Session Information
10 SES 06 B, Professional Identity and Teacher Education (Part 1)
Paper Session to be continued in 10 SES 07 B
Contribution
What do teacher students think influence their own learning of mathematics? Will flipped classroom have the ability to help teacher students develop the understanding of their own learning and then their capability to teach mathematics to youngsters?
Our study was initiated of the fact that Norwegian yearly research among student achievements - including topics in mathematics- shows meagre results among teacher students compared to other occupationgroups of students. Such reports are published in Norwegian media every second year and cause alarm and anxiety.
Our next step was to notice a work pointing to mathematics teaching in many schools in Norway is viewed as very traditional (Alseth et al 2003; Kleve 2007).
We also drew our attention to Skott et al (2011) who showed teachers’ teaching practice is dependent of their own mathematical education. Their conclusion is: Traditional education foster teachers giving traditional teaching.
In an initial and local research at our own university college (Maugesten et Nordbakke 2014, unpublished) the students were – in their own opinion - convinced that they got good results by doing a timeconsuming drill of rather similar tasks and by collegeteachers explaining the mathematic topics in the easiest way possible. The questionary was given to rather few students, so the value of this preliminary conclusion is limited.
With these works in mind, we wanted to try flipped classroom with a group of 28 teacher students (aiming for youngsters grade 5 to 10) to see if the students were able to observe different cognitive ways in their own learning. Our main research question was: What do teacher students think influence their own learning of mathematics? Will flipped classroom have the ability to help teacher students develop the understanding of their own learning and then their capability to teach mathematics to youngsters?
What do the teacher students see as of importance in their own learning of mathematics? We chose flipped classroom in two themes: fractions and algebra with 22 lessons on campus and the same amount of time estimated off campus. Off campus the students got a detailed scheme with targets, short films in addition to different types of tasks (traditional and inquiery). Articles of both mathematical and didactical character were also added to their homework. On campus the students were prepared and was given time to discuss and explain to each other different concepts and problems in their homework.
Theoretical framework:
The theoretical framework is divided: one part about possibilities in flipped classroom and one about mathematical learning and organizing/preparing for learning.
Flipped classroom is defined as «…a specific type of blended learning design that uses technology to move lectures outside the classroom and uses learning activities to move practice with concepts inside the classroom.» (Strayer 2012, s. 171). Another study, Ford (2014), tells about meaningful and reflecting discussions on campus instead of the earlier situations where priority activities was doing tasks and focusing on rules.
Different studies in a variety of subjects show teaching factors being important to get better results.
In higher education Bransford et al (2000) focuse on three principles relevant for our research question: Activating previous knowledge, making knowledge bases with understanding as a main principle and third activating metacognition. The mathematical knowledge for teaching(Ball et al 2008 ), were in focus when we prepared the themes fractions and algebra for our students . This is described further in our study.
Brown (1997) lifts the difference between surface knowledge and a deeper understanding. An understanding and use of this insight is of importance and helps students see relations in mathematics.
Method
Expected Outcomes
References
Ball, Deborah Loewenberg, Thames, Mark Hoover & Phelps, Geoffrey (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 59(5), 389-407. Boaler, Jo & Greeno, James G. (2000). Identity, Agency an Knowing in Mathematics Worlds. In J. Boaler (red.), Multiple perspektives on Mathematics Teaching and Learning (pp. 171 – 200). Westport: Ablex Publishing. Brown, George (1997). Assessing Student Learning in Higher Education. London and New York: Routledge. Ford, Pari (2014). Flipping a Math Content Course for Pre-Service Elementary School Teachers. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies. Gannod, Gerald C., Burge, Janet E. & Helmick, Michael T. (2008). Using the inverted classroom to teach software engineering. ICSE '08 Proceedings of the 30th international conference on Software engineering, New York, 777-786. Hiebert, James, Carpenter, Thomas P., Fennema, Elizabeth, Fuson, Karen C., Wearne, Diana, Murray, Hanlie, . . . Human, Piet (1997). Making sense. Teaching and learning mathematics with understanding. USA: University of Wisconsin Foundation. Hiebert, James, Morris, Anne K., Berk, Dawn & Jansen, Amanda (2007). Preparing teachers to learn from teaching. Journal of Teacher Education, 58(1), 47-61. Hill, Heather C., Ball, Deborah Loewenberg & Schilling, Stephen G. (2008). Unpacking "pedagogical content knowledge": Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students. Journal for Research in Mathematics Education, 39(4), 372-400. Kilpatrick, Jeremy, Swafford, Jane & Findell, Bradford (2001). Adding it up. Helping children learn mathematics.: National Research Council. Lage, Maureen J., Platt, Glenn J. & Treglia, Michael (2000). Inverting the Classroom: A Gateway to Creating an Inclusive Learning Environment. The Journal of Economic Education, 31(1), 30-43. McGivney-Burelle, Jean & Xue, Fei (2013). Flipping Calculus. PRIMUS: Problems, Resources,and Issues in Mathematics Undergraduate Studies, 23(5), 477-486. Naalsund, Margrethe (2012). Why is algebra so difficult? A study of Norwegian lower secondary students' algebraic proficiency. (Doktoravhandling). NCTM (2014). Principles to actions. Insuring mathematical success for all. National Council of Teachers of Mathematics. Skemp, Richard R. (1976). Relational Understanding and Instrumental Understanding. Mathematics Teaching, 77, 20-26. Skott, Jeppe, Larsen, Dorte Moeskjær & Østergaard, Camilla Hellsten (2011). From beliefs to patterns of participation – shifting the research perspective on teachers. Nordic Studies in Mathematics Education, 16(1-2), 29 – 55. Strayer, Jeremy F. (2012). How learning in an inverted classroom influences cooperation, innovation and task orientation. Learning Environ Res, 15, 171–193. Talbert, Robert (2014). Inverting the Linear Algebra Classroom. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 24(5), 361-374.
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