Learning recursive functions: A survey

4 - Recursive Enumerability

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Minimization and NP multifunctions

The 2013 curriculum-based integrative thematic learning model is a learning strategy that involves several subjects into a learning theme that uses an interdisciplinary approach to provide meaningful experiences to students in the learning process. The application of this learning model requires adequate infrastructure and mature teacher understanding concepts. Integration and success in this learning model can be seen from the aspect of understanding of the learning model, aspects of the learning strategy, and aspects of the use of media in learning. Because every teacher has their own characteristics in conveying learning to students, in order to achieve learning objectives. Therefore the writer wants to examine more deeply how the application of the 2013 curriculum-based integrative thematic learning model in MIN Yogyakarta II and MI Ma'had Islamy Kotagede Yogyakarta?. This study aims to determine the mastery of integrative thematic learning models, the strategies applied and the media used by teachers in the application of integrative thematic learning models. This research is categorized in the type of field research (Field Research) which is descriptive with qualitative research methods using theories about integrative thematic learning models then proceed to drawing conclusions. The results showed that in general these two institutions had applied the integrative thematic learning model well. The teacher's mastery of the learning model and the methods used by the teacher in linking learning material are already good so that learning becomes a unified and meaningful whole for students. Then the strategies used by the teacher in planning learning activities, preliminary activities, core activities and closing activities are quite diverse and adjusted to the needs and interests of students. The media used have their respective characteristics and are always adapted to the learning material to be taught. Although they have differences in learning strategies and the media used in teaching, however, they have the same goal of achieving success in teaching so that the expected goals can be achieved and provide meaningful experiences to students.

The modern theory of computability is based on the works of Church, Markov and Turing who, starting from quite different models of computation, arrived at the same class of computable functions. The purpose of this paper is the show how the main results of the Church-Markov-Turing theory of computable functions may quickly be derived and understood without recourse to the largely irrelevant theories of recursive functions, Markov algorithms, or Turing machines. We do this by ignoring the problem of what constitutes a computable function and concentrating on the central feature of the Church-Markov-Turing theory: that the set of computable partial functions can be effectively enumerated. In this manner we are led directly to the heart of the theory of computability without having to fuss about what a computable function is.The spirit of this approach is similar to that of [RGRS]. A major difference is that we operate in the context of constructive mathematics in the sense of Bishop [BSH1], so all functions are computable by definition, and the phrase “you can find” implies “by a finite calculation.” In particular ifPis some property, then the statement “for eachmthere isnsuch thatP(m, n)” means that we can construct a (computable) functionθsuch thatP(m, θ(m))for allm. Church's thesis has a different flavor in an environment like this where the notion of a computable function is primitive.One point of such a treatment of Church's thesis is to make available to Bishopstyle constructivists the Markovian counterexamples of Russian constructivism and recursive function theory. The lack of serious candidates for computable functions other than recursive functions makes it quite implausible that a Bishopstyle constructivist could refute Church's thesis, or any consequence of Church's thesis. Hence counterexamples such as Specker's bounded increasing sequence of rational numbers that is eventually bounded away from any given real number [SPEC] may be used, as Brouwerian counterexamples are, as evidence of the unprovability of certain assertions.

<p>One of the goals of mathematics learning is that students are expected to have good understanding mathematics concept abilities. The application of discovery learning model in the process of learning mathematics is one of the learning modelsthat can improve students understanding of mathematics concepts. The learning process uses the discovey learning model so that students can find the concepts of the material being studied and can conclude their own concepts that have been found based on their ability to understand. This research aims to determine that: (1) students understand the mathematics concepts of discovery learning model in effective;(2) students understand the mathematics concepts of conventional learning model in effevtive; (3) the effectiveness of discovery learning model and conventional learning for understanding mathematics concepts, and to know in 11<sup>th</sup> Senior High School at SMA N 1 Gamping. This type of research is an experimental quasi experiment with research design Posttest Only Control Design. The population in this study were students of class XI IPS SMA N 1 Gamping. The sample in this study was class XI IPS 1 as an experimental class and class XI IPS 2 as a control class. The instrument used in the study was the observation sheet of the implementation of learning and the students understanding mathematics concepts test questions. Analysis of the data used is the t-test and the prerequisite test used are normality and homogeneity test. The result showed that using discovery learning model and conventional learning model were effective that students understand the mathematics concepts, and learning using discovery learning model was more effective than conventional learning model when viewed from students understand the mathematics concepts.</p>

The learning model is one of the most important things in the learning and learning process. A good learning model will make students more enthusiastic in learning because the model is interesting and effective. The purpose of this study was to analyze the comparison of learning models of problem based learning and problem solving models with student problem solving on cube and block material on the skill process in elementary schools. The method used in this study is a quantitative method with a comparative type. The population of this study was 72 students from two schools, included 40 women and 32 men as students, were the subjects studied. The instruments used are student process skills observation sheets and learning questionnaire models. Data collection techniques used in this study were questionnaires and observation sheets. The data analysis technique used is purposive sampling. The results of the description can be said that based on the T test it can be said that the problem-solving learning model is superior to the problem-based learning model. From the results of the T test for the learning model of students' science process skills, it can be seen that there are differences in the learning model.

The learning process at SMP N 6 Tualang is not satisfactory due to the relatively low teacher's competence. Therefore it is necessary to improve teacher quality. The improvement made is the ability to use the learning model. One of them is the use of the Contextual Teaching and Learning (CTL) model through In-House Training (IHT) activities. The purpose of this study is to describe and explain how effective the In House Training activities for improving teacher skills in the application of the CTL model. This study involved all teachers of SMP N 6 Tualang. The researcher conducted a pre-survey to find out the learning process in the classroom. Observation, Pre-test and interview techniques were also used to collect data. Each cycle's pre-test and post-test showed better improvement in the teacher's ability to apply this model. The teacher's assessment in designing the lesson plan learning model CTL in cycle 1 shows the average teacher's ability of 75.62% (good), in the second cycle it becomes 90.57% (very good). The results of supervision from 70.05% (good) in cycle 1, to 82.40% (good) in cycle 2, and teachers felt positive benefits from IHT activities. In conclusion, IHT activities were able to improve teacher competence using the CTL learning model.

Reflective thinking is a student's ability to select knowledge that has been owned and stored in its memory to solve every problem it faces to achieve goals. This study aims to improve student learning outcomes by using a reflective learning model in Civics subjects. The subjects of this study were all 21 grade III students. While the object of this research is the results of student learning in Civics subjects with the theme "Rights and Obligations" with the application of a relective learning model. Data collection tools using observation and tests. Previously the learning process was carried out using the lecture method, question and answer, and assignments to students. As for the weaknesses in the learning process, namely the impact on learning understanding, there are misconceptions between teachers and students, a solution is needed to increase student understanding by applying a reflective learning model in Civics learning. It can be concluded that using a reflective learning model in the learning process can improve student learning outcomes when applied to Civics lessons in Class III Subsidized Swakarya Elementary School, Laut Dendang Village.

In this paper we proved that the function class CFRF and its proper subclass CFPRF are respectively the partial recursive functions and primitive recursive functions of context free languages (CFLs). Also we discussed the relation between them and recursive functions defined on other domains. It is indicated that the functions of natural numbers and/or symbol strings (words) are functions of CFLs. Several frequently used primitive recursive functions on words were given, including logical connectives, conditional expressions. Also the powerful operators (bounded maximization and minimization operators) for constructing primitive recursive functions were defined. Two important nontrivial algorithms, the characteristic function of arbitrary CFL and the parse function of CFL sentences were constructed. Based on them, the method for extending or restricting function domain was described.

Computation of recursive functionals using minimal initial segments

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This study aims to determine the increase in student physics learning outcomes, teacher and student activities, the teacher's ability to manage learning, as well as student responses to the application of the Problem Based Learning (PBL) models in Newton's Law material during the learning process. This type of research is Classroom Action Research (CAR). The subjects in this study were class X students of one of senior high school in Pargodungan for the 2020/2021 academic year with a total of 29 students. Data collection instruments that researchers use in research are observation sheets, tests and questionnaires where the three data are analyzed with descriptive statistics. The results showed that (1) the percentage of individual completeness as a whole increased from cycle I to cycle III, namely 69%, 80%, and 94%, and the percentage of classical completeness as a whole also increased, namely 40%, 70%, and 80%; (2) there is an increase in teacher and student activity during the learning process; (3) there was an increase in the teacher's skills in managing learning from the fairly good category with an average of 2.59 to good with an average of 3.4; (4) student responses tended to be positive where 100% of students expressed pleasure in learning using this Constructivism-Problem Based Learning model. From this study it can be concluded that the application of the Problem Based Learning (PBL) Learning Model can improve the physics learning outcomes on Newton’s Law topic.

Background: One of the causes of students' lack of understanding of a concept is teacher-centered learning and a lack of motivation from students in following the learning process. Then we need an innovative learning model that can help students in the learning process. To achieve learning objectives, teachers are required to be able to choose suitable learning models to be applied at an educational level.
 Method: This research was conducted from January 14 to February 14, 2020 using descriptive methods, student learning outcomes are seen through the final value that is seen based on cognitive aspects (LKS), affective and psychomotor and pre-post test scores. Measurement data were analyzed using the t test formula.
 Results: Based on the t test, obtained the results of tcount 1.573 and ttable 2.010, tcount <ttable, the hypothesis (H1) was rejected and (H0) was accepted.
 Conclusion: There is no difference in the learning outcomes of students taught using the Problem Based Learning model and Group Investigation on the material of the human digestive system in class VIII SMP Negeri 7 Ambon, but there is an increase in learning outcomes after teaching and learning using the Problem Based Learning and Group Investigation models so the results of the t-test show that tcount <ttable (1.573 <2.010).

This research paper aims to analyse the role of cognitive processes in language learning from a psycholinguistic perspective. The paper reviews the individual differences in language learning due to cognitive attitude and its role in the cognitive process of individual learning from a psycholinguistic perspective. Quantitative design was selected to review the role of the cognitive process in learning. The analysis approach selected is statistical review which was selected to review the cause-and-effect relationship from the perspective of psycholinguistic learning. 74 students from languages and translation department at Haql College were participated in this paper.The findings of the paper addressed the role of cognitive learning processing to raise the quality of language learning abilities, the cognitive process's role in improving the psycholinguistic learning perspective such as memory, problem-solving solving and attention are related factors that are affecting the cognitive process of psychological learning. The teaching-learning providers will address the implementation of critical factors addressing the cognitive development of the students while language learning strategies. Keywords: Cognitive processes, Language learning, psychological perspective,Cognitive development, Language acquisition, Learning strategies.