Problem solving is one of the main competences we seek to teach students at school for use in their future lives. However, when dealing with mathematical problems, teachers encounter a wide variety of difficulties. To foster students' problem-solving skills, the authors developed "strategy keys." Strategy keys can serve as material to…

Dot arrays provide opportunities for students to notice structures like commutativity and distributivity, giving these properties an image that can be manipulated and explored. These images also connect to ways that we organize discrete objects in everyday life. This article describes how the authors developed an array of dot tasks that have been…

The phenomenon of outbreaks of dangerous diseases is both intriguing to students and of mathematical significance, which is exactly why the authors engaged eighth graders in an introductory activity on the growth that occurs as an epidemic spreads. Various contexts can set the stage for such an exploration. Reading adolescent literature like…

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…

Spatial abilities help students identify features of various shapes and the relationship that exists among these features. Being able to mentally manipulate images and tell what those images represent are important spatial skills. Research has highlighted the relationship between mathematics performance and spatial abilities. This article's…

As much as ever before, mathematics teachers are searching for ways to connect mathematics to real-life scenarios within STEM contexts. As students develop skill in proportional reasoning, they examine graphical representations of linear functions, learn to associate "slope" with "steepness" and rate of change, and develop…

Given a 5-peg by 5-peg geoboard, how many different lengths can be made by stretching a rubber band to form an oblique segment between any two pegs? This investigation requires students to make connections to the Pythagorean theorem, congruence, and combinations. With its use of visual representation and a range of mathematical ideas that can be…

This article describes techniques that can be used to enhance mathematics instruction for English language learners. Using the strategies suggested in this article, such as scaffolding instruction and accommodating their linguistic needs, mathematics teachers can help ELLs both succeed and increase their mathematics achievement. (Contains 3…

The article describes a unit for seventh-grade students, using children's literature to teach visual, auditory, and algebraic patterns. (Contains 7 figures.)