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Math Professional Development, or Why Invert and Multiply Doesn’t Have Any Staying Power

Invert and multiply. Does this ring a bell? It probably does for most adult education math teachers because this is how we were taught to divide fractions, and this is how many of us still teach this algorithm. Does this approach to teaching fraction division work? For the most part, no, or we wouldn’t be reteaching fraction division over and over again to the vast majority of adult learners we serve.

What are some of the better ways to teach fractions, which should include concepts, not just algorithms, and what is World Education’s role in supporting the professional learning of adult education math teachers?

JSI/WEI Photo Library Photo
Numeracy workshop
Adult Numeracy Instruction-Professional Development
(ANI) is one of the best things going to support math teacher development. Authored by Donna Curry and Mary Jane Schmitt of TERC (Technical Education Research Centers) through an OVAE-sponsored contract lead by MPR Associates, Inc., ANI consists of three 2-day institutes focused on more effective, hands-on, conceptual approaches to teaching adults math. ANI stresses the four big ideas in numeracy based originally on the work of the National Council of Teachers of Mathematics, and reinforced by the Common Core State Standards and recent College and Career Readiness Standards for Adult Education:
  • Connections (recognize and use connections among mathematical ideas),
  • Communication (communicate mathematical thinking clearly to others),
  • Mathematical proficiency (conceptual understanding and procedural fluency), and
  • All strands developed at all levels (all content applies across all levels).
ANI institutes are full of hands-on teaching approaches and activities for immediate classroom use, focusing on number and operation sense (whole numbers, fractions/decimals/percents, and integers); geometry; data, statistics, and graphs; and algebra. Between sessions, participants try out ANI activities in their classrooms and meet regionally with their colleagues.

To date, eleven states have participated in ANI: Georgia, Arkansas, Colorado, Indiana, Connecticut, Delaware, Mississippi, Louisiana, Wisconsin, Rhode Island, and New York (Finger Lakes Region). Montana, Washington, and Louisiana are on board for 2014. The first year of ANI implementation was coordinated through the LINCS Region 1 Regional Professional Development (PD) Center located at World Education, and ANI is provided to state cohorts through the LINCS network of Regional PD Centers. LINCS covers the cost of the trainers and their travel; states cover the cost of participant travel, training materials and supplies, and the training venue.

As one recent participant in ANI noted, “I just returned home from our first ANI conference. IT WAS SOOOOOOO FUN!!!!! Oh my gosh. I’m completely exhausted and feel like I haven’t breathed in two days, but the content was fantastic and the presenters were stupendous. What a wonderful experience…. If you’d  told me 1 year ago that I’d be going to a math conference… and loving it…”

If you’re interested in participating in ANI, please talk with your state adult education director who will, in turn, contact the LINCS Regional PD Center for your state.

World Education also provides online numeracy professional development. Visit http://elearningpd.worlded.org. Courses are available to individuals ($189/course) and to state cohorts, and include: Algebra: Introducing Algebraic Reasoning; Data: Helping Students Interpret Numeric Information; Foundations of Teaching Adult Numeracy; Geometry: Teaching About Shapes and Their Measures; Number Sense: Teaching About Parts and Wholes; and Teaching Reasoning and Problem-Solving Strategies. Courses run about six weeks, are provided once or twice a year, and are facilitated by experienced adult education math practitioners.

In Massachusetts, through the System for Adult Basic Education Support, World Education and the West Regional Support Center at Holyoke Community College have developed a series of math trainings including Introduction to Algebra: Content and Instruction; The Basics of Teaching Math; Math in Context: The Health Connection; Giving Meaning to Geometry; and College and Career Readiness Standards ABE Math: an Overview. SABES courses are provided through the five Regional Support Centers and are free to Massachusetts practitioners and programs. There are also several new courses in development by the West Regional Support Center and TERC which will be ready to be piloted in FY15. These courses are built on the ANI model – a long-term, multi-session approach with required activities between face-to-face sessions. And, just like the ANI model, these new courses are designed to help teachers develop their own conceptual understanding of math topics. This is critical since many of us as teachers only learned to “invert and multiply”; how can we teach differently if we don’t know any other way?

Why such an emphasis on math professional development? First, because, as in prior national assessments of U.S. adults’ skills, the recently published results of the Program for the International Assessment of Adult Competencies 2012 (PIACC) ranks U.S. adult math proficiency as significantly lower than 18 other countries (only Italy and Spain are lower than the U.S.) with 10% of Americans age 16-65 scoring below level 1, 20% at level 1, and 34% at level 2. At the higher levels (more comparable to the postsecondary-level skills required for many family-sustaining jobs such as for STEM occupations), only 27% of U.S. adults scored at level 3, and 9% at level 4/5. (Literacy, Numeracy, and Problem Solving in Technology-Rich Environments Among U.S. Adults: Results from the Program for the International Assessment of Adult Competencies 2012, National Center for Education Statistics, Institute of Education Sciences, October, 2013) Second, because we know from our experience teaching math that many of the adults who come to our classes have gaps in their math skills and little mathematic conceptual understanding, and that the GED mathematics test is historically the most difficult to pass (2012 Annual Statistical Report on the GED Test, GED Testing Service). Third, we suspect, also, that many of us who teach math to adults are less prepared to teach math than we are to teach reading and English language skills development.

Why is math professional development important to me? I taught math to adults for more than 15 years, and have recently returned to math teaching part-time, as a volunteer at a local program. Common myths aside, I know at the core of my being that math concepts and skills are not intrinsically more difficult to master than reading, writing, and English language skills, and that they are just as critical. I know from my teaching that almost all of us can be “good” at math, that learning math can be lots of fun, and that mastering a subject that was previously experienced as too difficult, feels wonderful. So, I want to be a better math teacher. And as T, a student in my Bridge to College math class last year said, “Why is a minus times a minus a plus? I’ll never be able to remember this if it doesn’t make sense to me.”


Written by Sally Waldron, Vice President at World Education.