Math — Applications for Living V

The class (Math119, called “Math — Applications for Living”) is now covering quite a bit of statistics, and I thought I would share a problem from yesterday’s class that incorporates ‘measures of typical values’ (aka ‘average’). 

So, here is the situation described:  “A small local company has 8 workers, and here are their hourly rates of pay:   $9, $9, $9, $10, $11, $18, $36. What is the average hourly pay?”

In this case, I had students work on this problem in pairs; they had directions for finding the mean, median and mode.  The big question was “Which average reflects ‘typical’?”

This was a good situation to show the weakness of the mean as an average or typical value; those outliers create false impressions.  The group actually thought that the mode was the best average because 3 workers had this pay … even though it was the lowest.  Numerically, the median was the best and we talked a bit about the pros and cons of each average. 

Essentially, this work on the ‘average’ supports the cynical statistician view of the world — we don’t have the answer, all we have are hints at something that might (or might not) be true.  Fortunately, this same class gave a chance to talk about distributions of data, and begin ‘distributional thinking’.  The students got the idea that we should try to represent a set of data with one number.

Some students in class had already noticed that the median was used for some things (like home prices, and the net wealth discussion — see http://www.pewsocialtrends.org/2011/07/26/wealth-gaps-rise-to-record-highs-between-whites-blacks-hispanics/).  It was also clear that the word ‘average’ used so often does not state which one — too often, it is the mean (as in ‘the average number of televisions per household is 2.4’).

The class is going to move on to other statistical topics, some of which have more exciting uses in life.  The one above might be of interest, or at least be enjoyable to read.

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Student Success — New Life at Grayson (TX)

Some of the best work in the profession is being done at smaller colleges.  Grayson County College (Denison, TX) exemplifies this in their good work in developmental mathematics.

This year, Grayson is running pilot sections of both New Life courses — MLCS and Transitions — as part of their plan to completely replace the traditional developmental math courses next year.  Like most of us, the Grayson math department is primarily adjunct faculty; three of the full-time faculty — Stanley Henderson, Shawn Eagleton, and Sherre Mercer — have  been willing to share some of their ideas and tools with us.

Here are some comments from Sherre Mercer:

We are using a “recipe for success” in our new courses.  The document was developed by Stanley Henderson, one of the professors in the department, and is based partially based on his first day of class activities over the years. Students are asked to grade themselves on their recipe for success and encouraged throughout the semester to make improvements in their study/life habits with regard to the four areas on the recipe.

The recipe for success is this document RECIPE FOR SUCCESS SPRING 2012 Grayson County College

Also, Sherre goes on to say:

The students are required to write verbal explanations frequently.  As part of the focus on conceptual understanding, my class was required to complete writing assignments before and after each exam.  These documents were developed by Terra Diehl, one of the presenters at NADE last year.   The students are asked to complete the pretest page before the exam.  They complete the post-test page after the graded exam is returned. 

 The math department at Grayson is doing a very good job, and showing generosity in sharing both the ideas they use and some of the tools that have helped students succeed.  Thanks, Grayson County College!!

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What do you need?

The purpose of this blog is (primarily) to help more people make the transition from the traditional developmental mathematics program to a model which serves our students better (either New Life, or Carnegie Pathways).  Most of the posts have dealt with specific or general issues … based on what I am thinking about and conversations I have.

I would like YOUR thoughts on this question:  What do you need?  What would help you make this transition?

Write your comment, with some description of what would help you. 

Perhaps you need some further description of the two models (described briefly on pages in this blog, and elsewhere).  Perhaps you need either some general ideas of how to start the process of changing … or a conversation with somebody who has done it.  Perhaps you need ideas on instructional materials that could be used.  Perhaps it’s professional development that concerns you.  Perhaps you have other areas in mind.

Take a few minutes, and post a comment.  I’ll reply to everybody, and we will work together to get you what you need.  And, your comments might help provide some direction for areas I can address in future posts

“TIA” (thanks in advance)
Jack

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Student Success in MLCS

The six major areas of focus of the MLCS course at Rock Valley College are numeracy, proportional reasoning, algebraic reasoning, functions, mathematical success, and student success.  Each unit addresses all of these facets.  Specifically, the course and accompanying lessons are designed to improve a student’s chance of success in a math class.  Here are some examples:

The approach of the course begins with real, relevant content and covers topics differently than they are in a traditional text.  That automatically increases motivation, an important component of student success.  Students have commented repeatedly that the course is interesting; they like what is taught as well as how it is taught.  For example, direct instruction and group work are balanced with each lesson beginning and ending with group work.  This improves attention, understanding, and engagement.  Students are shown respect for their prior knowledge by allowing them to tackle real mathematical problems instead of working from a premise that all the content is new.  Many of the specific skills of the course are not new to these students because in reality, most of them have had several years of algebra prior to the course.  What they lack is understanding, retention, and application.  To improve that, considerable time is spent on solving thought-provoking problems and seeing traditional topics from a unique perspective.  All problems are taught through a context and do not start with abstract ideas.  Instead, the development moves from concrete to abstract, which builds student confidence and understanding.  Further, students are treated like adults, most of whom work and have many varied experiences.  They learn how math is used in the workplace and see those ideas in practice in class.  For example, they learn how Excel is used.  They also learn how the concepts taught can be used to solve problems they will likely face in and out of college.

Next, specific student success activities are included in every unit.  Each student success lesson is different but all have mathematical ideas in them.  So beyond the traditional ideas of time management and test anxiety, issues that these students will face are covered.  For example, students learn how college math is different than high school math.  This is done in the context of determining what components are necessary to be successful in a college math class.  To visualize the various components, students hone their skills with graphs and percentages.  They study job statistics to compare STEM and non-STEM fields in terms of their earning potential and unemployment rates.  This approach brings in some statistics concepts.   The topic of grades is addressed often and deeply.  Components include how grades can be figured (points vs. weights), how GPA is figured and how it can be increased, and why it is difficult to pick up points at the end of the semester as opposed to the beginning of the semester.  Students learn about means, weighted means, what can and cannot be averaged, and how algebra can help solve problems that arise in this context.  Additionally, the first week has many activities to help students begin the semester on the right foot in terms of prerequisite skills, working in groups, and understanding course expectations. 

Another component of the course is helping students learn how to study.  Students think they should just “study more” but do not understand what that means in practice.  To remedy this problem, students are given very specific and explicit strategies that they can act upon.  Students receive a detailed list with actions they can do before class, during class, between classes, before tests, during tests and after tests.  Also, students tend to really like online homework but they can get dependent on help aids and sometimes can’t write out their work.  So every online assignment has an accompanying brief paper set of problems similar to the online ones, but they must write them out and have no online help aids.  With skill homework, they have conceptual homework on paper that is about quality over quantity.  That is, they have fewer problems that take more time so as to work deeply with the concepts at hand.  The test review has a detailed plan to teach students how to study for math tests, beyond just working problems.  Additionally, students are held accountable for all the work assigned so that they learn good study habits and personal responsibility.

Lastly, metacognition is emphasized regularly.  The developmental student often doesn’t fully understand how they think or learn.  Most problems are taught using 3-4 approaches to work at verbal, conceptual, graphical, and algebraic understanding.  For example, when students solve equations, they do so first with tables, then with algebra, and last with graphs.  Once they have learned all those techniques, they are asked to think about which makes most sense for them and keep that in mind going forward.  This approach of solving problems in multiple ways is used often in the course to broaden their mathematical skills, but also give them a deeper understanding of the topics.  This method has an additional benefit for students on test day.  They have several tools in their tool belt to use if one technique is not making sense or their anxiety is affecting their memory.

Together, these techniques support the developmental student in being successful in this course and future math courses.

Kathleen Almy     kathleenalmy@gmail.com
Heather Foes    heather.foes@gmail.comRock Valley College
Rockford, IL

For more information, please check out this blog: http://almydoesmath.blogspot.com

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