Mathematical representations are 'visible productions' that embody mathematical ideas. The author guides teachers with suggestions for the use of representations in mathematical problem solving with students. Representations can be used to help make abstract mathematical ideas accessible, allowing teachers and students to interpret, communicate,…

Educational institutions around the world have been integrating AI into their educational practices. Many studies and reports highlight both the advantages and disadvantages of this integration. This paper focuses on the positive aspects of AI in education, specifically through the lens of a high school geometry project at a technology-focused…

The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance,…

As educators and business people consider what children need to be successful in this rapidly changing society, creative and critical thinking, problem solving, communication, collaboration, and persistence are recognized as the most important skills for success in education and the workforce. Among these, creative thinking is referred to most…

In this paper, the authors introduce a research instrument (Draw a STEM Learning Environment: D-STEM) and its accompanying rubric (the D-STEM Rubric), both of which were developed based upon relevant research studies. The authors describe their usefulness to school principals in commencing conversations with their school's STEM [Science,…

This article reports on a study in which researchers asked children to "make up as story and a picture about marbles for this number sentence: 3 x 5 = 15." Students in this study came from pre - dominantly low- to average-income families living in three distinct geographical areas within the United States. A similar division task was…

This practical article presents activities that support previous research suggesting the integration of art with science is beneficial to the learning and cooperative processes of children. The project showcased here highlights the ability of elementary school children to collaborate with their peers for problem solving and critical thinking…

Drawing structures, mechanisms, and syntheses is a vital part of success in organic chemistry courses. ChemDraw for iPad has been used to increase classroom experiences in the preparation of high quality chemical drawings. The embedded Flick-to-Share allows for simple, real-time exchange of ChemDraw documents. ChemDraw for iPad also allows…

This article describes some of the benefits derived from encouraging math drawing in a class of seventh-and eighth-grade students in line with promoting mathematical proficiency. The authors report teaching pictorial representations as part of the solution process, where both students and teachers gained insight into various areas of…

Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to meet Sam to complete one segment of their journey. We determine Fay's optimal path minimizing segment length, and thus maximizing the number of times they meet…

In this article, the author describes an art project wherein students make fanciful connections between art and medicine. This project challenges students to interpret "ear idioms" (e.g. "blow it out your ear," "in one ear and out the other") by relying almost entirely on realistic ear drawings, the placement of them, marks, and values. In that…

Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…

The author states that she finds it challenging to create new and innovative lessons for her college-level design students. Most of her students are first-year art students, and some never took art in high school. Here, she describes a lesson as one solution she developed that made the students look at themselves, and integrate their personalities…

Most often radio dials of analogue radios are not uniformly graded; the frequencies are cramped on the left side or on the right side. This makes tuning more difficult. Why are dials made this way? We shall see here that simple calculus can help understand this problem and solve it. (Contains 7 figures.)

In the author's ongoing attempt to design creative challenges that are relevant, based on observational drawing, and that place students squarely in the creative problem-solving driver's seat, she chose cars and engines as subjects. After all, they have a parking lot full of them and their administrative staff members, who park side-by-side, were…