M.A.T.H. Tips: Vol. 23
Condense, Customize, Collaborate, and Complete: Thank you to Nicole Franics, Vikki Maurer and Claire Burke for sharing their experience!
Our mathematics department at Linn Benton Community College in Oregon was struggling with how to solve several problems within our developmental sequence. First, many students were daunted by the need to take four quarters of mathematics before reaching college level and, as with many schools, our students were dropping out without completing their mathematics requirements. Second, our courses had been designed years ago to support mathematics in several Career and Technical Education departments. Since then, the CTE departments have adopted the computation portion into their own courses and were not utilizing our math classes, so we were including topics that weren’t relevant to our students. Third, we recognized that developments had been made in mathematics instruction to improve student retention and performance. We weren’t using these developments and our mathematics homework wasn’t using the most recent technological advances. Finally, as always, we wanted to improve our pass rates.
Before fall quarter 2017, our developmental math consisted of two tracts. We had a traditional developmental algebra sequence that consisted of 4 classes. Math 20, Math 60, Math 65 , and Math 95 and an alternative pathway for non-Stem majors that consisted of only Math 98. With the exception of Math 98, our classes had a very traditional style of curriculum with instructor-led lecture classes , written homework, and paper and pencil exams. Our change was motivated by recent research in retention and performance in collaborative learning environments and our desire to improve student success by shortening the pathway to college level mathematics and incorporate adaptive software. We took our four traditional classes and replaced them with three collaborative learning courses that utilized Aleks adaptive homework.
In addition to changing the number of classes and the instructional style, we adapted our classrooms to facilitate collaborative learning. We use hexagonal tables that seat 4-6 students, each table with their own portable whiteboard for reporting. We added projectors so that material presented would be easily visible from any seat in the classroom, and we required our students to bring either laptops or tablets in lieu of graphing calculators.
Our classroom time is spent now doing activities, writing reflections, and holding discussions. The structured group activities require critical thinking and communication skills. The topics can range from practice problems for a particular topic to solving complicated real world problems. We teamed with other departments, such as Agriculture, Physics, and Business, to find interesting and challenging math application problems to use in our classes
Outside of class, the students use Aleks adaptive homework. Aleks uses a comprehensive initial knowledge check to identify a student’s skills and weaknesses. We use the results of these initial knowledge checks as a placement aid, in addition to directing our classroom instruction. Students have weekly objectives of approximately 20 goal topics plus any of their personal prerequisites. The progress on these weekly objectives is considered their homework grade.For testing students take proctored Aleks comprehensive knowledge checks and also written paper and pencil concept tests.
Like any change, there were some challenges. First and foremost there was, and still is, the challenge of convincing our faculty members that collaborative style learning is effective. Many instructors feel like if they don’t say it the students won’t learn it. We’ve found in our experience (and this is supported through the literature) that the opposite is often true. The more you lecture, the less they learn. We’ve addressed this issue through a department-wide professional development, presentation of timely literature supporting collaborative learning, and a mentoring program for new faculty.
There is some resistance among students as well but generally speaking this is more-easily overcome. Students may be hesitant at first but most come to enjoy the classes. Many students have told me the class is more engaging and fun than any other math class they have taken. One student wrote on their classroom evaluation, “I loved working in my group. We all seemed to know our strengths and helped each other when we were in need of explaining a step or how we got to the answers.” The students become invested in solving the application problems and enjoy the feeling of success after struggle. Very few students have anything but praise for Aleks homework. They appreciate not having to do problems they already know how to do, just because it is listed in the assignment. They also feel supported because Aleks identifies their weaker areas and provides them with the information and support they need on those topics. Again, a quote from a student, “One thing I would keep the same is doing homework on the Aleks program. It is really nice to the alternative of doing 30 problems on one topic and hoping you got it right when you turn the homework in.”
After one full year of our new style of teaching we are happy with the preliminary results. Since there are now fewer classes, it is difficult to do a perfect comparison but our pass rates have increased across our courses. The following tables present our comparison pass rates, which light blue being our previous courses and dark blue our current courses.We also compared the initial knowledge checks in the next class in the sequence, students coming from our previous classes are coming in about the same level as preparedness. Finally, students who continue on to the next course do about the same as their peers coming from other math programs.
Overall we are very pleased and encouraged by the change in developmental math curriculum. There is still work to be done, activities to improve, and skills to enhance but we feel that our curriculum has made a positive impact on our students success.
Right about now both students and instructors start to feel the mid-semester burn. The energy of the beginning of term subsides and the weight of work and expectations begins to weigh on students. How can we help ourselves and our students reset?
Try having at least one day or activity that breaks from the normal mold. For example, instead of lecturing have students work in small groups to explain a concept then report the results back to you. A speed dating format where students meet in 5-minute intervals can also keep things interesting. If you started off the semester with a goal worksheet have students to a mid-semester check-in to assess their progress. Are they meeting their own expectations or are there actions that can be taken to get back on track?
For instructors, it can seem that the mid-semester is a wall to be overcome. Try taking scheduling a 5-minute break mid-day to go outside and reset, if going outside isn’t an option there are hundreds of nature relaxation videos online that are accompanied by natural sounds. Another stress reducer tip is to create a prioritized to-do list starting with the one item that must get done to make everything else runs smoothly. Focus on that item and then move on to the next.
Finally, to help students with test anxiety, give students 5 minutes at the end of class to set-up study groups. Working in groups can help boost retention of material by giving students an opportunity to discuss and explain concepts with peers. And for those students willing to try something out of the box, Math Mama Writes provides a guided meditation on her blog to aid in success on math tests:
When teaching children to read, no one said we can’t sneak a little math into the lesson as well. There are many children’s books with math themes. You can have your future Elementary Teachers create a sample activity or lesson around one as an assignment.
- Sir Cumference and the First Round Table
- The Grapes of Math
- Reese’sPieces Count by Five
Who could resist?!
Here’s a list of almost 200 books with math themes or connections. Access the Excel File: Math_for_Elem_Teachers_Math and Literature
Even books that aren’t overtly about math, like The Grouchy Ladybug, can lead to math lessons. Ex. Create ladybug pictures with different spot combinations on their left and right sides. Have children compare the sides to learn about the ideas of less and more. Here’s a sample lesson based on the book:
Pinterest has loads of ideas and lesson plans connecting children’s literature with math. Have fun with it.
In 2015 Standard & Poor’s, Gallup, the World Bank, and George Washington University crafted a short five question quiz to test financial literacy across the globe, two-thirds of respondents failed the quiz, and the United States didn’t make the top ten for financial literacy : https://bit.ly/2Echnr2.
Most Colleges and Universities have some form of math course for non-majors and non-STEM students. The course, sometime called Liberal Arts Math, tends to cover a variety of topics and the flow of the course can be individual to the instructor and the specific institution. Financial topics are an area that lend themselves for use in such courses. And, with some scaffolding, it is possible to cover a variety of slightly more complex and extremely pertinent financial topics. Using the ideas covered in the financial literacy quiz we have provide an outline for a unit on Finance.
- Budgeting – In this section give students an average first year out of college salary for your area and have them craft a budget, including rent, any loan payments, food, gas, utilities. Once they have crafted a budget have them see how long it takes to create a three-month and then six-month emergency fund. You can also have them identify any savings goals they would like such as buying a new car or taking a trip and add them into the budget.
- Simple and Compound Interest – Now that they have a budget, students can compare the different types of savings accounts available to a savings vehicle such as a CD. Have them decide what works best for their savings goals.
- Annuities – In this section students can examine the more complex relationship between payments and interest. Ordinary annuities and tax-deferred annuities are good topics to cover.
- Amortized loans- In this final section students bring everything together. You can cover examples ranging from student loans, to home and car loans.
- Final Budget -Tying everything back to their original budget have student talk about how their initial budget would change now that they have a better understanding how savings and loans work.
Depending on your course this outline can be modified to be completed in two to five weeks and can work for both assessment and project-based courses. As a bonus you can give your students the five question survey before and after the unit to see how well they have learned the material.
The Bletchley Circle series is more Downton Abbey than Imagination Game. A lot like Numbers in the way characters pause mid- procedural to explain a code breaking concept, the Bletchley circle series center on a group of women (amateur) crime investigators who formerly worked at Bletchley Park. The first series is 3 episodes and one case. The second series has 4 episodes split between two cases. Both series are set in London and are available on PBS streaming or DVD/Blu-ray. The newest series is set in San Francisco. Some of the original cast returns. This 8-episode series came out in July of this year and can be streamed on Brit-Box.
There are many nods to WWII era code breaking techniques and the machines of the era. The original two series pre-date the Hidden Figures phenomenon. These are a quick binge for those who like the procedural genre with a little math thrown in. A more serious treatment of women at Bletchley can be found in the book The Bletchley Girls, by Tessa Dunlop
For a book on women code breakers during WWII in the United States try Code Girls: The Untold Story of the American Women Code Breakers of World War II, by Liza Mundy
When a student enters your college and “isn’t prepared” for their college level math coursework how are they described? Are they remedial, basic skills, pre-college, developmental, adult basic ed (ABE), under prepared, or perhaps differently prepared? These various labels each come with baggage and in some cases political and financial implications. What do you do with them? If you are a selective college, maybe you don’t accept them in the first place. If not, do you offer boot camps, online prep, traditional sequenced coursework, a pathway, a co-requisite structure?
If you are looking for an organization that focuses on working with these students and the many ways you can do so NADE (National Association for Developmental Education) may be a resource for you. https://thenade.org/ Their motto is: Helping underprepared students prepare, prepared students advance, advanced students excel.
The organizations stated mission is, “To improve the theory and practice of developmental education at all levels of the educational spectrum, the professional capabilities of developmental educators, and the design of programs to prepare developmental educators.” With goals of
- To promote educational opportunity for all individuals, appropriate to their needs, goals, and abilities
- To promote the retention of students
- To encourage educators and institutions to utilize multiple forms of assessment that will ensure proper placement of students based on levels of academic preparedness
- To encourage educators to maintain academic standards while helping learners to acquire competencies needed for success in academic coursework
- To encourage educators to consider the development and application of cognitive and affective learning theory
- To facilitate partnerships between educators, employers, and the community at large
Their national conference is in Georgia this year. https://thenade.org/2019-Conference