This has been a really popular question lately as we are well into the school year. What to use for a math intervention? Sometimes educators are looking for a strategy, sometimes a process and sometimes a thing. I always assure them that if there was a “magic” mathematics anything, I would know about it and be sure to tell them but there isn’t. There are some better rabbit holes for us to go down as we try to find what helps our students learn mathematics and what educators can use to help students “get it,” or get “caught up.” Let us just agree, that those terms in quotes are ambiguous at best. In this blog I am going to help you find a few rabbit holes you may want to explore.
In previous blogs, I have shared about Number Sense and Learning Trajectories. I first learned of Learning Trajectories directly from Doug Clements at math SCASS (Math State Collaborative on Assessment and Student Standards), which is the mechanism nationally or how people who have my job get “smart” together about the good stuff to bring back to our individual states. It is put on by CCSSO (Council of Chief State Officers). The same group that brought us the mathematics standards.
Anyways, I didn’t “get it.” It wasn’t that Doug did a bad job of teaching me, it was because I had a secondary mathematics background and I didn’t know what I didn’t know. Which the experience made me realize, I do not know what I need to know about K-5 mathematics. I needed to get “smart” about K-5 mathematics and quick. So I asked some of the AEA consultants, how do I get smart about what I need to know about K-5, and they said take Number Sense from Christina Tondevold.
After taking the Number Sense training, then and only then did I “get it.” Eureka, I understood that I had not had Number Sense myself! No wonder I didn’t understand the Learning Trajectories ! I didn’t even understand the 4 early Number Concepts and the 4 Number Relationships (subitizing, verbal counting, object counting, cardinality, spatial relations, 1/2 more/less, benchmarks of 5 & 10, part-part-whole.) This was the reason that I didn’t understand the Learning Trajectories and how to use them to help students. But by connecting the Number Sense learning with the research based Learning Trajectories activities, I realized how powerful they could be to use with students.
This brings us to the topic at hand. Can they be used as a math intervention? An intervention is a combination of program elements or strategies designed to produce behavior changes or improve health status among individuals or an entire population. Educators learning more about Number Sense and then using Learning Trajectories, to give students experiences to increase their Number Sense along research based Learning Trajectories could help teachers take students from where they are at to where we want them to be more quickly than perhaps what we are currently doing.
Example: A student still counting on their fingers may need more subitizing. (I know this because I understand the information in Number Sense .) I know I need to give the student experiences so I go to the Learning Trajectories and select subitizing and I can get close to where I think the student is at and then work them forward along the subitizing trajectory. See the screencast here.
A few last tidbits. Number Sense is closing for purchasing individual accounts on October 28, 2019 and will not re-open for a year. Schools purchasing multiple accounts can do so at any time. The Learning Trajectories are open sourced and you just have to create an account. I encourage you to watch the video snippets. Lastly, for those who are looking for Learning Trajectories more bells and whistle or sophistication in computer program, diagnostics, intervention, be sure to check out Building Blocks or Number Worlds which packages the work of the Learning Trajectories.
I share this information as a potential rabbit hole that you may want to explore. Will we do a better teaching and learning with increase Number Sense ? Yes. Will we have researched based activities to use with students if we use Learning Trajectories ? Yes. Could this help teachers love to teach math, help students love learning math and help them learn more math? You be the judge. Let me know your thoughts in the comments.