Analysing the nature of potentially constructed mathematics classrooms in Finnish teacher guides – the case of Finland

Figures & data

Table 1. The analytical tool of form and function.

Main category	Subcategory	Description of the category
FORM	A. Visual features	Description of how the recurrent activities in the TGs are visualised/actualized or what they exhibit. How and where are the recurrent activities presented? Are they located in the same place each time? How is the activity designed?
	B. Social participants	Description of how the actors are involved and the manner in which they participate. Which students are involved in the recurrent activities and how? What do the teachers do and how are they involved?
FUNCTION	C. Intention	Description of why the recurrent activity might occur or how it should be implemented. The text could include words such as input, purpose, aim, or objectives to refer this subcategory.
	D. Action	Description of how the recurrent activity might occur or how it should be implemented.
	E. Expected outcome	Description of the expected result of the recurrent activity and what it might/should lead to. What should the content and layout of the activity lead to? That is, how are they related to students’ learning? The text could indicate the outcome/result, product, or effect of the activity.
	F. Inferred meaning	Description of how the recurrent activity is relevant to students’ learning. Draw conclusions about the function by reasoning. These could be some kind of derived senses or meanings, which could be either conditional, concrete, or indirect.

Table 2. The merged summary of Games and Playing Activities (Abbreviated GPs).

Form		Function
Visual features	Social participants	Intention	Action	Outcome	Inferred meaning
A heading conveying “Games and Playing Activities” (GPs) is sited on suggested lesson pages and located in the same place within a series (see Figure 1). Each lesson includes 1–8 GPs related to the lesson goals. “The TG offers ideas for activating exercises, games and playing activities, etc., for instance, that suit working in pairs and groups.” (Koivisto, Salonen, Sintonen, Uus-Leponiemi, & Ilmavirta, 2007, p. 5) → (ii) (iii) (v)	“ … the child needs help to be actively engaged in a range of experience-based learning experiences. Just counting is not enough. TG therefore has many suggestions for different oral and activating exercises.” (Lilli et al., 2011, p. 4) → (ii) (iii) (v) “the teacher [who] select activities for the class” (e.g. Asikainen et al., 2012, p. 4) → (v) “The teacher is to guide pupils to practice tasks according to each pupil’s skills and needs.” (Rikala et al., 2008, p. 5) → (ii) (v) “Working together [in pairs and groups] is fruitful, especially … for example in routine training with the help of games.” (Salonen et al., 2004, p. 4) → (ii) (iii) (v)	The lesson goal is “to amplify the understanding of the concept of fractions and the fact that a fractional number in which the numerator and denominator are the same always means a whole.” (Lilli, Putkonen, Sinnemäki, & Mikkonen, 2012, p. 66) and corresponding to Figure 4. “Tips provide activating ideas for teaching math. The suggestions of GP activities will motivate pupils to study math.” (Asikainen, Nyrhinen, Rokka, & Vehmas, 2012, p. 4) → (i) “Exercises, games and play train the objectives of the lesson or previously learned moments.” (Lilli, Putkonen, Sinnemäki, & Mikkonen, 2011, p. 7) → (iv) “Activating lessons reflect either the lessons learned or represents the basics of the future, learning math, in the form of games and play.” (Asikainen et al., 2012, p. 4) → (iv)	“It is worthwhile to bravely try different working methods during math lessons.” (Koivisto, Salonen, Sintonen, Uus-Leponiemi, & Ilmavirta, 2007, p. 5) → (ii) (v) 1 out of 6 offered GPs: “1. Memory Stick Cards (Appendix 5b). The cards in the attachment are cut off. Cards are spread on the desk. Pupils can collect pairs (for example, 10 mm and 1 cm), either alone or in pairs, when the cards are facing up or, as in the memory game, facing down.” (Asikainen, Nyrhinen, Rokka, & Vehmas, 2012, p. 208) → (ii) (v) GPs are quite explicitly described, as shown in the sequence play below. “A counting game. Pupils sit in a circle. There might be two circles instead in a larger class. The numbers 1–10 are counted going around the circle. After reaching 10, the counting starts again from the beginning, number 1. The pupil who says 10 sits down. The game continues until only one pupil is standing. The game is to be repeated by counting the numbers backwards from 10 to 1. Then the pupil who says 1 sits down.” (Rikala, Sintonen, & Uus-Leponiemi, 2008, p. 17). → (ii) (iii) (v)	“The focus areas in teaching mathematics besides computational skills are also, e.g. collaborative skills, communication skills, games, and playing activities” (Lilli, Ranta, Putkonen, & Sinnemäki, 2011, p. 7) → (ii) (iii) “ … through different senses and by being actively engaged … the child will experience learning.” (Salonen, Sintonen, & Uus-Leponiemi, 2004, p. 4) → (ii) (v) “Pupils can participate in songs by clapping and playing, making it easier to learn and memorize things.” (Haapaniemi, Mörsky, Tikkanen, Vehmas, & Voima, 2012, p. 5) → (i) (v)	Our analysis shows at least five key features: (i) motivating and stimulating students’ learning (ii) offering variety in teaching (iii) offering all students the opportunity to communicate mathematics (iv) creating a common ground for further teaching (v) activating teachers and students → The bold key features are the same features that emerged within all the five activity types.

Figure 1. An example of a suggestion for a mathematics lesson in a teacher guide (Lilli et al., 2012, pp. 50–51, reproduced with permission).

Figure 2. Strategies for computing decimal numbers in addition and subtraction (p. 78, reproduced with permission).

Figure 3. A typical homework assignment. (Lilli et al., 2011, p. 41, reproduced with permission).

Figure 4. A game about fractions played in pairs. (Salonen et al., 2004, p. 119, reproduced with permission).

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