![]() Desmos ActivityBuilder offers a collection of professionally developed mathematics tasks and allows teachers to copy and edit activities as well as create new activities (Desmos, 2020c Seaton, 2020). Desmos has evolved over the years, developing a teaching activity tool separate from the geometry and graphing calculator tool. In 2011, an undergraduate Yale student Eli Luberoff released Desmos as a free online graphing calculator. Additionally, showing student work and process is more difficult when using the physical balances in the classroom. Teaching preservice teachers to use a balance may be a useful task, but it is time-consuming when it is not the focus of the lesson. The balancing tasks with physical scales are more challenging, however, because teachers may not have enough balances to distribute among the groups of students. The logistics of the leveling out tasks are relatively straightforward in class: passing out physical blocks, students build and change configurations, and final solutions are easily shared using a document camera. In-Person Leveling Out and Balance of Weights Tasks: Advantages and Disadvantagesīeckmann's (2018)’s leveling out and balance of weights tasks were adapted and implemented in Desmos during the pandemic to support learning at a distance. GAISE argued that moving students from viewing the arithmetic mean as fair sharing to balancing the more abstract deviations supports students in later understanding of center and variation. The mean (balance point) is the value where the sums of positive and negative deviations are equal. When a data point is greater than or less than the mean, the distance is called positive or negative deviation, respectively. After physically or visually finding the balance point, students begin calculating and summing deviations (distance between data point and mean). To build on this understanding, the focus shifts to viewing the mean as the balance point of values viewed as weights along a rod. PSTsĮxperiment by leveling or redistributing physical or visual block towers (Beckmann, 2018). To understand the meaning of fair sharing (or redistribution or a leveling out) of values in a data set, students combine and then redistribute values of all elements so each is equal. posited students must first understand finding mean as fair sharing and then as a balance of weights, to move toward understanding it as a point where positive and negative deviations sum to zero. The arithmetic mean is calculated by dividing the sum of all data values by the number of values in the data set. ![]() The Guidelines for Assessment and Instruction in Statistics Education ( GAISE, 2016) report described levels of conceptual understanding needed to develop a robust understanding of the mean (Franklin et al., 2007). Other organizations echo the recommendations for K-12 teachers’ statistical understanding (e.g., Association of Mathematics Teacher Educators, 2017 Conference Board of Mathematical Sciences, 2012). ![]() The American Statistical Association (ASA) and the National Council of Teachers of Mathematics (NCTM) advocate for high-quality statistics education for in-service and pre-service teachers (PSTs) to develop statistical reasoning skills in K-12 students (ASA & NCTM, 2013). We use Desmos to focus on the conceptual meanings of mean, to enact a set of related tasks from Beckmann (2018). In this paper, we share how we transformed in-person interactive mean tasks to be online, interactive, and supportive of productive mathematical discussions. ![]() In class, their strategies and explanations can be easily shared to support the group and whole class discussion of concepts. Desmos ActivityBuilder saves its solutions and reflections automatically. Before class, students interact with manipulatives and then write out their noticings and wonderings in response to the task. Since going back to teaching in-person, we have used Desmos ActivityBuilder to support out-of-class tasks and reflections, and in-class discussions. To illustrate, in this paper we have chosen one tool and one topic: Desmos ActivityBuilder and a central tendency measure, mean. We plan to build on and integrate our new knowledge and tools to improve our future teaching. Over the past year as we quickly changed teaching formats, we learned to be flexible with lesson planning and delivery. Using Desmos to Support Visualizing and Interpreting Mean
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