Received 12 February 2011 Volume 4, Number 2-3, 2011 [614268]

Received 12 February 2011 Volume 4, Number 2-3, 2011
HOW MATHEMATICS TEACHERS DEVELOP THEIR PUPILS ’
SELF-REGULATED LEARNING SKILLS
Iuliana Marchis

Abstract. Self-regulated learning skills are important in mathematical problem solving. The aim
of the paper is to present a research on how ma thematics teachers guide th eir pupils’ mathematical
problem-solving activities in order to increase self-regulation. 62 teachers have filled in a
questionnaire developed for this research. The results are show that more than two third of the
teachers promote the methods of understanding the problem; de velop pupils’ self-efficacy and
self-control. But only one third of the teachers ask pupils to use different strategies for solving a
problem; ask students to explain the solution to their colleagues. In case of unsuccessful problem
solving only one third of the respondents ask pupils to present previous knowledge about the problem or/and recall and try different methods.
Keywords: self-regulated learning, mathematics educa tion, mathematics teacher, developing self-
regulated learning skills, mathematical problem solving.

1. Introduction
Self-regulated learning (SRL) is an academically e ffective form of learning, through which the learner
sets goals and makes plans before starting to l earn; monitors and regulates his/her cognition,
motivation and behaviour during the learning process; and reflects on his/her learning process [9, 10,
16]. Self-regulated learners analyze the task ( understand the problem; identify the given data, the
unknown data and the relations between these data, r ecall prior knowledge related with the problem),
solve the problem (select, apply, and evaluate plan s and strategies, check outcomes and results, revise
and abandon unproductive plans and strategies), and evaluate their performance. Motivational goal-
orientation, self-efficacy, perception of task di fficulty, self-control, self-monitoring, self-judgment,
and self-reaction are important skills of a self-regulat ed learner. These skills are also important for a
successful mathematics problem solving.
Romanian pupils’ self-regulated learning skills ar e around average [6,7]. Secondary school pupils’
(10-15 years old, 5th-8th grades) have low inter est for studying mathematics, low self-efficacy and
high level of anxiety [7]. High-school pupils (14-19 y ears old, 9th-12th grades) also have low interest
for mathematics, low goal-orientation, self-efficacy and self-control, but a high self-judgment [6].
Pupils’ mathematical results are in strong correlation with their interest to study mathematics, their
task analysis and self-control skills, and their task difficulty perception.
There is a need to motivate pupils for learning mathematics and to develop their self-regulated
learning skills. The mathematics teacher h as an important role in this process.
The aim of this research is to study how mathem atics teachers guide their pupils’ mathematical
problem-solving activities in order to develop self-regulation.
2. Developing students’ self-regulated learning skills
In traditional mathematics education the teacher proposes a problem to be solved; shows a method
which should be used; and gives ex ercises to practice solv ing this type of problem [15]. Thus the
student: [anonimizat]’t promote the development of ma thematical thinking, problem solving skills, and
self-regulation learning.

10 Iuliana Marchis

Acta Didactica Napocensia, ISSN 2065-1430 Teachers should be aware that they should use t eaching methods and strategi es which develop pupils’
problem solving and self-regulation learning skills.
Lester t al. [3] during a 12 week intervention in a seventh grade class used a chart with problem-
solving tips to be used by the teacher and the student s. Some of the tips contained in this chart are
related with SRL, for example “be sure to check your work along the way” instruct to self-control. In
this research no substantial differences were ob served between pupils’ activities before and after
instruction because of the intervention’s short time and the alternative use of problem-solving
instruction with regular mathematics teaching.
Pape, Bell & Yetkin [8] reported the results of a one year long intervention of developing pupils’ SRL
skills in a seventh grade class. Du ring the classes students were encouraged to make their solutions
public, to name and describe their strategies, to use multiple representations while solving the
problems. After the intervention period students were more able than previously to communicate
mathematical understanding and justify their math ematical reasoning. A small proportion of students
recognized the relationship between the stra tegies they used and the grades they got.
Samuelsson [13] has studied the impact of three different teaching method, traditional (with mostly
frontal activities at the blackboard), independent work, and problem-solving on seventh grade pupils’
arithmetic and self-regulated learning skills. The results show that students’ self-conception is affected
more with traditional or problem-solving method. This is because with these methods they get
feedback from the teacher and from their colleagues. The interest of the pupils towards mathematics
was the best developed by the problem-solving method.
Gandhi & Varma [2] have showed that the strategic content learning (SCL) approach promotes self-
regulated learning in mathematics of class eight. Students taking part in the experiment gain in task performance, perception of task specific sel f-efficacy, and metacognitive awareness about
mathematical tasks and strategies.
3. Research
3.1. Design of the research
The aim of the research is to study how mathematics teachers guide their pupils in problem solving.
The focus is on that type of guidance which cont ributes to the development of self-regulated learning
skills.
The research was conducted during May-June 2011 in Romania.
A questionnaire was developed as the main tool for collecting the data. The first 4 items are
demographic questions, the next 16 items are relate d with the topic of the research and they are
affirmations which have to be evaluated by the teac hers on a 5-point Likert scale: from 1- not at all
typical for me to 5 – totally describes me. The affi rmations were formulated based on the theory of
SRL and on the previous researches about teach ing methods which develop students’ SRL skills.
Cronbach’s alpha reliability for the test is .0.892.
The questionnaire was anonymously filled in by the respondents. 62 mathematics teachers have
completed the questionnaire, 16.1% of them are male , 83.9% female. As regarding their age, almost
half of the respondents (48.4%) have between 31 and 40 years old, 19.4% between 41 and 50 years
old, 17.7% between 25 and 30 years old (see Figure 1).

How Mathematics teachers develop th eir pupils’ self-regulated skills 11

Volume 4, Number 2-3, 2011 Respondents' age
11%
18%
49%19%3%0%
less than 25
25-30
31-40
41-50
51-60
more than 60

Figure 1. Respondents’ age
One third of the teachers (32.3%) have between 11 and 15 years of teaching experience, 19.4%-19.4%
between 2 and 6 respectively between 7 and 10 year s of experience (for more details see Figure 2).

Respondents' teaching experience
5%19%
19%
33%16%8%less than 2
2-6
7-10
11-15
16-25
more than 25

Figure 2. Respondents’ teaching experience
50% of the respondents are teaching in primary sc hool (grades 1-4, pupils’ age between 6 and 11),
25.8% in secondary school (grades 5-8, pupils’ age between 10 and 15), 4.8% in high-school (grades 9-12(13), pupils’ age between 14 and 19), a nd 19.4% both in secondary and high-school.
3.2. Results
The responses are recorded in Table 1 and Table 2.

Table 1. How teachers’ guide th eir pupils’ during problem solv ing (the header is from 1- not at all typical for me
to 5 – totally describes me, the numbers in the table are representing percentages)
Affirmation 1 2 3 4 5
I ask pupils to read carefully the text of the problem. 0.0 1.6 12.9 14.5 71.0
I ask pupils to reformulate the text of the problem with their
own words. 0.0 11.3 27.4 32.3 29.0
I ask pupils to write down data of the problem and the relations
between these data. 0.0 1.6 21.0 21.0 56.5
I ask pupils to check if all the data are used during the problem
solving. 0.0 3.2 29.0 27.4 40.3
I ask pupils to check, if the solution is correct. 0.0 1.6 19.4 30.6 48.4
I ask pupils to solve the problem using different strategies. 1.6 32.3 30.6 29.0 6.5
I ask pupils to choose the more efficient strategy if the problem
can be solved in different ways. 0.0 8.1 38.7 29.0 24.2
I ask pupils to write down the detailed solution. 0.0 3.2 40.3 32.3 24.2
I ask pupils to explain the used strategy to their colleagues. 0.0 18.1 47.5 27.8 6.6
I ask pupils to explain their strategy while solving the problem 0.0 14.5 35.5 33.9 16.1

12 Iuliana Marchis

Acta Didactica Napocensia, ISSN 2065-1430 Table 2. How teacher reacts if a pupil can’t solve the problem (the header is from 1- not at all typical for me to 5
– totally describes me, the numbers in the table are representing percentages)
Affirmation 1 2 3 4 5
I ask him/her to read again the text of the problem. 0.0 1.6 16.1 22.6 59.7
I ask him/her to tell what is his/her difficulty.. 1.6 3.2 27.4 35.5 32.3
I give him/her ideas, but I don’t give the necessary strategy. 0.0 3.2 17.7 37.1 41.9
I write the solution on the blackboard. 35.5 46.8 11.3 0.0 6.5
I encourage him/her to try more methods. 3.2 11.3 46.8 29.0 9.7
I ask him/her to present previous knowledge about the problem. 1.6 12.9 46.4 24.8 14.3

In the following we add the percentages from colu mn 1 and 2 to obtain the percentage of those
teachers who don’t assume the given affirmation, and we add column 4 and 5 to get the percentage of
those teachers whom typical.
3.3. Discussion
Understanding the problem is one of the most import ant steps of the problem solving. Pupils should
read the text of the problem, identify the contex t of the problem, rephrase the problem in their own
words, write down the given and unknown data, dr aw diagrams and figures to help themselves to
understand better the problem and see the relations betw een these data. Most of the teachers (85.5%)
ask the pupils to read carefully the text of the problem, 77.5% of them guide pupils to write down the data of the problem and the relations between these data, but only 61.3% ask the pupils to reword the
problem (Table 1).
Self-efficacy is student’s judgments about their ability to successfully complete a task, as well as
students’ confidence in his/her skills to perform the task [12]. The questions related with this skill is
about explaining their difficulties in case of an unsuccessful problem solving and evaluating the
correctness of a solution. 79% of the teachers are aware about the importance of checking the
correctness of the solution (Table 1). 67.8% of the teachers are asking their pupils to explain the
difficulties what they have encountered in case of an unsuccessful problem solving (Table 2).
Self-control and self-monitoring are important skills of a self-regulated le arner. While solving
mathematical problems “control has to do with the decisions and actions undertaken in analyzing and
exploring problem conditions, planning courses of action, selecting and organizing strategies,
monitoring actions and progress, checking outcomes and results, evaluating plans and strategies,
revising and abandoning unproductive plans and stra tegies, and reflecting upon all decisions made and
actions taken during the course of working on a proble m.” ([3], p. 4) From Table 1 we conclude that
the percentage of those teachers who ask pupils to check data and outcomes is high: 67.7% of the
teachers ask pupils to check if they have used all the data of the problem, 79% ask to check if the
solution is correct. The percentage of those teachers who ask pupils to use more strategies for solving
a problem is much lower, only 35.5%. A higher percen tage, 53.2% of the teachers ask their pupils to
choose the more efficient strategy if a problem ca n be solved using different strategies. These low
percentages can be explained with the fact that tr aditional mathematics teaching is still widely used in
Romania: the teacher presents a method that giv es problems to practice that method. This is
encouraged by the national tests, where problems are not challenging; they need only to apply
formulas or algorithms [4, 5].
Asking pupils to explain how they solve a problem is important for developing their SRL skills.
Questions as “What (exactly) are you doing? Why ar e you doing it? How does it help you?” ([14], p.
206) help students to reflect on their strategies a nd to verbalize their reasoning. “When thinking is
articulated regularly, patterns of thinking develop th at are iterative. Thinking cannot be articulated
unless students reflect on the problem and the strategi es they use to solve it; articulation, in turn,
increase reflection, which leads to understanding.” ([1], p. 188) The collaborative learning helps
students to develop their self-regulation competencies [11] and gives the opportunity for the pupils to
verbalize their thinking, to explain their reasoning. 50% of the teachers ask pupils to tell how they

How Mathematics teachers develop th eir pupils’ self-regulated skills 13

Volume 4, Number 2-3, 2011 solve the problem and only 34.4% of the teachers guid e students to explain the used strategy to their
colleagues (Table 1).
In case of unsuccessful problem solving there are some steps one can make: reread the problem, recall
previous knowledge, try different methods, search fo r similar worked examples, seek for help, etc.
Only 39.1% of the teachers ask pupils to present pr evious knowledge about the problem and 38.7% to
recall and try different methods.
4. Conclusions, recommendations, future directions of investigations
The results are shown that more than two third of the teachers promote the methods of understanding
the problem; develop pupils’ self-efficacy and self-cont rol. But only one third of the teachers ask
pupils to use different strategies for solving a prob lem; ask students to explain the solution to their
colleagues. In case of unsuccessful problem solving only one third of the respondents ask pupils to
present previous knowledge about the pr oblem; recall and try different methods.
The research limitation is the size of the sample. To get stronger conclusions the research should be
extended to a wider sample. As a future research, it would be interested to study the correlation
between teachers’ problem solving guidance in th e classroom and their pupils’ self-regulation level.
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Author
Iuliana Marchis, Babes-Bolyai University, Cluj-Napoca, Romania.
E-mail: marchis_julianna@yahoo.com
Acknowledgement
This work was supported by CNCSIS – UEFI SCSU, project number PNII – IDEI 2418/2008.