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Jon R. Star, Martina Kenyon, Rebecca M. Joiner and Bethany Rittle-Johnson

Consider the following, perhaps familiar, scenario. A mathematics teacher is circulating around the classroom, looking over the shoulders of students who are busy solving linear equations such as 3x + 2 = 5x + 8. The teacher notices that one student, Paul, persists in using his own somewhat idiosyncratic and quite inefficient strategy (see fig. 1). Although Paul's strategy is not fundamentally incorrect, the extra steps required can lead to more calculation errors and wasted time.

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Percival Matthews, Bethany Rittle-Johnson, Katherine McEldoon and Roger Taylor

Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the equal sign assessed by different types of items, and provided empirical evidence for a link between equal-sign knowledge and success on some basic algebra items.

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Jon R. Star, Martina Kenyon, Rebecca M. Joiner and Bethany Rittle-Johnson

The ability to estimate is not only a valuable math skill but also an essential life skill. Many adults use estimation daily: when tipping a waitress, determining the cost of a sale item, or converting units. Within mathematics, the ability to estimate is linked to deep understanding of place value, mathematical operations, and general number sense (Beishuizen, van Putten, and van Mulken 1997) and allows students to check the reasonableness of their answers to mathematics problems in a variety of contexts.