The number and variety of repetitions we offer children in order to learn matters substantially. Ideally we offer each child a scaffolded number of repetitions until they reach mastery. What's heartbreaking for a teacher like me is to have to limit repetitions due to time and strict directives with regard to content. Instead I'd like to continually coach children up the math skill, concept, and knowledge ladder in ways that matter.
For example, I worked with a young girl today who, like most children, was completely capable of learning the material. However, she did require quite a few repetitions to become comfortable with the learning and get close to mastery. I fear that we are rushing the curriculum too much for too many children, and therefore not helping children to reach the mastery possible when a sufficient number and variability of practice items are offered.
To enable the kind of coaching I desire means that we would have a large number of wonderful learning experiences for children to engage in as they learn math. One learning experience would lead to another and every learning experience would include review, new concept, and enrichment options. The learning experiences would not be tied to grades or ages as most learning is now, but instead tied to where a child is developmentally with regard to math concept, knowledge, and skill.
Note the inequity that currently exists with regard to age- or grade-level math standards. This inequity arises for many reasons. Let's say you're a young, bright student who comes from a family that hasn't had the privilege of lots of education, and a family whose general math foundation is not that strong. Also, let's add that you go to a school with large numbers of students in the class and students who have many, many needs. It's likely that you'll arrive at fourth or fifth grade with less of a math foundation than a child whose parents both are highly educated, work in the math field, afford an education with low teacher-student ratios in classes where students have less extensive needs, and also have the time to enrich your education with math tutors, clubs, experiences, play, and more. How students present in elementary school has a lot to do with the environment in which they live, the amount of academic support/experience they have access to, and the amount of teacher time and good teaching they get in school.
In time, students who have access to good educational supports and a positive, developmental approach to math learning and teaching catch up to one another. Students in high school and college who believe they can learn, know how to access learning supports, and put the time in, can succeed as well or better than anyone else. The key here is not to discourage students in the early years with artificial grade level and age level standards since the experiences and supports that young children bring to school vary greatly. What's important is that we encourage all children to follow a developmental path that begins with extensive play, exploration, and positive math experiences and leads ahead with multiple empowering, targeted, and open-ended learning experiences that students engage in as they are ready no matter how old they are.
This kind of teaching mirrors what students do in Montesorri programs and other more holistic learning/teaching programs--programs that put the children ahead of the content standards. This kind of teaching takes into account the latest cognitive science--science that demands we give learning the connections, meaning, and repetition the learning requires for success.
When we don't teach with the latest research in mind, we exacerbate the inequity and opportunity gaps that exist. Because students enter fourth grade with dramatically different foundations in learning, we send the message that some are "smart" and others are not as "smart," when the reality is that some have had greater learning experiences and support than others--that's the difference. When we push curriculum that year after year sends a child the message that he/she is behind, we never really give that child the chance to learn in ways that matter--ways that mirror latest cognitive science, growth mindset and learning research. We essentially continually hinder students rather than promote a positive, multi-year developmental path to learning math well.
How can we change schools to meet the real, positive potential that exists to nurture enthusiastic, confident students who get the amount of repetition, solid learning experiences, and coaching they need to continually move forward to a strong foundation of knowledge? I know we can do this, but it will take leadership from the state level to change schools and leadership from unions, educators, administrators, and community members to foster this positive change to meet the potential and promise that exists.