This week, I explored some new (and old) technologies used to support algebra learning. I have been sharing a lot of what I have learned in my CEP 805 course through these blog posts, but I realized I rarely discuss my background and where my mind is before learning all of the wonderful content in this course. So, before I dive into what I learned, I first want to outline the mindset that I entered this week with.
Algebra is one of my favorite content areas in math for a multitude of reasons. I have had outstanding algebra teachers in my life who have had robust Mathematical Knowledge for Teaching (Hill & Ball, 2009), combining each of the six areas of MKT perfectly to thoroughly teach their students. These teachers made me fall in love with math and lit a spark in me which has grown larger the further I explore the content. Because of my relationship with Algebra content, I have formed specific relationships with the tools I use in algebra learning. I was excited entering this week’s technology exploration because I have always found great use of algebra technologies. While watching a peer’s reflection on the technology “Wolfram Alpha”, I realized that I have a different relationship with certain technologies when they are used in algebra settings than when they are used with other content areas (ex. calculus). With this specific app, I always held a caution around using it with students because I only ever used it in a calculus setting, after spending hours attempting problems to no avail, and resorting to this app to find the right answer. Because I had a very specific connection between this app and my calculus experience, I always assumed other students would use it in the same way and wanted to avoid its use entirely. The narrative changed when I looked at a very similar app, PhotoMath. I had used PhotoMath in my algebra courses, and had positive relationships with it. Even though this app is structured the same as Wolfram Alpha, I used the app to assist in my learning, rather than merely get the right answer for me. It was used in low-stakes environments, with no stress or expectations. My teacher allowed the use of PhotoMath in introductory lessons. We would spend 5-10 minutes attempting to solve a problem before learning the content. We would then spend 5 minutes with the PhotoMath answer, getting acquainted with the process for ourselves, and then would dive into the content and learn what each of the steps in PhotoMath told us. In this way, we used the same type of technology in a way that allowed us to form a positive relationship with it and not abuse it. Looking back on this use, I can see where my teacher had a really developed Knowledge of Content and Students (Hill&Ball, 2009), knowing how we learn, what tools were out there, how we might abuse them, and setting the norm for how they should be used before we have the chance to abuse them. Moving forward with my learning, I want to keep these realizations in mind and address any other biases I may have towards certain technologies before I explore them further. Resources: Hill, H., & Ball, D. L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68–71.
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These last two weeks my mathematical focus switched from exploring measurement to data and probability - which is very exciting and timely for my professional context! I have studied both the content and technological aspects of data and probability, diving into the Common Core State Standards as well as playing around with some pretty neat online tools.
When I look at the data and probability content standards, I notice that this is the math that I actually use in my everyday life and not just because I work with numbers and data sets. Data and probability show up in many aspects of my everyday life, from knowing the probable outcome of sporting games, coin flips, or drawing a card from a deck. The Principles and Standards for School Mathematics (PSSM) for grades 9-12 encompass what many adults should know in order to have logical conversations and make logical decisions. One standard that I think I see often in my professional role is “formulating questions that can be addressed with data and collecting, organizing, and displaying relevant data to answer them” (NCTM, 2000, p. 324). Knowing I use this content often, I explored some technologies I use in conjunction with this content, particularly focusing on expanding my Knowledge of Content and Teaching (Hill & Ball, 2009) by sourcing new technologies that could be used to teach data and probability content to either K-12 students or adult learners. There is an expansive list of resources that could and should be used to strengthen data and probability learning. Because this content is so pertinent to daily life, there are many technologies in various modalities that can support student learning. A website that I explored this week was random.org. This website does a great job of sourcing commonly used data and probability technologies and provides them in a concise list. I think this is a great tool for all learners to have handy and there is large potential for its use in the classroom. Teachers can utilize this resource to support their Knowledge of Content and Students (Hill & Ball, 2009), knowing what content students need to master, how they will best master the content, and finding a support from random.org that can support their mastery. I have also been exploring the incorporation of Teaching Mathematics for Social Justice in data and probability lessons. Mathematics is a difficult subject to incorporate social justice into and, in my experience, it is omitted entirely. I find that teachers focus their social justice efforts in subjects such as ELA or social studies, but data and probability is a wonderful place to teach mathematics for social justice. Issues of social justice can be difficult to incorporate into certain content, like geometry, but an easy way for teachers to start incorporating TMFSJ is by emphasizing that all students can achieve in mathematics regardless of color, size, shape, age, or ability. Creating a classroom culture where all students are encouraged to excel can open doors for other TMFSJ content. References: Common Core State Standards Initiative (CCSSI). (n.d.). Mathematics standards. Mathematics Standards | Common Core State Standards Initiative. http://www.corestandards.org/Math/ National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. The National Council of Teachers of Mathematics. Hill, H., & Ball, D. L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68–71. |
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