Molnar Math Learning Inventory

In my 43 years of teaching math, I have taught math to children of all ages, from toddlers to teenagers. I have taught large classes in inner-city schools, classes in the Berkeley public schools containing a huge range of math levels, small classes in my home, and individual students. I have worked with children with dyscalculia, dyslexia, and ADHD. I have taught in settings as diverse as UC Berkeley, a First Nations Reservation in British Columbia, and a residential psychiatric center for young children in San Francisco.

I have taught children who had been identified as profoundly gifted and others who had been placed in Special Education because they struggled to make sense of 2 + 3. For decades I have been designing math problems and methods of teaching to meet the very specific needs of every child I have worked with.

The goal of my work has always been to draw students into the beauty and joy of math and to help every child understand and relish math, whether they are bewildered by the difference between 4 and 5 when I first meet them or are eager to dive into calculus at age ten.

To do this, I have explored these questions:

  • Why is math so much easier for some people than others?
  • Why do children learn math at such tremendously different rates?
  • What are the components that make up being successful at math?
  • How can I best develop as many of these capabilities and qualities as possible in all my students so that each child is learning as much as possible at every stage of their development?

I have identified 24 factors which play a significant role in a child’s ability to learn math.

The Molnar Math Learning Inventory

1 number sense able to subitize; understands the connection between a group of objects and the number that represents this; able to compare and order numbers
2 focus/attention able to direct attention toward a problem and hold attention there long enough to solve it, filtering out both internal and external distractions
3 working memory able to hold onto and manipulate a number of pieces of information at one time
4 long term memory formation

(including procedural memory)

  
5 memory retrieval  
6 understanding of the 4 basic operations and of relational symbols  
7 automaticity with addition and multiplication facts addition facts up to 10+10 fully memorized by the end of 1st grade; multiplication facts up to 12×12 fully memorized by the end of 3rd grade
8 formation of critical mathematical schemas in long-term memory  
9 mastery of algorithms age-appropriate mastery of the most efficient algorithms for +, -, x, ÷
10 capacity to take in and process short clear explanations  
11 logical reasoning  
12 processing speed Note: Students with slow processing speeds may still be able to do math very well but a fast processing speed is an advantage in class and on tests.
13 spatial sense  
14 willingness willing to do what is asked when the mathematical task is at an appropriate level; willing to practice a new skill to the point of full mastery
15 pattern recognition  
16 structure recognition recognizes familiar elements or a familiar structure in a new kind of math problem
17 sorting and classifying able to sort and classify numbers and shapes by properties
18 pleasure experiences satisfaction in solving math problems
19 eagerness leans into learning
20 daily practice does math at the appropriate level (not too hard, not too easy) at least 5 days a week
21 actively seeks help able to recognize when help is needed and is willing to ask for it
22 persistence/stamina  
23 reading able to read and make sense of grade-level instructions and word problems
24 writing able to write legibly and keep multi-step written responses neat and orderly