Sentence examples for equivalence problems and from inspiring English sources

Using two intact seventh-grade classes and a staggered treatment design, students were assessed at three time points on their (a) ability to solve equivalence problems, and (b) reasoning abilities about true false number sentences.

Using two intact seventh-grade classes, students were assessed at three time points on their ability to solve equivalence problems and on their reasoning about true false number sentences.

Using two intact seventh-grade classes, students were assessed at three time points (Time 1, Time 2, and Time 3) on their (a) understanding of the equal sign symbol, as operationalized by the ability to solve equivalence problems, and (b) their relational thinking, operationalized by the ability to reason structurally about true false number sentences.

Findings showed that the gesture group solved more equivalence problems correctly in the post-instruction test compared to peers who were instructed not to gesture.

Students in the Intervention First group were able to maintain their scores on the test of equivalence problems 4 weeks after the conclusion of the intervention.

This result may be due to the relatively weak psychometric properties of the relational thinking measure used, but could also be attributed to the complex nature of relational thinking relative to what is involved in solving mathematical equivalence problems.

Moreover, for the Intervention First group, the level of performance on equivalence problems persisted for 4 weeks after the intervention ended, but the students' relational thinking was not maintained.

The improved performance on equivalence problems in both groups has important implications, particularly with respect to relational thinking, as researchers have previously argued that students who struggle to understand the equal sign appear to engage in meaningless computations instead of reflecting on the relationships that exist between numbers [17, 20].

In one line of related work with elementary school students, one group was told to gesture while solving algebraic equivalence problems (e.g., 5 + 4 = 3 + 4 + ____) by putting their fingers in a "V" formation when referencing the addends of an equation whereas another group was not told to gesture (Broaders, Cook, Mitchell, & Goldin-Meadow, 2007).

These analytes are shown in blue (or in black or red if there was also a potential equivalence problem) in Figures 3 and 4, and some examples of boxplot representations [ 24] of these data are shown in Figure 5 to assist further interpretation.

In particular, we study the evaluation problem, the satisfiability problem, and the equivalence problem for GFODDs under the assumption that the size of the intended model is given with the problem, a restriction that guarantees decidability.