Using Cuisenaire Rods, metric measurement, and mapping, students worked collaboratively to calculate, keep records, build, and problem solve with use of decimal fractions as a key element.

The problem of determining the angle ? at which a point mass launched from ground level with a given speed v[subscript 0] will reach a maximum distance is a standard exercise in mechanics. There are many possible ways of solving this problem, leading to the well-known answer of ? = p/4, producing a maximum range of D[subscript max] = v[superscript…

Differences exist between engineering and liberal arts students because of their educational backgrounds. Therefore, they solve problems differently. This study examined the brain activation of these two groups of students when they responded to 12 questions of verbal, numerical, or spatial intelligence. A total of 25 engineering and 25 liberal…

This paper presents findings from a two-year qualitative study examining integration of computer science (CS) and computational thinking (CT) into elementary mathematics instruction. Integrated units were developed by elementary teachers and CS/CT coaches with support from university faculty with expertise in CS/CT and elementary mathematics.…

Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.

When asked to determine the number of tens in twenty-five, most second graders who have had instruction on place value can quickly provide the correct answer of two. However, when asked to show how the numeral 2 is represented in a set of twenty-five objects, many children struggle to draw a connection between the digit 2 and twenty objects in the…

Students learn scientific concepts and mathematical calculations relating to scientific principles by repetition and reinforcement. Teachers and instructors cannot practically spend the long time required during tutorials to patiently teach students the calculations. Usually, teachers assign homework to provide practice to students, hoping that…

Preschool education focuses on the efforts to provide fun and meaningful learning opportunities to children aged four to six years old. The main focus is the process of teaching and learning which is children-centered, emphasis on the findings inquiry concept, the use of integrated teaching and learning, thematic learning, learning through…

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

A Number Talk is a brief activity (10-15 minutes in length) that is designed to support students' mathematical sense making and promote flexible thinking. During a Number Talk, students engage in mental computations. Number Talks help students do the following: (1) Develop number sense focused on making sense of quantity and mathematical…

The perspective that computing and computational thinking (CT) are necessary competencies for the 21st century is increasingly pervasive. Computational concepts and methods--problem solving, designing systems, refining the steps in a process, and tinkering toward creative solutions--are relevant in nearly every discipline, profession, and…

Background: Math is a difficult subject with which many upper middle-school students struggle. In addition to knowledge, skills, and motivation, effective learning strategies play an important role in learning math. Aims: This study aimed to examine the effects of comprehension-oriented learning strategies (perceptual and abstract grouping of…

This brief "Math for Real" article introduces Ohanna, a seventh grader who lives in New York City and regularly takes the bus to get around the city. Ohanna pays $2.50 per bus ride when using her MetroCard. She earns a 5% bonus when she refills the card with a minimum of $5.00. For example, if she adds $10.00 on her MetroCard, her…

This investigation presents students with the challenge of determining the total number of eggs in a photograph of a stack of egg trays. The perspective of the photograph does not allow students to count all the individual eggs in the top tray but does allow them to see the number of eggs in one row and one column of the top tray. During this…

Reduction is one of the key techniques used for problem-solving in computer science. In particular, in the theory of computation and complexity (TCC), mapping and polynomial reductions are used for analysis of decidability and computational complexity of problems, including the core concept of NP-completeness. Reduction is a highly abstract…