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We teach children about numbers, but how do people come to know what numbers are, given that they are abstract? There must be some process of learning that takes place. This paper explores this problem, offers several alternative accounts of what a number is, and argues that the concept of a number can be learned by learning to recognize the size of a set or collection of entities. Teachers call this subetizing

"While teachers may always be the best line of defense for students falling behind, busy schedules don't always permit the special attention and feedback that students need. That's where artificial intelligence-powered teaching assistants might come in handy. "These intelligent tools can adapt pacing based on the student's ability … and provide targeted, corrective feedback in case the student makes mistakes, so that the student can learn from them," states an eSchool News report released earlier this year. "These tools also gather actionable insights and information about a student's progress and report the data back to the teacher." Understandably, there is still some hesitation at the idea of using this technology, as education professionals fear the day robots will replace teachers. However, as Thomas Arnett, a writer at the Christensen Institute, explains in his report, Teaching in the Machine Age, these advances are not meant to replace teachers but help them bring students to new heights. "Innovations that commoditize some elements of teacher expertise also supply the tools to raise the effectiveness of both non-experts and expert teachers to new heights and to adapt to the new priorities of a 21st-century workforce and education system," writes Arnett. Schools have already begun to adopt machine learning initiatives to help teachers and students fill learning gaps, and the results have been received well so far."

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