# Other Resources

- Tina wrote a series of articles for the National Council of Teachers of Mathematics (NCTM) blog for the Mathematics Teaching in the Middle School (MTMS) journal. Each one expands on a section in the book, adding more examples as well as anecdotes and detailed explanations.

Internalizing the Order of Operations

Reason Why When You Invert and Multiply

- The community comes through once again! Owen, OTmath, is transforming the sections of Nix the Tricks into beautiful videos.

- Total Means Add
- Bigger Bottom Better Borrow
- Add a Zero
- 0-4 Hit the Floor, 5-9 Make the Climb

- Tina did an interview with Chris of STEM Everyday.
- Listen to the episode.
- Those of us who contributed to Nix the Tricks believe that conceptual understanding is more important than procedural knowledge. Here are a few studies which back up that claim:

- Data from the 13 million students who took PISA tests showed that the lowest achieving students worldwide were those who used a memorization strategy – those who thought of math as a set of methods to remember and who approached math by trying to memorize steps. The highest achieving students were those who thought of math as a set of connected, big ideas.

- Boaler, Jo. "Memorizers Are the Lowest Achievers and Other Common Core Math Surprises - The Hechinger Report." The Hechinger Report. N.p., 07 May 2015.

- While
it is clear that the national movement for reform in mathematics
teaching supports thoughtful mathematics in schools, districts are
nevertheless wary about how the implementation of those
recommendations will affect standardized test scores. The
Kenilworth story turned out to be a positive one. The
implementation of a thoughtful curriculum did
*not*hurt their standardized test score profile. Indeed, in moving from a curriculum that emphasized computation to one that emphasized thinking and problem solving and de-emphasized computation, students improved markedly in concepts and problem solving, while generally maintaining their scores in computation.

- Maher, Carolyn A. "Is Dealing with Mathematics as a Thoughtful Subject Compatible with Maintaining Satisfactory Test Scores?: A Nine-Year Study." Journal of Mathematical Behavior 10 (1991): 225-48.
- I conjecture students may develop these beliefs as a result of their experiences with mathematics.

Belief 1: The processes of formal mathematics (e.g., "proof") have little or nothing to do with discovery or invention. Corollary: Students fail to use information from formal mathematics when they are in "problem-solving mode."

Returning to the statement of Belief 1, what if anything - from the student's point of view - does mathematical argumentation, or proof, have to do with constructions? In brief, virtually nothing. In these students' experience, proofs had always served as confirmation of information someone (usually the teacher or mathematicians at large) already knew to be true.- Schoenfeld, Alan H. "When Good Teaching Leads to Bad Results: The Disasters of "Well-Taught" Mathematics Courses." Educational Psychologist 23.2 (1988): 145-66.