Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a formal, algebraic way, leveraging key mathematical ideas about inverses, the structure of our number system, and fundamental properties. We identified the use of carefully chosen comparisons as a key feature of logical necessity and documented three types of comparisons students made when solving integer tasks. We believe that logical necessity can be applied in various mathematical domains to support students to successfully engage with mathematical structure across the K-12 curriculum.
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机译:f3任意参数的“ g”数字实施解码程序的加法函数结构(Σ CD Sub>)[ 1,2 Sup> S g Sub> h1 Sup>] f(2 n Sup>)和[ 1,2 Sup> S g Sub> h2 Sup>] f三元表示法f(+ 1,0,-1)和双逻辑微分d 1,2 Sub>的算术公称(2 n Sup>)位置格式“额外代码RU” / dn→f 1,2 Sub>( + Sup>←↓- Sub>) d / dn Sub>“水平”活动参数2“并删除“级别1”中的活动逻辑“ +1”,“-1”→“ 0”(俄罗斯逻辑版本)