Professional development on assessment for learning and its effect on pre-service teacher’s self-regulated learning

Abstract The purpose of this study was to determine the extent to which professional development on assessment for learning improves pre-service teachers’ self-regulated learning. Helping students develop self-regulation abilities in learning and assessment remains difficult due to the widespread culture of summative assessment in teacher education. A one-group pretest-posttest quasi-experimental research design was utilized to explore the influence of professional development in implementing assessment for learning on pre-service primary mathematics teachers’ self-regulated learning skills. Three mathematics teacher educators who offered the algebra course, as well as their 52 students who attended the course, engaged in a job-embedded, context-specific, and content-based comprehensive professional development and training program on assessment for learning. A paired sample t-test result demonstrated that the self-regulated learning skills of pre-service teachers after the intervention were significantly higher than their self-regulated learning skills before the intervention, and there was a statistically significant mean difference between pre- and post-measurements of each of the achiever levels. Nevertheless, a one-way ANOVA showed that there was no statistically significant mean difference in the self-regulated learning skills across achiever levels after the intervention. This study contributes to our understanding of the influence of enhanced implementations of assessment for learning on students’ self-regulated learning skills.


Background
The development of pre-service teachers as lifelong, self-regulating learners is a desirable consequence of initial teacher education. Initial primary school mathematics teacher education has received attention in recent years due to its importance and influence on children's development (Alex & Roberts, 2019). Preparing a well-qualified beginning primary school mathematics teacher is critical for any country seeking to improve the quality of primary school instruction. Teacher educators' understandings of teaching, learning, and assessment, as well as how they respond to pre-service teachers' questions, dilemmas, and previous experiences, have enormous power to shape and support pre-service teachers in reshaping their previous conceptions of teaching, learning, and assessment, which may or may not reflect best practices of today's teaching and learning practices (DeLuca et al., 2018).
Despite researchers' and teachers' commitment, the crisis in mathematics teaching and learning is growing increasingly dispersed and severe. Mathematics tends to be considered an uninteresting discipline by adolescents and adults (Ferretti et al., 2018). For many years, the mathematics education community has explored the challenges students face with algebra. Different parts of algebraic thinking, regarded as necessary to overcome those obstacles, have been explored by scholars utilizing a number of theoretical frameworks. Based on study results, different approaches to rectifying such challenges have been offered and their efficacy studied (Warren et al., 2016). Nevertheless, because of the abstract nature of the topic and the diversity of symbols employed in the teaching and learning of ideas, methods, and problemsolving strategies, teaching and learning of algebra is challenging in mathematics education (Cousins-Cooper et al., 2017;Ferretti et al., 2018), and this needs to be addressed through alternative approaches that mitigate felt challenges.
Assessment for learning (AfL) is a crucial aspect of classroom teaching and learning practice, and its appropriate implementation can boost students' learning, according to a growing body of research data. Assessment for learning moved to center stage when Black and Wiliam (1998) summarized over 250 research reports related to assessment and learning and concluded that the deliberate use of assessment in the classroom increases learning and improves student success. Thus, implementing professional development on assessment for learning could be seen as an alternative to impacting teachers' practice and ultimately affecting student success.
In light of this, a fundamental requirement for properly implementing an assessment for learning is a sufficient understanding of the learning goals to be attained. Teachers must determine where they wish to lead their pupils, that is, what they need to learn, and students need to know what they know and can do. Only with clear learning goals can teachers determine what information they need to collect, the most appropriate strategies to gather the information, what evidence shows that learning has taken place, what they need to pay attention to, and when gathering information should be a formal process (Ruiz-Primo, 2016). Likewise, they need to provide learners with feedback to help them identify their learning, learning progression, and level.
According to Wiliam and Thompson (2007), assessment for learning can be thought of as a set of techniques that include the following five fundamental strategies: 1. Clarifying and sharing learning intentions and criteria for success; 2. Engineering effective classroom discussions, questions, and learning tasks; 3. Providing feedback that moves learners forward; 4. Activating students as instructional resources for one another; and 5. Activating students as the owners of their own learning (p 15).
In spite of the importance of AfL, researchers and educators agree that teachers' classroom assessment techniques, particularly in AfL, lag behind the current research foundation. The conservative character of school culture and the lack of suitable professional development for teachers in AfL are some of the causes of this gap. Furthermore, despite the fact that AfL is becoming an increasingly important component of effective and successful educational practice at institutions, most practicing instructors have a basic and often superficial grasp of how to appropriately integrate these tactics and practices into their classrooms (Deluca & Volante, 2016). In accordance with this, the implementation of assessment for learning at teacher education colleges and universities in Ethiopia is very poor, and both instructors and their students have demonstrated inadequate understanding and unfavorable attitudes towards assessment for learning (Sintayehu & Ashenafi, 2017;Teklebrhan & Samuel, 2015;Yiheyis & Getachew, 2014).
In relation to this, Darling-Hammond and her colleagues reviewed 35 studies over the last three decades to determine aspects of effective professional development and found seven features of effective professional development. According to Darling-Hammond and her colleagues, professional development is content-driven, incorporates active learning utilizing adult learning, supports collaboration typically in job-embedded contexts, uses models and modeling of effective practice, provides coaching and expert support, offers opportunities for feedback and reflection, and is of sustained duration (Darling-Hammond et al., 2017). Personalized professional development research is still in its early phases. It is vital to study how to design individualized professional development that better supports individual teacher educators' learning experiences, as well as whether this sort of professional development would improve instructional practice (Zhang et al., 2021).
Moreover, teachers develop as professionals as a result of their long-term and day-to-day work, which is why job-embedded learning opportunities should be at the core of all professional development initiatives. Throughout these times, instructors seek assistance from school leaders and peers (Zepeda, 2013). Furthermore, context-specific, job-based, and content-based teacher professional learning is critical for meeting the unique needs of students (and thus teachers) in a variety of settings (Darling-Hammond et al., 2017).
Although the focus on assessment for learning appears to align very well with theories of selfregulated learning and also seems to be the main reason for many researchers' interest in assessment for learning, the actual relationship between assessment for learning and selfregulated learning is an issue of debate (Panadero et al., 2016). Andrade and Heritage (2017) believe that assessment for learning can scaffold the self-regulated learning skills of students, although the link between assessment for learning and self-regulated learning so far, they think, is mostly theoretical. They also argued that practices in assessment for learning, such as providing constructive feedback, by the teacher and by students, help students take control of their own learning.
Besides, teachers and students use effective assessment for learning to articulate learning targets (preparatory phase goal-setting), collect feedback on where students are in relation to those targets (performance phase monitoring), and prompt adjustments to instruction by teachers, as well as changes to learning processes and revision of student work products (appraisal phase adjustments and revisions) (Panadero et al., 2018). In addition, Panadero et al. (2018) argued that when implemented properly, assessment for learning supports students in conceptualizing what they are attempting to learn, how they will know they are learning, and how they will proceed with future steps. These procedures engage students' cognitive and motivational capacities, concentrate them on their learning objectives, and give feedback and suggestions to help them achieve their objectives. In general, assessment for learning can assist students in self-regulating their learning.
As Zimmerman stated, Self-regulated learning refers to how pupils become masters of their own learning processes. Neither a mental capacity nor a performance skill, self-regulation is instead the self-directive process by which learners turn their mental talents into task-related skills in many areas of functioning, such as academics, sports, music, and health. Self-regulation is described as a changeable process rather than as a personal quality that is either present or absent. Even the feeblest learners seek to manage their functioning, but the quality and consistency of their processes are low (Zimmerman, 2015).
Broadly, Interest in students' self-regulated learning as a formal issue arose throughout the 1970s and early 1980s out of wider attempts to research human self-control. Promising investigations of students' use of self-regulatory processes like goal setting, self-reinforcement, selfrecording, and self-instruction in such areas of personal control as eating and task completion have prompted educational researchers and reformers to consider their use by students during academic learning (Zimmerman, 2015). A comparatively modest number of studies, utilizing various techniques, have been conducted in elementary and secondary schools. As Allal (2020) argued, a fundamental task for future study is to merge, in a systematic fashion, two fields of inquiry. The first is quasi-experimental research that permits the identification and estimation of the impacts of various assessment for learning strategies on students' self-regulated learning skills.
As Andrade and Heritage (2017) argued, the relationship between assessment for learning and self-regulated learning is primarily theoretical, and in principle, measures such as providing feedback on progress toward learning goals will help students take charge of their learning. They also argued that teachers can scaffold self-regulated learning by helping students plan, monitor, and evaluate their learning. Setting specific goals for their own learning, as well as selecting useful learning strategies and scheduling regular study times, are all part of the planning process. Monitoring includes students directly attending to whether or not they grasp an assignment, reading passage, or lecture, as well as assessing their progress toward their goals by, for example, self-testing. Evaluation entails reviewing whether or not their goals were fulfilled, as well as the effectiveness of the learning methodologies they utilized.
Moreover, research by Meusen-Beekman et al. (2016) on formative assessment intervention in sixth grade writing assignments revealed that using formative assessment to help students acquire self-regulation was successful for both self-assessment and peer-assessment intervention groups. Additionally, no significant changes in self-regulation, motivation, or self-efficacy were seen between the peer-assessment and self-assessment interventions.
In addition, in his study of factors that influence Self-Regulation Learning of university students, Chalachew found that the improper use of assessment for learning by university lecturers impaired students' ability to self-regulate their learning (Chalachew, 2018). Likewise, in their study of the effect of high-quality assessment for learning on self-regulating in university classrooms, Fisseha and Michael (2016) found that students who were taught using quality assessment for learning strategies on lessons of a general psychology course reported more self-regulating learning than students who were not taught using quality formative assessment on lessons. As a result, the implementation of high-quality assessment for learning contributes to students' increased participation and experience with self-regulating learning, with a magnitude of near-to-high effect size. Zimmerman (2000) also asserted that self-regulation occurs in three cyclical phases. The first step is forethought, during which goals are established, plans are made, and strategies are chosen. The subsequent phase, performance control, comprises procedures that occur during the learning process (e.g., self-monitoring and adjusting strategies). The last step, self-reflection, includes activities such as self-evaluation, adaptive inferences, and reflection that occur following learning or performance.
Besides, classroom assessments that give process and self-regulation level feedback have the potential to be extremely helpful in encouraging both accomplishment and self-regulated learning. Feedback is most beneficial when it is followed by an opportunity for the instructor to make improvements to instruction and/or for students to modify and improve their work. Further, revision by pupils should be done on the learning or assignment on which they received feedback, not the following one. In summary, good feedback provides students with information on which they may take action in order to progress their learning (Andrade & Heritage, 2017).
In summary, Self-Regulated Learning (SRL) can be established through a number of instructional interventions that aid and guide students in employing various self-regulated learning strategies. However, little research has looked at the function of assessment for learning in fostering SRL. Besides, it is argued that the relationship between assessment for learning and co-regulation of learning deserves more empirical study, and research about this relationship needs to be conducted in classrooms (Panadero et al., 2018). Moreover, research that investigates the effects of implementations of assessment for learning on students' self-regulated learning skills before and after intervention is of the utmost importance, especially in Teacher Education institutions. It is equally important to see how continuous professional development contributes to the assessment for learning practices. Therefore, it has become essential to explore the effect of improved implementations of assessment for learning strategies, accorded through continuous professional development, on students' self-regulated learning skills. To this end, this study tried to investigate the effect of assessment for learning on pre-service elementary mathematics teachers' selfregulated learning, especially in the teaching and learning of algebra courses at a teacher education college in Ethiopia and provide empirical evidence. The professional development on assessment for learning was conducted as an intervention for both the teacher educators and the preservice teachers, and the pre-service elementary mathematics teachers who participated in this research were grouped as low, average, and high achievers based on their pre-test scores on an achievement test. Pre-service teachers whose score was below one standard deviation from the mean were categorized as low achievers; those who scored above one standard deviation from the mean were categorized as high achievers; and the remaining pre-service teachers who scored between one standard deviation from the mean were categorized as average achievers.

Objective of the research
The main objective of this research was to examine the effect of a job-embedded, context-specific, and content-based comprehensive professional development in assessment for learning on preservice elementary mathematics teachers' self-regulated learning skills. For this purpose, the following specific research questions were developed: (1) Is there a significant mean difference in the self-regulated learning skills of pre-service elementary mathematics teachers before and after intervention?
(2) Is there a significant mean difference in self-regulated learning skills between each of the achiever levels of pre-service elementary mathematics teachers before and after intervention?
(3) Is there a significant mean difference in self-regulated learning skills among achiever levels of pre-service elementary mathematics teachers after intervention?

Theoretical framework
Various theories of learning guide the teaching and learning of mathematics at different levels.
The abstract nature of algebra and the use of various symbols and the rules for using them correctly make the teaching and learning process challenging. Sociocultural theory helps us see how knowledge is jointly developed in communities of practice and, correspondingly, how meaningful participation may be harmed in unsupportive learning environments (Shepard et al., 2018). Sociocultural theory of learning gives us excellent models for developing collaborative learning activities that let students actively participate in the learning process, assist their teachers in creating an information literacy community of learners where students interact with one another, and assist teachers in understanding ZPD so that students can reach their full developmental potential (Wang, 2016).
The sociocultural theory viewpoint amalgamates the many models of professional development into one single coherent framework that has the predictive and explanatory ability to account for diverse features of teacher development in distinct sociocultural situations. A crucial advantage of Vygotsky's approach to professional development over other models is that it attempts to surface the gap between theory and practice and embraces both the theoretical and practical aspects; it makes connections between theory and practice by explaining the complex mechanisms of learning processes in actual sociocultural contexts. Moreover, it shows the crucial significance of followup support systems in preserving the efficacy of teacher education (Shabani, 2016).
Sociocultural theories have been applied more effectively in teacher education research to increase our knowledge of teachers' learning. Rather than obtaining new information or perspectives that are internal to the individual, sociocultural theories describe teacher growth as transforming involvement in social behaviors that create their professional identities. Although much sociocultural research on mathematics teacher education has focused on analyzing teachers' learning, sociocultural viewpoints may also be utilized to support interventionist research that includes improving classroom practice (Goos, 2013).
As Clark stated, theoreticians believe that SRL predicts better academic achievements and motivation because students develop the adaptive and autonomous learning traits needed for increased involvement in the learning process and eventual success. The theory of assessment for learning is found to be a unifying instructional theory, which guides classroom practices and improves the learning process by develop SRL strategies of learners (Clark, 2012). This research was guided by sociocultural theory as this research involves context-specific, job-embedded, and content-based professional development where mathematics teacher educators and pre-service elementary mathematics teachers were involved in a community of practice in implementing assessment for learning strategies in the teaching and learning of an algebra course.

Research design
Though the professional development was guided by socio-cultural theory, the attempt of this study was to examine the effect of the professional development on assessment for learning on SRL of students. Accordingly, a quantitative research approach was employed to examine the effect of an educational intervention on a group of students in a teacher education college. A quasi-experimental research design with a pre-test and post-test was adopted since the main objective of the research was to examine the effect of the implementation of improved assessment for learning strategies on pre-service teachers' self-regulated learning skills. This quantitative research design helps to examine the effect of the intervention on participants in their natural setting without altering the sections or classrooms in which they are assigned.

Population, participants and sampling techniques
The population of this research was all second-year pre-service elementary mathematics teachers in Amhara regional state. The participants of the study were second-year pre-service elementary mathematics teachers in a teacher education college that was selected randomly using a lottery method from ten Teacher Education Colleges in Amhara regional state. There were three sections of second-year pre-service elementary mathematics teachers in the selected college and the three mathematics teacher educators who were teaching the Fundamental Concepts of Algebra course at the chosen teacher education college took part in the twelve-week professional development program. A total of 52 pre-service elementary mathematics teachers (of whom 18, 17 and 17, were enrolled in Sections 1, 2, and 3, respectively) took part in the study. The pre-service elementary mathematics teachers were enrolled in the college to complete their three-year diploma program to be elementary (grades 5-8) mathematics teachers. The medium of instruction for the courses was English.

The intervention
Three mathematics teacher educators, who were assigned by the college to offer the Fundamental Concepts of Algebra course to pre-service mathematics teachers, participated in a comprehensive professional development (both theoretical and practical) that lasted for twelve weeks. The professional development was designed based on information gathered from the teacher educators through semi-structured interviews about their strengths and gaps, their perceptions of the nature, purpose, strategies, and principles of assessment for learning, as well as the challenges of its implementation. Furthermore, the professional development included information acquired from the three teacher educators' classroom observations and utilizing the classroom observation procedure during the implementation of assessment for learning. The course's teaching module was upgraded to incorporate critical AfL components and integrate learning objectives for each subtopic, as well as summaries of key topics presented in each chapter, extra summary activities for each chapter, and self-check items. The pre-service elementary mathematics teachers were trained in self-assessment, peer assessment, and how to give and receive quality feedback using examples. They were also taught to the importance of understanding definitions in the teaching and learning of algebra. Moreover, pre-service teachers were oriented that making mistakes is natural in the teaching and learning of mathematics in general and that we learn a lot from our errors. Besides, they were taught the importance of asking any question and responding to oral and written questions without getting afraid of making mistakes.
Classroom observation was done once every two weeks to examine the improvement of implementations of assessment for learning techniques and the provision of feedback to mathematics teacher educators who can scaffold the observed self-regulation challenges of pre-service teachers. Feedback was offered to teacher educators on how to enhance the implementation of AfL practices as part of comprehensive professional development. They were given a number of options to help them clarify the learning intentions of the subtopics under discussion and identify potential misconceptions and difficulties with the subtopics. They were also provided support based on research findings and their teaching experiences to design appropriate oral questions and class activities, provide quality and constructive feedback to their students while taking their strengths and gaps into account, and encourage their students to assess themselves. They were also encouraged to observe one another's classes using a classroom observation protocol that allowed them to rate implementations of the five strategies identified beforehand for assessment for learning in a single class session, reflect on each other, and provide feedback and scaffold on possible ways to improve implementations of the AfL strategies as a continued engagement to boost their professional capability and empower pre-service teachers' selfregulated skills.

Instrument used and its psychometric properties
The instrument used to measure pre-service teachers' self-regulated learning skills before and after intervention was an adapted form of the learning strategies section of the Motivated Strategies for Learning Questionnaire (MSLQ) developed by Pintrich et al. (1993). The MSLQ is a selfreport tool that assesses college students' motivational orientations and usage of various learning strategies in a college course. It is recommended that the MSLQ's fifteen different scales be used together or separately. Besides, it is stated that the scales are modular and can be customized to meet the needs of the researcher or educator (Pintrich et al., 1991). The researchers got permission to translate the instrument to Amharic and use it for research purposes by citing it appropriately.
In the study of SRL, the MSLQ appeared to be the most reliable and frequently used instrument (Roth et al., 2016). The MSLQ's learning strategy section has 50 items, with 31 of them pertaining to students' use of various metacognitive and cognitive strategies. The learning strategies section consists of 19 items concerning student management of different resources. The 50 items were translated into Amharic by one of the researchers in collaboration with teacher educators, and they were back translated into English to see if there was a match between the original meaning and the translated one. The congruence of the original items and the adapted items was ensured through face and content validation by experts. The adapted questionnaire was pilot tested on third year pre-service mathematics teachers, and the omega coefficient was found to be 0.924, which shows that the adopted questionnaire is a reliable instrument to measure pre-service teachers' self-regulated learning strategies.

Procedure of data collection
Prior to administering the questionnaire in this study, pre-service teachers were briefed on the purpose of the questionnaire, and the data collection ensured that each of the participant preservice teachers had the option to decline participation in the study if they so desired. Moreover, they were instructed to carefully read each of the statements in the questionnaire before circling what was true for them and were told that there was no correct or wrong answer. The adapted section of the Motivated Strategies for Learning Questionnaire was administered to all second-year pre-service elementary mathematics teachers in the intervention group at the beginning of the semester to gather data about their use of self-regulated learning strategies before the intervention. In addition, the adapted section of the Motivated Strategies for Learning Questionnaire was also administered to those pre-service teachers at the end of the semester.

Data analysis
A paired-sample t-test was used to compare the mean scores of self-regulated learning skills of pre-service elementary mathematics teachers before and after the intervention. The assumptions of the paired sample t-test were checked using SPSS version 20 and were not markedly violated. The normality of pre-and post-measures of SRL of students was tested using skewness and kurtosis, and the data were found to be approximately normally distributed since each of the values is between −1 and 1. Moreover, since the dependent variable, self-regulated learning skills, has seven scales, it can be considered continuous and the observations are independent of one another since the pre-and post-measures of SRL of the pre-service teachers were conducted 12 weeks apart (Tabachnick & Fidell, 2013).
To determine the effect size of the difference between the post-score and pre-score measures of self-regulated learning of pre-service teachers at each achiever level and as a whole group, Cohen's d was used. A one-way ANOVA was also used to compare the mean scores of the three achiever levels' self-regulated learning skills of pre-service elementary mathematics teachers after the intervention. The observations are independent of one another since each pre-service teacher is grouped into only one of the achiever levels. Levene's test of homogeneity of variance, with a p-value of 0.845 for the data before intervention and 0.318 after intervention, shows homogeneity of variance among the three achiever levels.

Results
A paired sample t-test was conducted to determine whether there was a significant mean difference in self-regulated learning skills of each of the achiever levels of pre-service elementary mathematics teachers before and after intervention. In addition, a paired sample t-test was also conducted to determine whether there was a significant mean difference in self-regulated learning skills before and after the intervention of pre-service elementary mathematics teachers in the treatment group as a whole. The results of the paired samples t-test show that measures of low, average and high achiever pre-service elementary mathematics teachers' mean self-regulated learning scores after the intervention were M postlow = 5.3053, SD postlow = .5261; M postave = 5.3274, SD postave = .4634; M posthigh = 5.4243, SD posthigh = .3620 are significantly higher than their corresponding mean pre-intervention self-regulated learning scores M prelow = 4.3737, SD prelow = .7904; t(18) = 4.997, p = .000, d = 1.15; M preave = 4.5653, SD preave = .7542; t(18) = 3.434, p = .003, d = 0.79; and M prehigh = 4.8186, SD prehigh = .8812; t(13) = 2.490, p = .027, d = 0.67 (See Tables 1 and 2).
Moreover, pre-service elementary mathematics teachers' measures of the mean self-regulated learning score after the intervention M post = 5.35, SD post = .458 were found to be significantly higher than their measure of mean pre-intervention self-regulated learning score M pre = 4.56, SD pre = .807; t(51) = 6.338, p = .000, d = 0.88 (See Table 2).
A one-way analysis of variance was also conducted to examine whether there was a significant mean difference in the self-regulated learning skills after the intervention among different achiever levels. The result of the ANOVA revealed that there was no significant mean difference in the mean scores of measures of self-regulated learning skills among achiever levels after the intervention ðF 2; 49 ð Þ ¼ 0:288; p>0:05Þ (see Tables 3 and 4).
The results indicated above demonstrate no significant difference between achiever levels after the intervention, showing that the professional development did not indicate any effect on achiever level groups.

Discussion
The main objective of this research was to see how job-embedded, context-specific, and contentbased comprehensive professional development on assessment for learning in a teacher education college affected pre-service elementary mathematics teachers' self-regulated learning skills in an  algebra course. The findings of the study show that the scores of measures of self-regulated learning of pre-service elementary mathematics teachers after the intervention are significantly higher than their scores of measures of self-regulated learning before the intervention. The large effect size measure of Cohen's d = .88 shows that improving implementations of assessment for learning in elementary mathematics teacher education has a large positive effect in preparing initial mathematics teachers who are able to monitor, guild and evaluate their own learning to become independent learners. Similarly, the self-regulated learning of each of the three achiever levels of pre-service elementary mathematics teachers improved statistically significantly, with lower achievers benefiting more by scoring a large effect size d = 1.15.
The improved implementation of assessment for learning strategies in the teaching and learning of algebra due to the comprehensive professional development helped pre-service elementary mathematics teachers improve their self-regulated learning skills, especially helping lower achievers more than the average achievers, although each of the achiever levels benefited from the intervention. The finding of this study is in agreement with other research findings that showed improved implementations of assessment for learning have a positive impact on students' selfregulated learning compared to comparative groups that were taught the usual way (Fisseha & Michael, 2016;Meusen-Beekman et al., 2016). The result also showed that there was no statistically significant mean difference in their mean scores of measures of SRL skills among the three achiever levels before and after the intervention, although there was a smaller difference in their mean scores of measures of their SRL. This finding is in agreement with the findings of DiFrancesca et al. (2016), who argued that self-report measures of SRL did not correspond with measures of achievements, indicating that these measures should be used with care when investigating SRL skills in college classroom situations.
When discussing each subtopic with their students, the professional development enabled teacher educators to easily clarify the learning objectives of each subtopic to their students in multiple ways, and this helped pre-service teachers set their own goals when discussing each subtopic. Besides, the self-assessment and peer assessment helped pre-service teachers monitor their own learning by evaluating themselves and their peers' progress toward the learning  objectives of the subtopics they were discussing. Moreover, the implementation of improved assessment for learning strategies helped pre-service teachers identify their own gaps and seek help from their peers and their teachers.
It also assisted them in developing successful classroom discussions, questions, and learning exercises that may elicit evidence of learning, identify students' issues and misconceptions, and offer constructive feedback to both individual students and groups, allowing them to progress. Furthermore, the professional development enabled pre-service primary mathematics teachers to comprehend the learning intents of each subtopic, learn from their own and their colleagues' mistakes, and evaluate themselves and their peers. In general, the professional development assisted teacher educators in identifying gaps, difficulties, misconceptions, and strengths in their students and using these to improve teaching and learning. It also encouraged pre-service elementary mathematics teachers to monitor and evaluate their own learning and to learn from the interactions they had with the materials, their teacher, and their classmates.
Furthermore, the summaries included in the book assisted pre-service elementary mathematics teachers in determining whether they had grasped the main ideas of the topics covered in each chapter. Pre-service teachers also used the module to quickly reference what they should expect in each topic. Besides, the training of pre-service teachers on self-assessment and peer assessment offered them an opportunity to learn how to evaluate the work of themselves and their peers based on the learning objectives and how to give and receive quality and constructive feedback and scaffolding.
This study also provided empirical evidence on the effect of a comprehensive, job-embedded, context-specific, and content-based professional program on assessment for learning in the teaching of algebra on pre-service elementary mathematics teachers' self-regulated learning. Besides, this research provided empirical evidence about the effect of improved implementation assessment for learning strategies on the self-regulated learning of low-, average-, and highachieving students. This paper is part of a larger research program and it has its own limitations when presented for a only intervention group design. One limitation of this study is that pre-service teachers were not interviewed about how the improved implementation of assessment for learning affected their self-regulated learning in the algebra course teaching-learning. The research could have been very strong if interviews were conducted to gather additional data about how they received the training about self-assessment and peer assessment and how they thought it benefited them. In addition, the questionnaire is self-report and pre-service teachers may overstate the benefit of the training on their self-regulated learning in the questionnaire. Apart from these the use of only pretestposttest paired comparisons of an intervention group may pose an internal validity threat, but the results are indicative of the provision of empirical evidence on how the intervention brought about changes in self-regulated learning skills and an input for further research.
Implementations of the five strategies for assessment for learning by mathematics teacher educators and pre-service primary mathematics teachers have a positive influence on pre-service teachers' self-regulated learning in the teaching and learning of algebra. There was a positive, significant mean difference in measures of self-regulated learning of pre-service elementary mathematics teachers before and after intervention, following an enhanced implementation of the five strategies for assessment for learning strategies. The teaching-learning module of the algebra was improved, and pre-service teachers were trained on how to use self-assessment and peer assessment. This improved pre-service teachers' awareness of the learning intentions in each subtopic of the course, their collaboration with their friends, their class participation, their learning from their own mistakes, and the evaluation of their own work and their friends' work based on the learning objectives of each subtopic of the course and regulating their own learning accordingly. Activities were also included to help the pre-service teachers self-check their learning.
Professional development on assessment for learning that was embedded in the job, contextspecific, and content-based, as well as follow-up feedback and scaffolding, assisted mathematics teacher educators in successfully implementing assessment for learning in an algebra course, and this helped their students to set their own goals, plan, monitor their own learning, and evaluate their performances in the teaching and learning of algebra. The findings of the study provided mathematics teacher educators, curriculum developers, and policymakers with valuable insight into the need to improve assessment for learning strategy implementations in teacher education colleges. According to the findings, teacher educators should be provided job-embedded, contextspecific, and content-based comprehensive professional development on assessment for learning to improve the implementation of the five assessment for learning strategies and the preparation of initial elementary mathematics teachers who are able to learn independently.
Based on the findings of this study, it is suggested that mathematics teacher educators, principals of teacher education colleges, the Regional Education Bureau, and policymakers work to improve the implementation of assessment for learning in teacher education colleges by providing quality professional development to stack holders. In addition, recommendations for further research include a study on the effect of implementations of assessment for learning strategies in other mathematics courses using a comparison group in teacher education institutions on pre-service teachers' self-regulated learning using qualitative and quantitative data.