Sitting at an all-staff school improvement meeting, I wondered how I might bridge this apparent chasm in understanding about education.
A couple of years ago, I watched Eleanor Duckworth, an expert in child development who studied under Piaget, tease out three fifth-graders’ conception of proportion using different-colored paperclips to represent juice and water mixed. One kid felt it seemed a little strange, but all three decided that if you had two green and two white paper clips, that was the same "juiciness" as one green and two white paper clips. Following the demonstration, a classmate asked if she ever saw children demonstrate understanding of proportion at an earlier age. "Oh no, it would be a debate even into high school."
The new state math standards reflect too rigid an understanding of child development. Accomplished educators identified the grade level at which students should be able to master certain math tasks and content. Now, the expectation is that all students will master certain math tasks and content all on the same timeline. This assumes a particular interpretation of Piaget’s theory, one in which a child naturally progresses through stages that have more to do with age than environment. If you adhere to the first interpretation, a set curriculum that matches age levels, with remediation to fill gaps, makes perfect sense. And, I argue, we will continue to fail our kids when it comes to math.
In conversing about the proportion demonstration, a parent shared with me the story of his own child who began 9th grade struggling in Algebra. The parents talked with the teacher early on, concerned that this would have an impact on college admission. The teacher encouraged the parents to have patience, explaining that the ideas are abstract and kids grasp them at different points. Her advice, wait until spring and you’ll see, it will come together. It did, just barely. The student has since gone on to fare quite well on the math PSAT.
The context for this learner could hardly have been better. She attended a top-notch independent school here in the Northwest where all students go on to attend college, most at selective or highly-selective schools. The student-teacher ratio is 10-1. Access to teachers outside of class time is readily available. Most parents are highly involved in student progress and capable of assisting with time, content, and extra resources. Students engage in rich educational experiences within and outside of the school day. Even in a context I can only dream of as a teacher in a challenging public school, students develop at different paces.
A different interpretation of Piaget’s theory is one in which development is constructed as an interaction between the child and their environment. If you adhere to the second interpretation, you start with each child’s understanding and build appropriately challenging curriculum around that understanding.
What might the application of the standards look like if we adopted the second interpretation? Here are some questions we might ask ourselves:
- How do we gain evidence of how each child is developing?
- How can we both support and challenge with an individually-designed curriculum while simultaneously creating a community of learners?
- How can we stretch the system so that those who don’t meet an artificially imposed developmental deadline are not excluded from society’s economic and intellectual spoils?
I welcome your thoughts.
To see a classic Piaget demonstration (posted on YouTube by jenningh), click here.
Both Nancy and Travis raise a key point. Gaining “real, useful knowledge of students” takes time and yet, I too, teach in a world of 47-minute periods. I can’t say that I have the ideal solution to that, but I wonder what policies might flow from a shift in what is emphasized. At the building level, leadership could encourage qualitative notes to parents on learners rather than posting points in an on-line grading program. Buildings and districts could direct their professional development dollars and time to understanding student work instead of reading yet another table of test scores or demanding uniformity in use of this or that strategy that “research” says is effective. The state could commit to educational funding of the resources (staff time and capacity and non-employee-related-costs) necessary for achieving a basic education designed around individual students.
In a couple of blogs recently, I have seen Piaget repudiated–even construed as the “pernicious” source of bad teaching practice. Here’s a sample:
http://tinyurl.com/57yt3l
The thrust of his thinking seems to be that Piaget and other developmental theorists are just scholarly/archaic versions of excuse-makers. Since *some* kids can do things at a certain age, why are we setting standards that “limit” kids to what seems to be developmentally logical?
What’s missing is what you both identified: deep knowledge of students. And a commitment to serve kids who bring different learning capacities into the classroom. Real, useful knowledge of students’ abilities doesn’t come quickly or easily. More evidence that teaching is a complex skill.
It is a tough situation. I like standards and like the simpleness of them. However, that simpleness can sometimes be too simple (simply rigid). Balance is often the best course and in that balance, a crucial knowledge of the student and his/her needs is important. But where is the time in the school day for such thoughtful, reflective interaction? My classroom periods are about 47 minutes long. Yikes!