Mathematics Updates
August 2016
New School Year, New Opportunities!
UPDATED: Curriculum website math pages
Learning Resources shared folders
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Something to think about ...
Making math "mistakes" supports learning
Allowing students to make "mistakes" as they work through math problems is an essential part of their learning process, says David Wees, a formative assessment specialist in mathematics in New York. Wees shares why the focus should be on students' thinking as they attempt to solve math challenges, and not simply whether they reach the correct answer. Read more ...
Back-to-school resources
Fact fluency instructional flow
"Learning computational skills and developing conceptual understanding are frequently seen as competing objectives. If you emphasize understanding, then skills suffer. If you focus on developing skills, then understanding suffers. We believe that this analysis is wrong. It is not necessary to sacrifice skills for understanding, nor understanding for skills. In fact, they should develop together, In order to learn skills so they are remembered, can be applied when they are needed, and can be adjusted to solve new problems, they must be learned with understanding."
Hiebert, J. (2000). Making sense: Teaching and learning mathematics with understanding.Portsmouth, NH: Heinneman.
Math teaching: What we've learned from a decade of research
A new paper from the Institute for Education Sciences (IES) lists 28 ways federally funded research has changed what we know about how to teach whole numbers, fractions, algebra, and other math topics.
IES, part of the U.S. Department of Education, funded more than 200 studies about math instruction between 2002 and 2013. A synthesis of that research, published in July, lays out out what some of the contributions these studies have made to the field.
For example: IES-funded research found that:
- Switching up the formatting of arithmetic problems can help students better understand the equal sign. That is, instead of just presenting 9 + 4 = ___, teachers may also want to show ___ = 9 + 4.
- Students do better with fractions when they view them as numbers on a number line, rather than as parts of a whole. (This is a big change in many classrooms, and something the standards require.)
- Students should confront and analyze common math misconceptions. For instance, many students believe that 0.25 is bigger than 0.5, since 25 is bigger than 5. The teacher should show examples in which a student gets this wrong. "This stands in contrast to concerns by teachers that presenting and discussing incorrect solutions will reinforce and increase their use," the report states.
- Using gestures and physical movement can help students better understand math concepts. "For example, teachers [can use] gestures to simulate actions, such as placing their arm at different angles to simulate the action of altering the slop of a line," says the report.
There are two dozen more of these concrete findings in the report, as well as information on the research studies they were distilled from.
The whole report is worth a look -- particularly by teachers looking to incorporate more "research based" practices into their everyday instruction.
Inspiring students to math success
Research base
Boaler, J. (2013). Ability and mathematics: The mindset revolution that is reshaping education. FORUM, 55(1), 143-152. Retrieved from http://www.youcubed.org/wp-content/uploads/14_Boaler_FORUM_55_1_web.pdf
Dweck, C. S. (2006). Mindset: The new psychology of success. New York: Random House.
Hiebert, J. (2000). Making sense: Teaching and learning mathematics with understanding.Portsmouth, NH: Heinneman.
National Council of Teachers of Mathematics. (n.d.). Back-to-school resources. Reston, VA: NCTM. Retrieved from http://www.nctm.org/backtoschool/
Rittle-Johnson, B., & Jordan, N. C. (2016). Synthesis of IES-funded research on mathematics: 2002-2013 (NCER 2016-2003). Washington, DC: National Center for Education Research, Institute of Education Services, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncer/pubs/20162003/pdf/20162003.pdf
Schwartz, K. (2015). Seeing struggling math learners as ‘sense makers,’ not ‘mistake makers’. KOED News: Mind/Shift. Retrieved fromhttp://ww2.kqed.org/mindshift/2015/08/04/seeing-struggling-math-learners-as-sense-makers-not-mistake-makers/