As I prepped students' progress reports, I found myself focused on math fact knowledge. Thanks to our terrific fourth grade teachers, every child who took the facts fluency test had accuracy when it came to math facts. That's awesome! The challenge now is speed, and while speed isn't always the most important factor, a lack of facts speed hinders students' acquisition of deeper concepts and mathematical proficiency. It halts their ability to fluently synthesize a number of steps or concepts as they play with numbers, solve problems, and complete calculations.
Hence, I am thinking about how to build that fact fluency with greater speed and flexibility in the days ahead.
It was interesting to see that my good, but not strongest math students, often had fluency with sets of single operation signs, but struggled with sets of facts with mixed signs. I thought of the football exercises my sons have done, exercises that help them move from one physical action to another, and how their coaches have had them practice this to build greater flexibility on the field. The same is true for students' math flexibility--sets of mixed signs help students to gain brain flexibility and fluency with number sense. It's certainly not the only important aspect of math learning, but when mastered this can help students with their overall math learning.
It was also interesting to see that students who struggled with speed with single sets are my students that struggle the most overall with learning new concepts. These are bright and capable students who only need some engaging practice to get faster. One colleague suggested this online game. She used this game with a child she tutored and she said the facts growth was amazing. Since the system has not shown interest in buying this game, I'll propose it to parents of students who fall into this category. There are board games like Yahtzee that build this skill too. As a child, I played Yahtzee for hours and that truly helped me to be very fast with facts and number manipulation. I'm sure there are many other games too that are lots of fun and build this proficiency as well.
Facts are only one consideration with math proficiency, yet it's an important consideration. Most students who are fast with facts also have high scores in all other math work and study assessments. When reading Willingham's book, Why Don't Students Like School, his terrific explanation of the process related to short term memory versus long term memory matches what I am noticing. If students have their fact knowledge deeply embedded in long term memory, there's much more room for using short term memory to learn new concepts. Similarly Willingham's acknowledgement that knowledge begets knowledge matches this post too because students' knowledge of facts leads to greater math knowledge.
Math is a mix of skill, concept, and knowledge learning and synthesis. We can build math skill with facts while also building deeper and better mathematical thinking, concept, and knowledge through deeper problem solving study and project work. Our math teaching can include multiple parallel paths of study that support each other. I continue to explore this idea, and look for ways to embed it in process that matter with our fifth grade standards-based, foundation-building program. I am open to any advice you have as I continue to build my repertoire, knowledge, and skill in this area. In so many ways I see parallels with the sports training my sons have done and continue to do in swimming and football--in these sports it's a synthesis of many online/offline strategies to develop a successful athlete. I want to do the same with regard to developing strong and versatile math students too.