Making Meaning of Data Analysis Christine Browning & Gina Garza-Kling Western Michigan University Christine Browning & Gina Garza-Kling Western Michigan University

Two Main Ideas / Using student-generated representations of data to drive discussion. / Using technology-generated representations to extend discussion. / Using student-generated representations of data to drive discussion. / Using technology-generated representations to extend discussion.

Some Numerical Displays / Dot plots / Histograms / Interval lengths / Same interval lengths / Spaces in between intervals / Size of intervals; how many / Other / Dot plots / Histograms / Interval lengths / Same interval lengths / Spaces in between intervals / Size of intervals; how many / Other

Data Analysis and Probability Standard from the NCTM Principles and Standards for School Mathematics / In grades 3-5 all students should- / recognize the differences in representing categorical and numerical data / compare different representations of the same data and evaluate how well each representation shows important aspects of the data. / (NCTM, 176) / In grades 3-5 all students should- / recognize the differences in representing categorical and numerical data / compare different representations of the same data and evaluate how well each representation shows important aspects of the data. / (NCTM, 176)

Student Comments on Creating Their Own Displays for Data / I really like how we made our own types of graphs, and then discussed things about them together as a class. It really helped me learn now to do things correctly, and I learned from my mistakes and my classmates mistakes as well.

/ I have really learned a lot more about graphs and which is better for certain types of problems/data. Allowing us to create the representations and then progress to group feedback/discussion is a great method. I do not really like when teachers show you first. It does not show the teacher what the students may already know and where to go from there.

 I absolutely love the style of teaching in this course. Having us make our own graphs brings so much more conversation to the classroom. More questions come up that I feel would never come to topic had we been given the “ correct ” graph. This brings a deeper understanding to the material because we are learning what not to do as well- or in other words learning from our mistakes in a positive way

Thinking on Technology / Why use technology-generated displays? / When do we use them? / What displays to use? / Why use technology-generated displays? / When do we use them? / What displays to use?

Why? / Activities that engage students in connecting multiple representations (e.g., graphical, numerical, algebraic and verbal), and those that invite students to analyze or create images, visualizations, and simulations provide wide- ranging opportunities for mathematical exploration and sense-making Technology Position Statement (Association of Mathematics Teacher Educators, 2006) / Activities that engage students in connecting multiple representations (e.g., graphical, numerical, algebraic and verbal), and those that invite students to analyze or create images, visualizations, and simulations provide wide- ranging opportunities for mathematical exploration and sense-making Technology Position Statement (Association of Mathematics Teacher Educators, 2006)

When? /

What?

Technology, Pedagogy, & Content Knowledge / TPCK was presented as the interconnection and intersection of content, pedagogy (teaching and student learning), and technology (Margerum-Leys & Marx, 2002; Mishra, & Koehler, 2006; Niess, 2005; Pierson, 2001). / TPCK has, over time, been recast as TPACK, or the total package required for integrating technology, pedagogy, and content knowledge (Niess, 2008; Thompson & Mishra, 2007). / TPCK was presented as the interconnection and intersection of content, pedagogy (teaching and student learning), and technology (Margerum-Leys & Marx, 2002; Mishra, & Koehler, 2006; Niess, 2005; Pierson, 2001). / TPCK has, over time, been recast as TPACK, or the total package required for integrating technology, pedagogy, and content knowledge (Niess, 2008; Thompson & Mishra, 2007).