but now all of the supports are available.

Some faculty prefer training to gain a sense of the classroom culture and common issues as well as have a way to have specific questions for their school answered.  To address this request, we tailor professional development to meet your needs and timeline.  We can provide any of the following:

  • List of suggested lessons to cover to meet your course objectives and credit hour goals
  • Calls and webinars before and during piloting to answer questions
  • Face-to-face workshops (1/2 day, full day, or multiple days) for in-depth training
  • Training videos within MML (coming soon)

We offered a MOOC this past summer and learned much from that.  The key takeaway for us is that faculty would like a training course that is more like the Khan academy in that they would watch videos and complete assignments but would not have to interact with other faculty unless they desired to do so.  The MOOC this summer that we taught was an online course about pathways courses as opposed to a training course to teach them.

We are working on more online training for the future to address that request.  In the meantime, we can provide face to face training or webinars if travel is an issue.

Please contact us if you would like to set up training.

Wednesday, November 6, 2013

Math Lit FAQ: Do I have flexibility using Math Lit?

Answer:  Absolutely!

Since the beginning of the pathways movement, there has been an emphasis on using new pedagogy with developmental math students.  But doing so is unfamiliar to many instructors.  Because of that, we incorporated a lot of instructor support into the Math Lit book at every level:  course, cycle, and lesson.  Throughout the lessons, there are suggestions for teaching with groups or as a whole class, how much time for each part of a lesson, tips for teaching, and questions to consider asking.  We created tests, quizzes, rubrics, project templates and a ready-to-go MyMathLab course based on requests from class testers.  This level of support is provided to address direct requests we received for teaching with a new style.

However, some faculty see that level of support and would prefer to not use all of it all of the time.  Heather and I fall into that category and many faculty will too.  You are in charge of your classroom and you know your students and your style.  So you will have ideas on how you want to proceed and it's not necessarily going to match our suggestions.  That's great and to be expected because the book is not a script.

To give instructors who desire more assistance what they need, we have a lot of stepped out problems on the page.  If someone needs that and it's not there, they don't necessarily want to create it on the fly.  For the person who doesn't want it, we suggest ignoring what you're not interested in using and teaching how you would prefer.  I do this with all the books I teach from.  Because depending on the day, my students, current events, what have you, I will want to adapt and flex my instruction.  Sometimes I do every problem on the page and ask every question and some days I do something completely different.  That's your prerogative as an instructor.

There are many other places where flexibility exists.  You can omit lessons for which you do not need the content.  You can skip the focus problems or use them but skip the focus problem lessons in class.  You can swap out suggested activities for ones you would like to do.  For example, in lesson 3.5, we have an exploration where students measure a cup of flour by volume and then weigh it to see the variation in a 1-cup measurement.  I've done this for several semesters and it's always been fun and informative.  But this semester I wanted something different.  Heather had the idea of setting a timer on the document camera and starting it.  She asked students to put their heads down and close their eyes and look up when they thought a minute had passed.  They were then to see what time had really passed on the timer and write that time down.  We collected the actual times from students and used that as a data set to talk about natural variation instead of the flour weights.

Other options include having students do some of the Explores and/or Connects as homework instead of in class.  You could use the videos we will have in the spring to have students work on skills outside of class and do only the Explores and Connects in class.  This would emulate a flipped classroom approach.  You can teach everything in groups or everything as a whole class instead of the combined approach used in the book.

These are just a few examples.  The key takeaway is that you run your classroom.  The book is there to provide students with relevant problems for explorations, theory and terminology, and key examples for reference.  How you use the content and how much or how little you use the structure of the book and its lessons is up to you, just as it is with any text.  Make it work for you and your students.

Monday, October 28, 2013

Going to AMATYC?

I'm leaving soon for AMATYC where I'll present at the Developmental Math Summit on Wednesday of this week.  This is a 2-day event with speakers from major organizations like Carnegie, NADE, and the Dana Center as well as many faculty who have been leaders in developmental math reform.

On Friday, Heather and I will present a new session we have created that deals with solving authentic problems in a developmental math classroom, specifically the type that appear in pathways classes like MLCS, Quantway, and Statway.  It's a very active session with participants working in groups and then reporting out.  We will discuss findings from groups and then talk about best practices and tips for teaching with this kind of problem solving.  Join us at 2 pm this Friday in Platinum 4 to learn more about it.

Thursday, October 17, 2013

TEDx Cambridge: Inverting the Curriculum

Here is a great talk about the philosophy behind new courses like MLCS.  In 9 minutes, Ariel Diaz succinctly articulates one of the current problems in education and what we can do to make strides in fixing it.

Wednesday, October 16, 2013

Math Lit FAQ: Why are topics in the book ordered in that fashion?

The topic ordering of Math Lit, and all pathways materials for that matter, is decidedly nontraditional.  The traditional ordering of topics such as rational expressions in chapter 7 and writing expressions in chapter 2 is not the only correct ordering.  It's just a conventional one.  It's the one someone chose years ago in a textbook and others adopted.  The traditional order is linear, for the most part.  But there are some topics like proportions, variation, statistics, and geometry that seem to move around from textbook to textbook, always feeling not quite in line with the rest of the chapter.

The problem is that math is not completely linear.  Sure, there are topics which follow from each other in a particular order.  For those topics, we address them in a linear fashion in the book.  But many topics have great flexibility in where they can be explored.  And often, they make more sense when they are not in the traditional order.

So, back to the original question:  why are the topics in the book ordered in that fashion?

Answer:  Because it works.

To me, mathematics education isn't about "covering" topics.  It's about creating capable problem solvers.  To do that, we have to connect lots of areas of math.  Real problems are messy and not tightly defined as only an equations problem or only a geometry problem.  Real problems transcend multiple strands of math at once, requiring the student to integrate and apply.  So we develop the content in an integrated way, constantly applying what is developed.  The result may seem unusual at first, but only because we are so conditioned to a particular topic order.  That order isn't right or wrong; it's just familiar.

Consider this example:  In traditional beginning algebra texts, combining like terms is usually in chapter 1 or 2, in preparation for solving equations.  Later, in chapter 5, the exponents rules will be developed in preparation for multiplying and dividing polynomials.  These ideas are developed weeks apart and as separate ideas, but they need to addressed together to make sense of them.  So we develop like terms right around the time we're working on exponent rules to see if students really get when the rules apply and when they don't.  It leads to a much greater understanding of both topics.  And then we use both ideas in applied problems so that further connections are made.

We know these developmental students have not been successful in traditional algebra.  Doing the same content exactly as it was done the first time is not necessarily going to lead to different results.  Shaking things up and approaching content with problem solving in mind engages these students more and helps them make progress with their understanding.  It is exciting to move from a "check off this skill" culture to one where students are constantly making progress and capable of solving more involved problems.

It's also a lot more enjoyable to ebb and flow between topics, coming back to them regularly in a deeper way, after the mind has had time to work on other things.  This is quite different than taking a topic and going through every perspective of it all at once.  Students can get lost in the trees and forget there is a forest.

Does content being enjoyable matter?  Sure it does.  I don't believe my job is to entertain; it's to educate.  But students have to engage to learn.  And motivating them can lead to engagement.

At first, it may seem like a topic hasn't been "finished" because every facet has not explored before leaving it.  Give it a little time and it will come up again.  Students will be able to do more with it each time and increased understanding follows.  But it takes time and patience to see that.  Looking at three sections of any integrated text won't give the full picture of what it can help accomplish.

I think Einstein said it best:

"We can't solve problems by using the same kind of thinking we used when we created them."

Tuesday, October 15, 2013

Policy article on pathways and MLCS

This week, a new policy article releases on reforms in developmental math, including pathways like Math Literacy for College Students.  Rock Valley College's Math Literacy course using the text Math Lit is one of several reforms highlighted in the piece.  A full copy of the article is linked below.

From the Learning Works website:

"Experiments to reverse low community college completion rates by redesigning the remedial math most students must take are yielding promising results, defying assumptions about the kind of math students really need.  Changing Equations highlights a new movement in a growing number of the nation’s community colleges to prioritize statistics and quantitative reasoning, a major departure from the traditional one-size-fits-all remedial math sequence that emphasizes intermediate algebra.

Early results – including a dramatic jump from 6 to 51 percent in the proportion of students completing college-level math in their first year of college — are lending credence to the theory that the alternative pathways are better tailored to academic majors that don’t require intermediate algebra. About a quarter of California’s 112 community colleges, as well as numerous colleges in at least a dozen other states, have begun to develop these alternatives for non-STEM (science, technology, engineer, and math) students.

The alternative math pathways supplement other remedial math reforms that colleges and college systems have been pursuing for several years – including changes to instructional practices as well as placement policies.

This brief was written for LearningWorks by Pamela Burdman, a nationally recognized education policy analyst, philanthropy professional, and journalist."

Wednesday, October 9, 2013

Math Lit FAQ: Does Math Lit include factoring?

Answer:  Yes and no.

We include some factoring in Math Lit but the treatment is not the usual treatment given in algebra texts.  The reasons for that are logistical and philosophical.  First, there's only so much time.  In 4 months (1 semester), we are working to take a developmental student to college level.  There is a lot to be done and learned in that time.  So there isn't time to do all the traditional topics we once did and all the rich problem solving along with new topics.  We had to make decisions on what was most important.

Second, the decision to give factoring an abbreviated treatment was a philosophical one.  Heather and I decided early on that we would not cover topics in the book just for historical purposes.  Just because something has always been taught does not mean it is still relevant.  At one point in history, students had to know Latin to graduate from college.  But times change and so do requirements.  Factoring is rarely used in realistic settings.  Factoring the GCF is useful for rewriting formulas, so we cover that.  We also talk about factored form and its advantages.  The traditional treatment of factoring implies factoring will occur often so every technique is necessary.  But factored form really isn't talked about in any meaningful way.  Students don't see why factoring might be valuable and why it might not work (outside of simple prime polynomials).

The traditional reasoning for inclusion of factoring is that it develops critical thinking skills and prepares students for the algebra to come.  We already have critical thinking in spades in Math Lit.  Inclusion of factoring as a mental exercise is not a sufficient reason.  Also, it is not necessary for success in the non-STEM classes MLCS feeds into.

Until our STEM curriculum is updated, STEM-bound students need to factor.  So we cover it heavily in our intermediate algebra class, a course students can take after MLCS if they want to bridge to the STEM track.

Still, some schools want to factor in MLCS.  And that's certainly their prerogative.  MLCS does not have one set of objectives; it is meant to flex to the local and state needs of a college.  So some colleges add some additional sections on factoring.  Others make sure factoring is covered in detail in the first STEM course students may take after MLCS, something that benefits all students, not just ones coming from MLCS.

Tuesday, October 8, 2013

Math Lit FAQ: Can I teach MLCS as a 4-credit course using Math Lit?

Answer:  Yes

Actually, most schools that use Math Lit use it for a 4-credit hour course.  Illinois has certain requirements that raise the credit hours needed from 4 to 6.  But a 6-credit version of MLCS is not common outside of Illinois.

There is a lot of content in Math Lit to allow schools to choose the topics they want for their 4 credits.  We did some research to find out what topics schools want in their 4-credit versions.  The results showed a large amount of variation in the topics covered.  Some schools want geometry, others want more algebra topics.  Some want more statistics while others want a course that has a lower prerequisite.  So we couldn't remove topics to make the book 4 credits without removing options for schools and states.  We did not want to dictate what this course looks like.  It looks like whatever a schools wants it to.

We built the book with the idea that schools would be picking and choosing topics to meet their local and state requirements.  To allow for that, we marked several sections in the table of contents that could be omitted without a negative impact later in the course.  We have schools using various sections throughout the book while others basically use the first half or the last half.  The most common approach is to use all of Cycle 1 to set the foundation for the course and any necessary sections from the remaining cycles to address the topics of the school's choice.

Additionally, Heather and I work with schools to help them choose which sections to cover.  If you are planning a pilot or have adopted the book and want some ideas for choosing sections, please email us.  We will go through your goals in terms of topics and what courses you want MLCS to feed into to determine what can be deleted or reduced in terms of coverage to meet your goals.  There are a multitude of ways to mold the book to meet your needs.

New FAQ series starting on the blog

I'm starting a new series of posts, each one addressing a question I receive often.  Many are related to our book, Math Lit.  Others are about the MLCS course.  Questions include:

  • Can I teach the MLCS class as a 4 credit class using Math Lit?
  • Does Math Lit include factoring?
  • Why are the topics in the book ordered in that fashion?
  • Do I have flexibility using Math Lit?
  • Is there enough algebra in Math Lit for students to be successful in intermediate algebra?
  • We have an emporium model at our college.  Is there a way I can use Math Lit?
  • How is MLCS different than Quantway, Statway, and the New Mathways Project?
  • What is the Math Lit approach to statistics preparation?
  • What is the prerequisite for MLCS or Math Lit?
  • How does MLCS relate to the Common Core?
  • Does MLCS dumb down developmental math standards?
  • Do you provide training?
  • Will you offer the MOOC again?

Please check back often.  I'll be posting responses to all of these very soon.

If you have a question you want answered that isn't listed above, please post it in the comments.

Friday, August 9, 2013

Instructor support for Math Lit

In the Math Lit book, we've provided many supports for the instructor to make teaching the MLCS course easier and more enjoyable.  The preface explains the philosophy of the book and approach taken to develop content.  In the annotated instructor's edition of the text, we've included all the answers as well as detailed notes and tips for teaching the lesson.  There is also an Excel appendix and an instructor appendix in the back of the book.  Included in the appendix are broad notes for each lesson as well as a time estimate for the lesson, any materials needed, objectives covered, and tips for success.  Rubrics for grading the focus problems are also included.  Additionally, there is cycle-level support for the instructor including pacing information, tips on creating groups, and assessment.

Additionally, we have written an Instructor's Solution Manual and an Instructor's Resource Manual.  Both are available electronically within the MyMathLab course.  The Instructor Resource Manual includes:
  • A sample course syllabus for an MLCS course
  • Templates to help students write focus problem solutions
  • Rubrics to use when grading focus problems
  • Two quizzes for parts one and two of each cycle, including group quizzes
  • Two exams for each cycle
  • A comprehensive final exam
  • Answers to all quizzes, exams, and final exam
The Instructor's Solution Manual contains detailed solutions to all homework and cycle wrap-up problems in the book.

Also, the MyMathLab course is a Ready-To-Go course, meaning that it has premade homework assignments and quizzes.  To copy it, just search for 'Math Lit' or 'Almy' or 'Foes' within the Create/Copy Course option.

A TestGen database is available for instructors who would like to pick and edit test questions.

For those who want to teach an online or flipped or hybrid version of MLCS, we are creating videos to support the text.  A new version of the Math Lit MyMathLab course will be released in June 2014 with these videos embedded in the etext.

Edited 2/18/14

Thursday, June 27, 2013

Math Lit now available!

Math Lit printed early making it available now.  It might be another week before it can be purchased from vendors.  If you would like to see the full book in the meantime, check with your Pearson rep.

The MyMathLab course is being completed now.  It will go live the first week of August.  In it will be additional supplements in PDF form:

  • Instructor's Resource Manual 
    • Includes quizzes, exams, a final exam, and additional support for focus problems
  • Instructor's Solution Manual
    • Includes detailed solutions to all problems in the text

Wednesday, June 19, 2013

Is MLCS just "fun algebra?"

When I give talks and workshops and as I'm teaching the Canvas MOOC, I use example lessons to help illustrate what MLCS is and how content is taught.  Lessons start with realistic contexts in which the mathematics is pulled from them.  Many times an algebraic topic is developed.  Lessons close with contextual or mathematical connections to the topic that was developed.

I've realized that upon first glance, it looks like we're just taking algebraic skills and trying to make them interesting.  Certainly, we want student engagement.  Developmental math students have been unsuccessful at some point in their math career and because of that, they often shut down when a topic looks familiar.  The mind is powerful; if a student believes they cannot learn a particular topic, that can be a self-fulfilling prophecy.  So that students don't allow their preconceptions to dominate the learning experience, we deliberately try to come at topics in novel ways.  And it works.  I've had students work a long time with a concept, and successfully at that, and then realize, "hey, this is that y = mx + b thing, isn't it!"  One instructor said to me that it's almost sneaky algebra and I wouldn't deny that.  

Pathways courses use realistic and relevant content.  Adult learners are more motivated by content that they can use.  I don't believe something has to be immediately useful to be worth learning.  But if it is, it is much more motivating to students.  Motivation and engagement are necessary for a successful developmental math classroom.

But MLCS is much, much more than interesting, contextualized lessons.  

If MLCS were just fun algebra, we would be covering all the traditional topics in the traditional order.  That's not the case in this course.  We have added new topics and scrapped some traditional ones.  For all topics, the emphasis has changed because the goals for the student have changed.  The approach and development is different so that students can do more than successfully demonstrate a list of skills.  Instead, the emphasis is on understanding and use of skills, not just the skill knowledge itself.  Really, this course is good for students heading on the STEM path as well as the non-STEM one.  With a follow-up intermediate algebra course, STEM-bound students would have all the conceptual and applied knowledge they need from MLCS and any additional symbolic skills from intermediate algebra.  

Beyond the approach to an individual topic, the order of topics has been turned on its ear.  That change isn't meant to be confusing, but instead to create learning.  In all algebra courses, we instructors use a particular order of topics because every book uses it.  Someone at some point chose that order and it stuck.  But it doesn't mean that it creates learning.  For some people with some topics, it does.  But does learning mean the student can perform the skill successfully?  I would say no.  I believe real learning means the student understands the skill, can use the skill, and sees the connections between the skill and others.  The traditional linear order of topics doesn't always allow for the connections which are so important.  

The traditional approach gives the impression that math is made of discrete skills.  Often a problem in an algebra class is a rational equation problem or a graphing problem or a factoring problem.  Real problems are none of these.  They use these ideas and others and integrate them.  A real problem (be it in a mathematical setting or a real life one) will cross over into multiple areas of math at once:  algebra, arithmetic, geometry, etc.  

To help a student learn how to solve these more involved, real problems, the course integrates content.  There are key threads we want students to gain understanding of:  numeracy, proportional reasoning, algebraic reasoning and functions.  True learning takes time.  So each of these threads is not its own unit (as it would be in an algebra book) but instead appears in every unit.  Topics are almost always seen many times, each time going deeper and into different contexts.  That is intentional so that students learn and also take understanding into long-term storage.

To create learning, which is our utmost goal, we have to sequence and pace content very thoughtfully.  For example, slope as a rate of change is a really important idea that has some subtle features.  Most texts teach slope on one day and apply it almost always with 2 points or with an equation of a line.  We start with the idea of rate of change in the first 2 weeks and continue going with that concept into different mathematical settings and formalize it at a specific point, once students have more understanding.  We develop slope throughout each of the 4 units.  It takes a long time.  But in so doing, I can ask a student at the end of the semester if a situation is linear, why or why not, what is the rate of change, what does it mean for this context, etc. and they can answer all of the questions well.

The fact that MLCS uses interesting activities to learn content is the tip of the iceberg of this pathways course.  A micro view gives the impression that the only difference is the use of context.  A macro view shows a much more complex structure designed to elicit learning.  Each lesson, unit, assessment, and project has a role in developing long term understanding.  Much like the homework is deliberate with each problem serving a particular purpose, each component of the course is also deliberately chosen.  The result is a visible progression of learning with each student over a semester and the shift from the developmental level to the point of college readiness.  

And maybe along the way, we'll have some fun too.

Sunday, June 9, 2013

Math Lit Book Coming Soon!

Our textbook for the MLCS pathways course, Math Lit, releases the first week of July.  The MyMathLab course that accompanies the book goes live the first week of August.

Here's the final cover:

Tuesday, June 4, 2013

Pathways MOOC Update and Florida Legislation on Remedial Math

Yesterday was the first day of the pathways MOOC that I'm teaching with Heather on Canvas.  Registration is still open if you'd like join.  Follow this link to register.  Here's a picture of the front page of the course:

The course is already active.  I hope to see that activity level continue to grow.  It's fun and informative to talk with other educators and learn from each other. Somewhere we reached a tipping point about developmental math education in the U.S.  It's still a challenge to pilot pathways courses like MLCS in some schools and states but those walls are coming down all the time. It's not that algebra isn't important; it's that it's not the only thing that is important.

Related to pathways, I read an article in the Orlando Sentinel recently about changing legislation on remedial education. It reminded me very much of the changes in Connecticut.  The idea is that we are preventing students from taking college level courses and that with enough support, they can be successful.  Again, if you've taught developmental math and worked with adults who function in terms of reading and math at the 4th grade level, you know that putting them in statistics and just going slower with more tutoring isn't going to make them succeed.  I wish it were so, but it just isn't.  As math teachers, we've all seen students take a course repeatedly and fail it repeatedly.  We know that if they just went back and took the prerequisite course, they would save time and money in the course they're struggling with. You can sit me in a thermodynamics class and go really, really slow and I'm still not likely to pass it because I do not have the foundation skills and knowledge needed for that course.  That is a fundamental truth about some developmental students that has to be addressed and not ignored.  But that's not true for all students.  That is why we need a variety of options for developmental students because one size does not fit all.

One part of the article was encouraging, though:

"Those who take do remedial courses starting in 2014 will be given more options for getting help getting on track, including remedial classes with accelerated schedules. Colleges must submit plans for restructuring their programs to the state by March and make those changes by fall 2014."

Pathways courses like MLCS qualify as a  class with an accelerated schedule.  Most students nationwide who place into developmental math, place into beginning algebra.  That allows them to take MLCS.  And the course is one and done.  Meaning it's one semester. And after it, students can take the commonly required college level math courses like statistics and quantitative literacy.

I believe there are workarounds for other students in developmental math.  For students who don't place into beginning algebra, they could be put in bridge programs using products like MyFoundationsLab.  Not to learn the entire math sequence as an emporium model does, but instead to get the knowledge needed to take a course like MLCS.  Bridge programs do not count as courses, but do fall under placement, something the legislators want to improve as well.

For students headed to the STEM track but who still need intermediate algebra, that content could be integrated with college algebra and possibly make both courses better by making one, strong college level course.  Right now, we go so deep into some skills in intermediate algebra that really don't necessitate that for success in college algebra.  We could cut out some of the overly complicated problems for favor of getting the big idea and being able to use it (a philosophy we use in MLCS) and then move into the college algebra topics where the skill is actually used.  Let students learn the content at an appropriate level and then show them why we taught it.  We could also dramatically reduce the overlap between intermediate algebra and college algebra.  This is related to an idea we use in our college's traditional algebra redesign:  cut out overlap and spend more time on each topic, encouraging mastery and understanding.

All is not lost, but some creative thinking is needed to make things work for all developmental math students.

Thursday, May 2, 2013

What will we be doing in the pathways MOOC?

It's interesting to me how MOOCs are affecting higher education.  I'm not interested in using them for traditional courses, but for professional development and training, I think it could be a sound option.  In a perfect world, I would travel to each school that has asked for training and interact with their faculty using lessons and problems.  We would address the questions specific to that college and help instructors feel confident and usually quite excited to teach this new type of developmental math course, a pathways math course.

Unfortunately, real life makes that hard.  I just trained a school last week and enjoyed it tremendously.  They were lively and engaged and it made for a great day.  When possible, that's my goal:  to have to face to face training.  And I do that often.  But when that's not possible, a MOOC can provide a large reach more efficiently.

Our goals for the MOOC are still the same as with the face to face workshops:  engagement.  We want instructors working, talking, thinking and above all, interacting with each other.  These are the same goals in our pathways classrooms.  When those events happen, learning happens and people leave feeling their time was well spent.  We want that to happen in our MOOC as well.

So, what exactly will we be doing?  If you will take the course, this is what you'll do:

First, you will learn about the history of pathways courses.  We don't want to assume everyone knows the difference between Quantway and MLCS, for example.  So we delve into where pathways courses have come from and the timeline of their development.

Then we talk about philosophy.  That is, the philosophy of these courses and your philosophy of teaching.  We want to challenge you to see how you think math should be taught and how that aligns with the approach of these courses.  Often instructors are really excited about teaching these courses, but get uncomfortable when they see a different topic order or they don't see their favorite algebraic method taught when they used to.  Understanding your beliefs and the approach of the course will help make for a smoother transition.

Next we work on what it looks like to solve real problems as opposed to the traditional "word problems" usually seen in textbooks.  We will work on the challenges these problems pose in the classroom and how to overcome them.  We will also work on the role of algebra in pathways course.  It's present but it's different too.

Then we'll move into group work and assessments.  And we'll close with implementation at your school.

Throughout the course, we will have activities to help you explore something, learn something, and put that learning into practice.  This is the same approach we use to teach a pathways lesson.  You will talk to other faculty about challenges, ideas, questions, etc.  We are not the sages on the stage.  We'll share our ideas and experiences but we will also really want to hear from you.  We are lucky to have some participants who have already taught the course.  They can share their experiences so that you'll hear more than just what happens in Heather's classroom and mine.

We will work on a larger project for most of the course that will really allow you to dive into a challenging aspect of the course:  open-ended projects.

By the end of course, you should feel confident and ready to pilot with comfort both in terms of how the classroom will work and also in terms of implementation at your school.  Because we will have a large number of students, we probably won't be able to answer every individual question.  We will do our best to do so, though.  And the peer interaction will also help.  We don't want anyone leaving feeling like their questions are unanswered.

This course should provide growth for the novice pathways instructor to more experienced instructors who have taught a pathways course.  If you just want to observe and learn about them and see what others are doing, that works too.  But the more involvement we have from you, the better for all involved.

Interested?  Go here to register.

Sunday, April 28, 2013

MOOC registration going strong, new webinar recording available

If you haven't registered for the MOOC we'll be teaching this summer for Canvas, please do.  Our enrollment is increasing at a great pace.  Click here to register.

Also, I gave a webinar about Math Lit and MLCS a few weeks ago for Pearson.  Here is a link to the recording.

Tuesday, April 23, 2013

Canvas MOOC Registration Now Available!

The registration for the online MOOC that Heather and I will teach this summer for Canvas learning systems is now open!

Go to this site to register.

Important facts about the course:

  • It is an online course.
  • It runs from June 3 to June 30.
  • It is free.

The most important thing to know is that the course will help you learn much more about pathways courses and how to teach them.

Sunday, April 21, 2013

Illinois update and student reactions to MLCS

On April 6 at our AMATYC affiliate's meeting, IMACC, we voted and approved pathways courses.  That same weekend, our MAA affiliate, ISMAA, also approved Illinois versions of pathways courses.  Last week, the Illinois Articulation Iniative's General Education panel also accepted the new courses as alternative prerequisites for the following courses:  general education math, general education statistics, elementary mathematical model, and quantitative literacy.

We've been working for over 3 years to get pathways courses in Illinois as an approved alternative.  Several schools, including my school, have been developing their courses and piloting them.  We were granted pilots on a trial basis, so it's fantastic to be officially approved.


In other news, we often hear from schools class testing our book Math Lit for their MLCS courses.  Below are some comments from students in those classes.  Keep in mind that this school is in IL where the course is a 6 credit hour, 1 semester course.  Most states are not using this large of an MLCS course, but instead are teaching a 4 credit hour version.

Comments have not been edited for spelling or grammar.

“I really think this class has helped me a lot. When I came into this I did not know what to expect. At times I struggle, but when I have the groups I think for the most part we help each other to understand. I like that things are revisited because sometimes I may not fully grasp it, but then it comes back around; this time I get it. The class is very fast paced, and at first I was terrified I would fall behind, but I haven’t. I have learned a lot of things I have never heard before or have struggled with. I have grown leaps and bounds since the beginning of class.”

“In this course I learned more than just how to do Math, and solve algebraic equations. We learned what things meant and why the rules we use are the rules we use. Mrs. Thannum and Mrs. Peterson are great teachers and they’re experts at making you remember what we learned. I would recommend this class to anyone.”

“It has been great. I have learned so much. I want to achieve in a higher class but there was much I didn’t understand. Now when I first entered the class, I felt like I was put in a class for dumb people but it changed for me after I started learning. This course is needed very much. It breaks things down for me slower. It repeats what I missed . . . the teachers help explain."

“I like this course compared to others. I have learned more here than all of high school math. The only thing I don’t like is going four days a week and the weight of the Cycle Projects.”

“MAT 099 is an [sic] in your face example of how math should be taught. While not insulting your overall intelligence, it gets as personal/intimate as possible for the student to truly understand what to do by breaking down then showing how to apply the concept. Not just by saying here’s how you do it . . . move on . . . then you are scratching your head in confusion. Schools have entrance exams for a reason. Math, if not your strong suit should be as stated (based) on requirements for program or degree, should be given to ALL students with developmental issues concerning math. Coming from experience having taken 094 and bombed horribly only a semester ago, MAT 099 has by fair taught me how to not only break down the problem, but do it and understand it and actually apply it to real life.  I’m able to understand and apply math reasoning all from this course. As of summer, I will be able to go on to college level math as a result from this course.”

The pathways online course for Canvas will be posted this week for registration.  I will put info on my blog as soon as I have it.

Thursday, April 11, 2013

Webinar tomorrow

If you'd like to learn more about our book Math Lit, the MLCS course we teach, and see a sample lesson, please attend a webinar tomorrow April 12 at 12 pm CST sponsored by Pearson Education.  You can register here.

Tuesday, March 26, 2013

Pathways progress!

I've been traveling every weekend for the last two months, giving several talks and workshops on the pathways course we're teaching, Math Literacy (MLCS).  It has been exciting to see the tremendous amount of momentum and progress being made in regards to courses like this.  Many faculty are excited to see a new offering that is not algebra remixed and truly does something different for the developmental student.  I've heard more than instructor say, "This is long overdue."

So what progress is being made?

First, we have begun to see very promising data.  Carnegie has recently released their results, which are very encouraging.  I'm a big supporter of all pathways courses, not just MLCS. Fundamentally, I believe in this type of course and the philosophy of it, even with slight differences amongst the various pathways options currently available.

Like Carnegie, the results of our 2 year pilot are exciting.  Typically 55 - 70% of our students pass the Math Literacy course.  It is not an easy course by any stretch, so there aren't lots of A's.  But many students do pass.  If they will work, they can pass.

Additionally, we've been tracking students in their outcome courses like intermediate algebra, statistics, and liberal arts math.  And the data has so far has supported our hypothesis:  there is no statistically significant difference in the performance in outcome courses when comparing MLCS students and students who take the traditional algebra courses.  There is enough algebra for students to pass traditional intermediate algebra after MLCS.  And there is enough rigor (and mathematics) for students to pass liberal arts math or statistics after MLCS.

Our sample sizes are not large yet, so we will continue to track students for likely 2 more years.  As a veteran course redesigner, I know that redesign is not done when you roll out or even after a year or so.  Time has to pass, more faculty have to teach the course, and bugs will need to be worked out.  But I have seen that come to be over and over, so I have faith that will be the case with this course too.

Another point of progress are states allowing and considering allowing courses like MLCS to be piloted and accepted as an alternative to intermediate algebra.  There are already several states who have changed their policies.  Illinois has not yet, but we vote in less than 2 weeks.  I will post on the outcome.

Definitely there is a shift going on in the U.S.  Two years ago, the talk on redesign centered around emporium models.  While that is a valid approach for certain students, many faculty are concerned about that model of redesign across the board.  I believe the pendulum swung too far with using that approach at a very large scale, and am glad to see it swinging back to a balanced approach to redesign:  models that support STEM students and skill remediation and models that support non-STEM students and their outcome courses.  Faculty like seeing the emphasis on conceptual and applied understanding that exists in MLCS.  And really, both redesigns can live happily in a department.  We have modular (not emporium) algebra courses, an accelerated algebra course, and MLCS at our school.  Different timeframes and options for the variety of students and instructors who work with these courses.

Another point of progress is materials.  Our text, Math Lit, will be the first textbook for pathways courses published by a major educational publisher.  It releases in July of this year.  All the major publishers have projects in the works.  Some educational foundations are also making progress on materials.  While some of these projects have remarkable similarities on the surface, the functionality varies.  Our goal when writing was not just to create a product with a new content approach in mind, but also to create a product that works in the classroom for all levels of educators.  Pedagogy matters but more than that, instructor support is crucial.  Our goal was to provide a product that works for faculty made by faculty who know what today's classroom is like because we are in it like they are.  And we are in those outcome classes, so their specific needs are addressed too.  We want students to enter a college level non-STEM class and be completely prepared for what will be expected of them.

We're already looking down the road at what needs to be created based on instructor requests.  So we are planning our next projects, of which there will be several.  I'll post when decisions are definite.  But in the meantime, I can say this:  we are committed to providing materials and support to schools with a variety of needs, be it a smaller version of our course or this approach with other content.  Really, our work in this arena has just begun.

Our training and talks will continue.  The online pathways course that Heather and I will teach for Canvas will be open for registration next month.  I'll post info then.  We have started building the course and are so excited to teach it.  It will be engaging, informative, and also just fun.  The platform, Canvas, is amazing.  And we've really focused on working with students in that course the same as we do with our MLCS courses:  engaging activities, lots of interaction between everyone in the class, and putting in practice the ideas so that you can successfully and confidently teach a pathways course.

It's certainly an exciting time to be in mathematics!

Friday, March 22, 2013

Handouts from ICTCM and a video link

Below are the handouts from the talk we gave at ICTCM today since we ran out.  They include objectives from the course, a sample lesson, flowcharts to show possible implementation options, and a flyer for the book Math Lit with the unit structure and math topics listed.

The presentation today was brief and therefore it did not have as much detail as we often use.  To compensate for that, I've included a youtube video below the handouts of a similar but more detailed version of the presentation we gave today.  If you have questions, please email me.

This video was recorded in September 2012 so several things have changed since then.  The book is almost finished and is coming out in July of this year.  It will have a full MyMathLab course using Pearson's new design, releasing this summer.  A sample MyMathLab course already exists.  Please search for the book title, Math Lit, in MyMathLab to create a course.  Several schools have been class testing our materials and interim MML course over the past academic year.  We have conducted several workshops and plan to do more with training.  We will be offering an online training course in June using the LMS Canvas.  Registration information will be posted on this blog next month.

Friday, March 1, 2013

The Role of Algebra in Math Literacy

We don't approach algebra in the traditional order or using traditional methods in the MLCS course.  One reason for that is the audience.  The student taking this course has taken somewhere between 1 and 3 years of algebra, and yet they have placed into an algebra class at the high school level.  Taking the same approach, when it was not effective the first or second or third time, will likely not yield a new result.

So we approach problems and ways to solve them, not algebra and then problems using it.  It seems like a subtle change but the emphasis is incredibly different.  In MLCS, algebra is a means to an end, not the end itself.  We value algebra tremendously.  But there is an overemphasis on this wonderful subject at the developmental level.  I've often thought calling this area "developmental math" is a misnomer.  It should be called developmental algebra, because that's what we spend 80% of the time working on.  The remaining 20% is spent on numbers, geometry, and applications.

In reality, students will face problems with numbers in their lives and future classes, not necessarily algebra problems.  Knowing when and how to use algebra matters more if we really do believe this subject is important.  But that's not the traditional focus.  It's just on the mechanics, as though linear equations and polynomials are falling from the sky waiting to be solved and factored.

Another reality is that in real life, the numbers aren't nice.  Polynomials exist but they often don't factor.  And graphing by m and b is a lovely idea but real data doesn't make it nice to do.  And it's often possible to come up with an equation that is not easily solved without technology or numeric methods.  We do students a disservice by shielding them from these truths.  And in teaching them how to deal with them, the problems are far more interesting and students are more engaged.

Our approach is to always begin concrete and with numbers.  Bring in the algebra when it will make the problem easier in terms of solving and/or organizing the details.  Students will gravitate toward it often if they are not forced to use it because it is so powerful and often helpful.  And sometimes algebra completely obscures the issue at hand and is overkill.  Again, knowing when to use it is just as important as being able to use it.

This can be a difficult shift at first, especially if an instructor has taught traditional algebra for many years.  Nearly every book has the same ordering of topics and the same emphases.  So it's unusual at first to see commutative property after integer operations have been addressed.  But students can still be successful with integer operations because they've been using the commutative property since first grade as a natural behavior for numbers and certain operations.  It's not the name that matters; it's the understanding of the concept so that it can be used.  Intuitively, students can solve many problems without the formality we often put on them.

Take Pythagorean theorem for example, a topic I taught this week.  We came at the theorem and its uses from every angle.  Using it requires algebra but really an understanding of numbers, something we've been working on for weeks, will suffice when solving the equations involved.  When we get to equations like this, this is the approach we used since we haven't gotten to formal equation solving:

152 + leg2 = 222

Simplify the exponents.

225 + leg2 = 484

We need to find what adds with 225 to achieve 484.  That can be found by subtracting 225 from 484.  This approach uses the concept of addition and subtraction being inverse operations.  The result is 259.

          leg2 = 259

The length of the leg will be a positive number and it should square to be 259.  That is the definition of the principal square root of 259.  We write that next and then use the calculator to get a decimal approximation.

          leg  = √259 ≈ 16.1

It was also interesting when using the calculator for this problem.  Students used the square button and then the square root button.  I asked them if they notice anything about the placement of those functions on the calculator we typically use, the TI-30.  They are paired on one button with one function being the direct operation and one requiring the 2nd function to get to it.  I told students this is not a coincidence and asked if they could figure out why.  A student's eyes lit up and said, "they're inverses of each other!"  Exactly!  That's a valuable concept to know.

Can students solve problems like this without formal equation solving techniques?  Absolutely!  And it makes sense because we are working at the numeric level.  When we get to the formality of algebraic manipulation, it is always easier because a strong foundation in numbers has been established.

Some students remember equation solving from a previous course and prefer to use those steps.  We encourage them daily in this course to use methods that make sense.  Every concept that is taught uses multiple approaches to understand it, be it visual, numeric, algebraic, or verbal.  After we learn those methods, we ask students to reflect on the method they prefer going forward.  Learning how they learn provides a student tremendous insight on their understanding and is very helpful throughout college.

There are many people who feel this way about algebra, that our focus could use some updating.  But often they are the ones using the mathematics instead of teaching it.  I think it's worth listening to the people who use math for a living.  Of course not every concept has to be immediately useful to be worth learning.  But with the current traditional approach, there is too little that is useful and too many topics developed in a way that is unrealistic in terms of the real world uses.  For more on this idea, please watch this short video by Richard Feynman, Nobel prize winning physicist.


Saturday, February 23, 2013

Presentation handout

This is a handout I often distribute at presentations.  It can be downloaded.  For more specific information on our course objectives, please email me.

Monday, February 18, 2013

MyMathLab demo now available for Math Lit

If you'd like to see what the MyMathLab course will look like for our book, Math Lit, you can preview it by creating a course in MyMathLab.  Go to "Create/Copy Course" and search by the book name or Almy or Foes.

Click on any graphic below to enlarge it for easier viewing.

Once it is copied, this is what you'll see.

We use MML for the skill component of the course so that students can practice all the skills that are developed in a way that will help them develop mastery.  Additionally, an ebook is available as well answers to the conceptual homework in the text.

To guide students through the book structure, tabs correlating to cycle parts are available, each with the set of steps students complete to learn a lesson.  They include participating in the lesson, doing MML homework, and doing conceptual homework with answers provided for checking their work.

Within the instructor resources is a link to the Instructor Appendix, a document that supports instructors in teaching the course, cycle, and lessons.  Additionally, there is a link to a webinar I gave about the MLCS course.

Sunday, February 17, 2013

This and That: An Update

Although travel season never really ends for me, it does have its busy and less busy times.  I'm in the busy season now, traveling every weekend for the foreseeable future.  Recently I worked with the Maricopa college system in Phoenix on redesign.  It's interesting to see how large college systems work to implement change.  There are always challenges to redesign; they just vary due to things like size, funding, culture, and facilities.

I've been speaking at a series of three sessions to educate faculty in Illinois on new pathways courses.  We've had events at Southwestern Illinois College and Parkland College. Our remaining event is on March 2 from 10 am to 1 pm at College of DuPage.  Any faculty or administrator in Illinois is welcome to attend and learn more about the types of pathways courses we're testing in Illinois, the data to date, and when we'll be voting as a state.

Intermixed with the Illinois events, I'm speaking on MLCS in Houston this week for TCCTA.  Next month I'll be in Washington state (both Seattle and Spokane) for events to talk about pathways courses.  Then it's on to ICTCM in Boston and then IMACC at Robert Allerton Park in Monticello, IL.

Throughout this time, I'm doing training workshops with schools as they plan pilots.  Heather and I are working on the online course we'll teach on pathways this summer.  Information for registration should be coming in the next month or so.  Communication is often easier with face-to-face workshops, but it's hard to be everywhere at once.  The online course will give us an opportunity to provide training for MLCS on a much larger scale and in the convenience of your own home.

Lastly, we are in the home stretch of finishing the book, Math Lit.  A demo course in MyMathLab will be available very soon.  We've already seen a sample of it and it's fantastic.

It's been a lot of work for me and many, many others around the country who are committed to providing new developmental math avenues for students.  Seeing that work come to fruition is truly exciting.  Hearing about students enjoying new courses and feeling success in a math class for the first time makes all of it worthwhile.

Friday, February 1, 2013

New website for the book, Math Lit

Pearson has created a website for the book, Math Lit.  You can check it out here.  More information will be added to the site this spring.

Friday, January 25, 2013

Exciting News for MLCS and Math Lit!

We're back in the swing of things at our school, entering our second week of the semester and our fourth semester of piloting MLCS.  Things are never dull on the pathways front.  I'm waiting for more information that I'll post soon on the blog, but until then, here's a sneak peek:

Online MLCS Training
Heather and I will be teaching an online course this summer about teaching pathways courses like MLCS.  It will be 4 weeks and in June.  If you're thinking about teaching MLCS but want much more detailed help and the chance to talk to other educators in the same boat, this course is for you.  Plus, you don't have to travel!  This will be a great opportunity for faculty or administrators prior to a pilot or for schools who want a more detailed look at pathways courses than a webinar or presentation can provide.  

Registration information will be posted on the blog soon.

If there is interest, we will teach the online course on a regular basis.  I'm very grateful to be asked to do this by a company that can facilitate online classes like this.  Doing so allows us to offer the training on a large scale that we have heard so many requests for.  We will continue to do face-to-face workshops but it is hard to reach all the schools who want more help.  The online course will help that issue greatly.

We are committed to making MLCS possible at any school and have worked to make that happen through education, materials, training, and support.  Schools that class test with our materials are eligible for webinars with Heather and me to get their questions answered and brainstorm solutions to challenges.

Would you be interested in a discussion board about MLCS and/or the Math Lit book?  Email me or post in the comments if you are.  I can set up a discussion board that would be free and allow us to have an ongoing dialogue and resource for schools.

More to come soon!