Production failure (PF)
Promote students' conceptual knowledge by delaying teaching until after problem solving.
While PF has been well investigated among middle and high school students, little is known about its effectiveness among young students.
Studies that implemented a delay instruction design similar to the one used in the PF study in young samples showed mixed results.
However, these studies do not implement two core design components of PF :(1)
Compare and compare students
Solutions and specification solutions generated during the teaching phase (
Contrast activities), and (2)
Students combine in the initial questionssolving phase.
Both components are expected to contribute to the effectiveness of PF. In a quasi-
In the experimental study of 228 fifth-grade students, we implemented the first component (
All students must determine that in this case, solving problems before teaching is more effective in acquiring conceptual knowledge for young students than in direct teaching (i. e.
, Solve problems after guidance).
In addition, we tested the effect of the second component (
Solve individual problems)
The number of conceptual knowledge and solutions generated by students in the initial problem solving process.
We did not find any empirical support for one hypothesis.
In order to explore the extent to which the student's collaboration has truly fulfilled its potential and is relevant to the student's conceptual knowledge and solution ideas in PF, we analyzed the collaboration process.
Our study increased the mixed results of the advantages of solving problems before guiding young students, thus opening up a discussion about age --
As a relevant prerequisite for PF boundary conditions.
According to so-
Called production failure (PF)
Methods or methods of invention, students who solve problems before receiving teaching gain more conceptual knowledge than students who receive teaching first and then solve problems (so-
Direct directive act (DI).
Conceptual knowledge is defined as an understanding of the basic principles and structures of a domain (e. g.
, Why is the score of 1/5 smaller than the score of fraction, even if 2 is less than 5).
The effectiveness of these methods has been demonstrated in different fields and samples.
PF and caption methods are similar to each other in the order of the learning phase: solve the problem first, and then guide.
However, they differ in the implementation of the learning phase: the method of invention includes comparative cases in the problem --
The solution phase, while PF includes typical student solutions during the teaching phase.
Next, we will focus on the PF approach.
In the original question
In the resolution phase of PF, students usually work in groups.
They worked together to solve an unknown and complex problem.
The complexity of the problem lies in the interaction between the features of the problem and the learners (see also).
The learner who is most often concerned is characterized by the student's prior knowledge.
In PF, the students have not yet been formally introduced into the target concept, but haveconcepts (cf. ).
This means that they do not have enough prior knowledge to successfully solve the problem at hand, thus generating incomplete and erroneous solutions.
Regarding the features of the problem, in PF the given problem allows the student to generate and evaluate the idea of the solution.
In the subsequent teaching phase, teachers compare and contrast students' incomplete solution ideas and standardized solutions (i. e. , instructor-
Led contrast activity).
Three interrelated learning machines are mainly discussed to explain the effectiveness of PF methods: in the process of solving problems, students activate and distinguish their prior knowledge (mechanism 1).
At these two stages, students are aware of their knowledge gaps (mechanism 2)
And identify the deep features of the target domain (mechanism 3).
Overall, PF was well investigated among high school students, middle school students and college students aged 13 to 19.
However, little is known about PF's effectiveness for young students around primary school age (
Usually ranging from 6 to 12 years).
Some studies implemented a design similar to PF with a sample of primary school age.
These studies are comparable to PF in terms of teaching delay time (i. e.
Core Design components of PF)
The overall structure of teaching design (
Problem solving before teaching)
Typical control conditions (
Problem solving after guidance)
Measurement of learning outcomes (i. e.
Knowledge of concepts).
The results of these studies on conceptual knowledge acquisition for young students are mixed: only one study found that delayed teaching was more effective.
Primary school students who solve mathematical equivalence problems before teaching perform better than students who solve problems after teaching in conceptual knowledge.
However, this finding is not replicated in the above-mentioned other studies with young samples.
Although PF has commonalities with the research of older students and the study of young students using a design similar to PF, we found two core design differences, this may explain why young students do not always benefit from problem solving before teaching: the form of teaching at the teaching stage (i. e.
Activities without comparison and comparison)
, And the social form of learning during the problem --solving phase (i. e.
, Personal rather than collaborative problem solving).
Therefore, our primary research question is as follows: the beneficial effect of delaying teaching after the problem --
If other elements of PF design are used, solve the transfer to young students?
Comparison and comparison activities: Although a key design part of the PF teaching stage lies in the instructor-
Comparison and comparison between incomplete students
The generated solution ideas and standardized solutions, which were not used in previous studies designing young students similar to PF.
However, it is well known that teaching through comparison and comparison activities leads to higher student learning outcomes compared to teaching without such activities.
In a recent review, Loibl and colleagues stressed that solving problems before school is effective only if different solutions are allowed to be compared and compared.
The authors believe that such activities may trigger students' awareness of the knowledge gap and help them identify and focus on the deep features of the target area (cf.
PF learning mechanisms 2 and 3).
Due to their low cognitive ability, it may be more challenging for young students to focus on and focus on these related deep features without support.
Therefore, it may be particularly important for these students to compare and contrast activities.
Therefore, in this study, we have adopted an experimental design to realize-
Compare and contrast activities with Led and check (delayed)
Instruction time (i. e. PF vs. DI)
Sample of young students under these "improvement conditions.
To be more precise, we assume to solve the problem with the instructor --
Led contrast activities (i. e. , PF)
Compared to the teacher's problem-solving teaching, this will lead to higher conceptual knowledge for young students
Led contrast activities (Hypothesis 1).
Social form of learning
Collaboration and individual learning in problem solving: PF-
The type of study conducted for young and older students involves the form of social learning during the initial problemsolving phase.
Compared to most PF studies conducted with older students, the young students in the above study did not attempt to solve the problem in groups, but worked alone (
Or with the experimenter).
Although this has not been systematically studied in the PF literature, student collaboration is considered to be an important component of PF as it is intended to facilitate the activation and division of students' prior knowledge (cf.
PF learning mechanism 1).
In the process of solving problems in cooperation, students stimulate solutions to each other.
The process is generated by mutual interpretation, discussion and questioning of different solutions ideas and their constraints and implications.
As a result, teams may generate more solutions than individuals.
Research shows that the collaborative generation and discussion of solution ideas trigger detailed processes, suchself-)
Explain and feel
Both groups of processes are known to support students' conceptual knowledge acquisition (
Through constructive interaction with learning materials).
In this context, in this study, we have further studied (individual vs. collaborative)
During the problem
We expect to find higher concept learning among students in a collaborative PF environment than students in a separate PF environment (Hypothesis 2).
In addition, we assume that students in a cooperative learning environment will generate more solution ideas in the initial problems
The solution stage of PF is more than the solution stage in a single setting (Hypothesis 3).
In this study, in order to verify the above assumptions, we conducted a quasi-
Experimental study of 2 × 2 design, change the factor time of the instruction (i. e.
Problem solving before guidance, PF and
Problem solving after instruction, DI)
Social learning forms in the process of problem solving (
This leads to the following four experimental conditions: PF-Coll, PF-Ind, DI-Coll, and DI-Ind.
Instruction includes a lecturer-
Led comparison and contrast activities are the same under all conditions.
Students learned equivalent scores and were asked about their prior mathematical knowledge in pre-tests and conceptual knowledge about equivalent scores in post-tests (
See the methods section for more details).