Season-may Conklin's List: MARKERS

Hands on Fractions in both literature and activities supports the value of a physical approach to fraction exploration and similar to the FD1 reading Mills (2011) illustrates the benefits of concrete materials when used to assist students’ to understand mathematical concepts. The Foundation statement in the syllabus (2007) also supports and promotes real life applications stating ‘students are introduced to the concept of fraction through everyday experiences’ (p. 40).

The activities presented in Hands on Fractions use iteration concrete manipulates similar to those presented in Van De Walle which focus children on the numerator and the denominator when counting or repeating fractions to make a whole (2010, pp. 294-295). These activities are suitable for children to achieve NS1.4, NS2.4 and NS3.4 within the NSW K-6 mathematics syllabus (2007, p. 20).

The National Council for Teaching Mathematics (NCTM) illuminations Body Measurement sequence lessons support the ‘value of relating difficult concepts, especially abstract concepts, to students real-world experiences’ (Weinberg, 2001) as seen in M2. Throughout the NCTM lesson students use alternative materials for measurement (string, paper), estimation skills, analyze the measurements for relationships such as equal to, twice the length, half the length and one half times the length, as well as discuss and compare their data with the class (NCTM, n.d.). The provided lesson assists students in achieving MS1.1-MS2.1 as well as WMS3.1 through analyzing and questioning their results (Syllabus, 2007, pp. 19-23). For example: the NCTM illumination lesson also provides the teacher with questions that can extend students investigations into measurement which is also visible in Weinberg (2001). Weinberg discusses the importance of encouraging children to identify the ‘comparisons of standard and nonstandard measurements’. Van De Walle et al. also supports this notion through the length comparison activities supplied where students ‘use a variety of nonstandard units to begin measuring length’ shifting students attention from understanding measurement using units, to the procedure or process (2010, p. 374).

‘1. Very little probability taught in schools, 2. Teachers not prepared or educated to teach probability and statistics, 3. Probability and statistics being difficult concepts for students to understand, and 4. Students beliefs and attitudes toward statistics and probability’ (Barnes, 1998, p. 1). Both Barnes in S2 reading and Hea-Jin (1999) concentrate, inform, and discuss these main issues behind the misconceptions encountered with probability and statistics education.
‘Educators have been endeavouring to overcome the identified barriers to improving the teaching and learning of probability and statistics’ (Hea-Jin, 1999).
Eric Digest introduces recommendations for both the curriculum and teachers to overcome the barriers and obstacles often encountered when approaching probability in the classroom; ‘Promote increased awareness of the importance of probability and statistics in the curriculum’, and ‘confront students and teachers beliefs and concerns about probability and statistics’ (n.d.). Van De Walle et al. introduces characteristics that mathematics teachers need to endorse for continually professional development. If teachers continually develop ‘knowledge of the Mathematics’ (content), ‘persistence’, ‘positive attitude’, ‘readiness for change’ and reflective disposition’, they may be able to overcome with the common misconceptions related to probability and statistics (2010, pp. 80).

Aligning with the literature provided in SG2 Mildenhall, Swan, Northcote and Marshall (2008) Teaching Education Resources (TES) is a website that provides ‘a virtual representation of a physical manipulative’ (a battleship game on the IWB) through which ‘various dynamic processes may help develop mathematical conceptual understanding’ (p. 1).
As children engage with the virtual manipulative TES battleships, the resource is promoting thinking and assists students to ‘grapple with abstract mathematical ideas’ through applying them in a relevant context, move the learner from a ‘visual level of thinking to thinking through informal deduction and reasoning’, and classroom management can be better facilitated (2008, p. 2-4).
Whilst participating in TES battleships, students’ are achieving SGS3.2-3.3 ‘developing their representation of position through precise language and the use of grids and compass directions’ (syllabus, 2007, p. 189). A multiple of the activities presented in Van De Walle et al. (2020, pp. 218-219) could be adapted into the form of an IWB resource to reap the benefits previously discussed for example the Geoboard.

Sir Cumference and all the King’s ten is a great book resource that promotes the idea of enhancing children’s understanding of mathematical concepts through contextualizing mathematics learning in the form of a narrative (Neuschwander, n.d.).
Sir Cumference and all the King’s ten provides a clear explanation and resource example of the main issue contemplated in Pramling & Samuelsson, ‘Can play and learning be integrated in a goal-directed praxis?’ (2008). As children engage with the Sir Cumference literature and physically act out the story, they are developing basic understanding for place value which provides the foundation for learning number. Van De Walle, Karp and Bay-Williams also support this view explaining ‘children’s literature is a rich source of problems at al levels, not just primary’, encouraging children to be ‘more enthusiastic and more likely to see mathematics as a tool for exploring the world’ (2010, p. 38). Van De Walle et al. also provides examples of popular children’s book that have been used to enhance problem solving, as well as links to children’s literature at the end of each chapter that focus on important mathematical concepts within all the syllabus (2007, p. 4) strands that a teacher can use as a great resource for planning instruction (2010).