Intervention in quantitative reasoning as a possibility to develop arithmetic knowledge

Nogues, Camila Peres; França, Akira Borba Colen; Dorneles, Beatriz Vargas

doi:10.1590/S1678-4634202349254184por

The low performance in mathematical abilities at the beginning of school life can lead to learning problems in the long term. Therefore, we highlight the importance of knowing the basic mathematical abilities that influence specifically the learning of arithmetic, so that it would be possible to indicate interventions focused on performance predicting abilities in this area and help the development of students’ mathematical knowledge, as well as teachers’ practice. In this sense, this study aimed to investigate the effects of an intervention in quantitative reasoning on the arithmetic performance of students from the 4th and 5th Grades of Elementary School. We separated 40 children into experimental and control groups. The experimental group participated in an intervention program focused on quantitative reasoning, organized in 7 sessions, twice a week, lasting 45 minutes each session. The control groups participated in sessions with mathematical games and mindfulness practices. The results indicated that the intervention showed no significant effect when comparing the performance of both groups. However, we found a significant improvement in the performance of 5th Grade students who participated in the experimental groups. The findings of this study help understand efficient instructional principles and highlight the importance of educational practices based on evidence.

Keywords
Intervention in quantitative reasoning; Arithmetic performance; Elementary School

[1] Source: Research data.

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Mean (M) and standard deviation (SD) of ages: Total (M=10.58, SD=0.70); Experimental Group (M=10.58, SD=0.67); Control Group (M=10.57, SD=0.76).

	Total (N=40)	Experimental (N=22)	Control (N=18)
	N (%)	N (%)	N (%)
School-level
4 ^th Grade	19 (47.5)	9 (40.9)	10 (55.6)
5t ^h Grade	21 (52.5)	13 (59.1)	8 (44.4)
Sex
Female	25 (62.5)	13 (59.1)	12 (66.7)
Male	15 (37.5)	9 (40.9)	6 (33.3)
Age 1
9	10 (25.0)	4 (18.2)	6 (33.3)
10	17 (42.5)	12 (54.5)	5 (27.8)
11	12 (30.0)	5 (22.7)	7 (38.9)
12	1 (2.5)	1 (4.6)	0 (0.0)

Session	Description
1 and 2	Additive reasoning Types of situation: Composition; Comparison; Inverse relation between addition and subtraction; Transformation Learning objectives: a) Understand that any number can be composed of other two numbers b) Be able to use logical reasoning to know how to count; c) Understand verbal problems involving addition and subtraction; d) Understand the inverse relationship between addition and subtraction; e) Understand that when adding and subtracting the same number of blocks from a role, the original number of blocks does not change; f) Understand that when removing more blocks than adding, the answer will be “less”; and by removing fewer blocks than adding, the answer will be “more”.
3	Additive and Multiplicative reasoning Types of situation: Composition; Comparison; Inverse relation between addition and subtraction; Transformation; Direct relationship Learning objectives: a) Understand the composition of quantities; b) Understand the inverse relationship between addition and subtraction; c) Understand how to use different forms of counting to solve verbal problems of addition and subtraction; d) Understand the reasoning of one-to-many correspondence, using drawings to understand problem-situation.
4	Additive and Multiplicative reasoning Types of situation: Inverse relation between addition and subtraction; Transformation; Direct relationship Learning objectives: a) Understand the inverse relationship between addition and subtraction; b) Understand verbal problems involving addition and subtraction; c) ) Understand how to use different forms of counting to solve problems; d) Understand the reasoning of one-to-many correspondence.
5	Additive and Multiplicative reasoning Types of situation: Transformation; Direct relationship; Inverse relation; Proportion; Product measures Learning objectives: a) Understand verbal problems involving addition and subtraction b) Understand the reasoning of one-to-many correspondence; c) Understand the inverse relationship between two quantities, that is, that as one amount increases the other decreases; d) Identify the reason among the parts that form a whole from a proportional relation; e) Use counting to solve problem situations by combining possibilities.
6 and 7	Multiplicative reasoning Types of situation: Direct relationship; Inverse relation; Proportion; Product measures Learning objectives: a) Understand the reasoning of one-to-many correspondence; b) Understand the inverse relationship between two quantities, that is, that as one amount increases the other decreases; c) Identify the reason among the parts that form a whole from a proportional relation; d) Use counting to solve problem situations by combining possibilities.

Session	Part 1 – Mindfulness	Part 2 – Mathematical games
1	Do not swallow the candy – Each student received a candy. They were challenged to keep it in their mouths, without swallowing it, for 5 minutes. Objective: develop focus and self-control	To the middle – the aim is to use cards to move all your pieces to the center of the board. Abilities involved: correspondence of number and quantity; identification of quantities.
2	Attention to abdominal breathing – While sitting the students were invited to close their eyes and focus on their abdominal movements while breathing, for 7 minutes. Objective: develop focus and attention, reduce stress and anxiety; increase the ability to block external stimuli	To the middle (same game session 1).
3	Listen to the environment sounds – We invited students to list on paper all the environmental sounds they could perceive at that moment, for 5 minutes. Objective: develop focus and selective attention	Snakes and ladders – the board has snakes and ladders spread following the numerical sequence from 1 to 100. The aim is to be the first one to reach 100. Abilities involved: identification of quantities; addition.
4	Statue – Students had to walk around the class. When the researchers gave them a sign, they had to form groups according to a determined number of students and make a pose also indicated by the researchers. For example, researchers would say “feet with feet, five”. Students had to organize themselves into groups of 5 and touch their feet. This pose had to be kept until a second sign, also given by the researchers, then students could move around the room again. Objective: develop self-control, develop body consciousness, and tolerance to adversities	More is more – the aim is to get rid of your pile of cards. Each card can be discarded if there are more points of the same color than the reference card on top of the center pile. Abilities involved: comparison of quantities; identification of quantities.
5	Body Scan – With their eyes closed, the students should focus on specific body parts, guided by the researchers. Objective: develop body consciousness, reduce stress and anxiety, develop focus and selective attention	Neighbor numbers – the aim is to place different previous and following numbers, correctly creating a numerical sequence and thus discarding their cards as fast as possible. Abilities involved: correspondence of number and quantity; numerical sequence
6	Copy the animal – Each student received a card with a drawing of an animal. Researchers instructed them to look at the picture for two minutes, trying to memorize all the details. After this time, the figure was covered and they were asked to write all they could remember about the picture. After that, they compared their register with the card. Objective: develop focus and attention, work short-time memory, develop self-perception of own abilities	High five – create a numerical sequence from 1 to 10 starting with the number 5. To do so, they have to add one card in the sequence that corresponds to the previous or following number of the one on the table Abilities involved: correspondence of number and quantity; numerical sequence.
7	Do not swallow the candy (same activity as session 1).	Splashing monster – the aim is to establish the maximum number of pairs with the cards and not finish the game with the monster card. Each pair is formed by a number and its representation in quantity. Abilities involved: comparison of quantities; correspondence of number and quantity; identification of quantities.

	Experimental		Control		Comparison
	Mean (SD)	Min. – Max.	Mean (SD)	Min. – Max.	T (df)	p-value
Pre-test	13.1 (2.2)	9 – 16	13.0 (2.5)	8 – 18	0.12 (33.7)	0.90
Post-test	13.8 (2.9)	9 – 18	12.9 (2.3)	8 – 18	1.12 (38)	0.27

	Experimental Group				Control Group
	WD	ND	4 ^th Grade	5 ^th grade	WD	ND	4 ^th Grade	5 ^th grade
N	4	18	9	13	5	13	10	8
Pre-test Mean (SD)	9.7 (1.0)	13.8 (1.6)	12.2 (2.0)	13.7 (2.1)	11.6 (3.4)	13.5 (2.1)	12.3 (2.6)	13.9 (2.4)
Post-test Mean (SD)	9.0 (0.0)	14.9 (1.9)	11.9 (2.5)	15.2 (2.4)	10.2 (1.3)	13.9 (1.7)	12.7 (2.4)	13.1 (2.5)

Intervention in quantitative reasoning as a possibility to develop arithmetic knowledge 1

Intervention in quantitative reasoning as a possibility to develop arithmetic knowledge ¹