Through five waves of data collection, this longitudinal study investigated the development of spatial skills in 304 elementary school children (M = 7.64 years) as they progressed from the second to fourth grade. The study focused on whether multiple latent classes with different developmental profiles best explain development. Spatial skills were measured by tests featuring two-dimensional figures. Mathematics achievement was measured by the statewide end-of-year test and was included as a distal outcome variable. The role of covariates, including socioeconomic status, verbal working memory, and gender, was also explored. The results indicate a need to view two-dimensional spatial skills development as multidimensional with two developmental profiles predicted by socioeconomic status, verbal working memory, and gender. The developmental profiles predicted differences in mathematics achievement.

A flipped classroom describes a class where students complete readings and watch lectures outside of class, while in-class time is spent on activities to practice content learned. The implementation of a flipped classroom approach has been shown to increase student learning and student enjoyment of courses. This paper describes using the flipped classroom technique to improve learning outcomes and student interest in an organic chemistry course. We assessed student learning and enjoyment through a student satisfaction questionnaire and comparative analysis of grades. The survey consisted of 14 Likert questions and four open-ended questions. Results of the student satisfaction questionnaire confirm that the majority of students believed that the flipped classroom teaching approach helped them learn better/more, that it improved their learning outcomes, and that they liked it better than a traditional class. The results of grade analysis did not show a significant difference between the flipped and traditional formats.

Research has shown that the efficacy of learning with manipulatives (e.g., fingers, blocks, or coins) is affected by multiple variables, including the amount of guidance teachers provide during learning. However, there is no consensus on how much guidance is necessary when learning with manipulatives. The goal of this study was to examine the optimal level of guidance during instruction with manipulatives. The focus was on the timing and level of guidance. The researcher taught students a lesson on counting from one to 10 with pennies and nickel strips. Kindergarten students were taught over five consecutive days in one of four conditions: high guidance, low guidance, high guidance that transitioned to low guidance, and low guidance that transitioned to high guidance. Results showed no difference in learning across the conditions. These results provide valuable information to teachers on the areas of mathematics that do not require the effort of high guidance.

Spatial skills have been consistently linked to mathematics achievement in older students and adults, but we know little about their relationship to mathematics achievement in elementary school. This study examined how spatial skills influenced the development of number sense, and subsequent mathematics competency, as students progressed from the 2nd to the 4th grade. Gender, verbal working memory (VWM), and socioeconomic status (SES) have also been found to predict number sense development and to be linked to spatial skills; as such, they were included as covariates in this study. Participants were 304 second graders who were assessed at 5 points between 2nd and 4th grade. Two growth mixture models (spatial skills as time-invariant and time-variant covariates) were tested to determine whether different developmental trajectories were needed to explain the development of number sense. Both models revealed the presence of 2 latent classes. The classes differed in their initial level and in their growth rate, with the higher performing class beginning the second grade at an advantage and increasing that advantage over time. SES, VWM, and spatial skills influenced latent class membership and subsequent mathematics competency. SES, spatial skills, and VWM, but not gender, predicted the intercept but differences were found in predictors of the slope of number sense. The impact of number sense changed over time and differed as a function of latent class having an earlier impact on the higher performing class.

We present a volumetric communication system that is designed for remote assistance of procedural tasks. The system allows a remote expert to visually guide a local operator. The two parties share a view that is spatially identical, but for the local operator it is of the object on which they operate, while for the remote expert, the object is presented as a mixed reality "hologram". Guidance is provided by voice, gestures, and annotations performed directly on the object of interest or its hologram. At each end of the communication, spatial is visualized using mixed-reality glasses.