I had a great time at PMENA-37 this past weekend! What a supportive, engaging, and productive space for learning about mathematics education – rather, immersing oneself into the mathematics education community.
Friday afternoon, I presented my poster, “Digital resources in mathematics: Teachers’ conceptions and noticing” and I learned a lot through conversations I had with visitors to my poster. You can read the overview of this poster in PMENA-37 Proceedings (p. 1256).
This poster represents a moment in time in my dissertation study. I am beginning to look at what teachers notice (or paid attention to, or found important) in online tools and resources by first considering how they responded in our pre- and post-evaluations in the online master’s-level course “Learning Mathematics with Technology.” We (the instructor and I, as a teaching assistant) gave students a broad prompt:
Assume you are considering using these tech tools in your teaching. Evaluate the three tools to decide whether you would recommend using them. Write an evaluation of the three tech tools for an audience of other teachers who might be considering using them. Make your recommendation clear: which (if any) would you recommend? Argue your position. You will need to decide which elements, features, or characteristics of each tech tool to use in supporting your argument.
I considered the teachers in my study who chose the addition set of tools, and as I read and re-read their evaluations I created a list of tool features that the teachers paid attention to: Purpose of tool; Classroom use; Understanding (e.g., instrumental, relational); Thinking (e.g., critical, level); Engaging / Aesthetically pleasing / Distractions; Directions and Instructions; Customizable; Progress / Tracking; Preparation; Age / Grade-level; Interaction / Manipulative; Feedback / Responsiveness; Ease of Use / Accessibility; Differentiation / Learning styles / Learning needs; CCSSM / Standards Alignment; Mathematical representation; Teacher Support / Resources; Breadth / Variation. These were too many for the poster, so I narrowed them down to 12, and sorted them according to whether they seemed to be general, pedagogical, or mathematical characteristics (but recognizing the overlap in the categories, similar to the TPACK framework):
- General: Customizable; Engaging / Aesthetically pleasing; Ease of Use / Accessibility
- Pedagogical: Differentiation / Learning styles/needs; Progress / Tracking; Feedback / Responsiveness; Teacher Support / Resources
- Mathematical: Mathematical Purpose; Standards Alignment; Understanding / Thinking; Interaction / Manipulative; Mathematical representation
In the tables, I noted whether teachers mentioned a particular characteristic was included or favorable included in the tool (Y), was not included or included in an unfavorable way (N), and whether the teacher did not mention a characteristic (–). Because of the limited space of the poster, I chose three mathematical features to show teacher comments about: Mathematical purpose, Understanding / Thinking, and Interaction / Manipulative. I included comments for each tool from each teacher in the pre-evaluation (left) and the post-evaluation (right).
Discussion of Results (which are shown in the poster above)
It goes without saying that the online tool itself seemed to impact the features that teachers paid attention to and I had chosen the three tools to be different in (hopefully) interesting ways. One tool is built around a ten-frame representation of addition, and includes a symbolic representation (horizontal addition statements). One tool is a quizzing software that includes a symbolic representation (horizontal statement) of addition only. One tool is built around a base-10 blocks representation of addition, and includes a symbolic representation (vertical addition statement). The tools differ in a number of ways and the teachers noticed many of their differences. There is evidence that teachers moved, not just to noticing more characteristics, but also to more profound noticing by the end of the course.
One interesting result was the teachers’ attention to thinking and understanding in the Math Trainer applet. In the pre-evaluation, none of the four teachers commented on opportunities for students to think or develop understanding. In the post-evaluation, all four teachers commented on Math Trainer’s support of instrumental understanding (we read Skemp (1976) early in the course), and on the lack of opportunities to “explore or gain a deeper understanding,” or for “critical thinking.”
Another interesting result is the change in Nicole’s use of words from the pre-evaluation to post-evaluation in her description of the mathematical purpose of each tool. She did not change words at all in her description of Math Trainer’s purpose “to practice math facts,” but changed from practice to explore for NCTM Illuminations: Ten Frame Addition and NLVM: Base Blocks Addition. Her description of the purpose of NCTM Illuminations: Ten Frame Addition in the pre-evaluation was “to practice using a 10-frame to work with numbers” and in the post-evaluation was “to work with a ten-frame (or five-frame option) to explore addition and subtraction of whole numbers.” For NLVM: Base Blocks Addition, she wrote “to practice addition with base-ten blocks” in her pre-evaluation and “to explore addition with base-ten blocks” in her post-evaluation.
PMENA 2015 – Noticing and Technology – Final (pdf of poster)
PMENA 2015 Proceedings – Noticing and Technology (pdf of proceedings paper)