For this blog post I've decided to select a few quotes from chapter 4 and to reflect on each of them.
".the joy and fascination young children experience with mathematics are quickly replaced by dread and dislike when they start school mathematics....."
-my second son shows a lot of interest in counting items or finding numbers on labels, or counting with his cousin so they can race or play hide and seek. Other times you hear him invite everyone for "tea time" ensuring we all have matching cups and sauces. He creates yellow and red patterns with his magnoformers (something that was never directly shown to him). I can't help but wonder what will happen to his joy for learning and exploring when he is exposed to school mathematics. At what point will educators shift their thinking from I have to cover the curriculum to here is where my students are in their development what am I going to do to support them?
"When students see mathematics as a set of ideas and relationships and their role as one of thinking about the ideas, and making sense of them, they have a mathematical mindset."
-I wonder what would be the response from students if they were to be asked: what is you role as a math student?"
-I also wonder how different that response would be from students at other schools
".....number sense and mathematical mindsets develop together, and learning about ways to develop one helps the development of the other."
-As the numeracy teacher, I share in the responsibility (with classroom teacher and student) to help students develop flexibility with numbers as number sense is needed in all areas of mathematics but more importantly to see connections and relationships between ideas/concepts.
Any thoughts on these or other quotes from this chapter?
".the joy and fascination young children experience with mathematics are quickly replaced by dread and dislike when they start school mathematics....."
-my second son shows a lot of interest in counting items or finding numbers on labels, or counting with his cousin so they can race or play hide and seek. Other times you hear him invite everyone for "tea time" ensuring we all have matching cups and sauces. He creates yellow and red patterns with his magnoformers (something that was never directly shown to him). I can't help but wonder what will happen to his joy for learning and exploring when he is exposed to school mathematics. At what point will educators shift their thinking from I have to cover the curriculum to here is where my students are in their development what am I going to do to support them?
"When students see mathematics as a set of ideas and relationships and their role as one of thinking about the ideas, and making sense of them, they have a mathematical mindset."
-I wonder what would be the response from students if they were to be asked: what is you role as a math student?"
-I also wonder how different that response would be from students at other schools
".....number sense and mathematical mindsets develop together, and learning about ways to develop one helps the development of the other."
-As the numeracy teacher, I share in the responsibility (with classroom teacher and student) to help students develop flexibility with numbers as number sense is needed in all areas of mathematics but more importantly to see connections and relationships between ideas/concepts.
Any thoughts on these or other quotes from this chapter?
Great question- what is your role as a student of mathematics?
ReplyDeleteWhat if we add to this- what is your responsibility as a student of math?
Roles and responsibilities are something we all address throughout the year in almost all grade levels. These questions would make a very meaningful curriculum connection to the learning skills. These questions would also make a good entry point into journaling in math. I might get students to respond to these and post some replies!
There were a lot of words of wisdom in this chapter so looking for a quote that made us pause and think was a very effective strategy to construct meaning from this chapter. The one that really stood out for me was on page 35. "...the difference between high- and low-achievement students was not that low-achieving students knew less mathematics, but that they were interacting with the mathematics differently. Instead of approaching numbers with flexibility and number sense, they seemed to cling to procedures they have learned, using them very precisely, not abandoning them even when it made sense to do so. The low achievers did not know less, they just did not use numbers flexibly..." This makes me think how as teachers we need to clarify for ourselves what number sense really means? What mathematical states of mind are needed to be able to work with numbers mathematically? Teaching the number sense strand in the curriculum as a set of disjointed specific concepts is certainly not helping the students be flexible in their use of numbers. The author's diagram showing the methods to be learned and the concepts being learned is interesting. Sometimes when we teach math with a procedural mindset, we ignore the concepts being learned and instead focus on the methods. Students should be able to learn the methods as means to think deeply about the conceptual learning.
ReplyDeleteThe quote you reference, I also found to be very powerful. The point you raise about the number sense strand being taught as a set of disjointed specific concepts and helping students to use numbers flexibly is a good one. We are expected to report on this strand throughout the school year, so wouldn't it make sense to just integrate it within other strands than teaching it separately? And if the goal is for students to be critical thinkers; numerate learners, then shouldn't all strands be integrated?
DeleteYour other point about what number sense really means, is also a good one to explore. In the curriculum, the first sentence under the number sense and numeration heading is:"Number sense refers to a general understanding of number and operations as well as the ability to apply this understanding in flexible ways to make mathematical judgments and to develop useful strategies for solving problems." The paragraph goes on to state that, "A broad range of activities and investigations, along with guidance from the teacher, will help students construct an understanding of number that allows them to make sense of mathematics and to know how and when to apply relevant concepts, strategies, and operations as they solve problems." So what is teacher's role and what is the student's role in developing number sense?
You are right! Number sense is the string that connects all other strands together and should be taught as such. Teaching fractions with concepts of time, measurement and probability makes way more sense than teaching fractions as a concept on its own. When students develop a sense of numbers, they can use this to make sense of other mathematical concepts.
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