Good Instruction in Mathematics

2020 ◽  
pp. 47-77
Author(s):  
George A. Khachatryan
Keyword(s):  
Mathematics Instruction ◽  
Instructional Methods ◽  
Cognitive Engagement ◽  
Discovery Learning ◽  
Trial And Error ◽  
Mutual Support ◽  
Instructional Programs ◽  
Good Mathematics Instruction ◽  
General Guidance

This chapter applies the lessons of Chapter 1 (which discusses how to identify good instruction) to the case of mathematics. There has been much controversy about what makes for good instruction in mathematics. Nevertheless, scientific and humanistic sources do allow us to paint a picture. Some instructional methods are less guided (such as pure discovery learning) and others more guided (like teacher-led instruction); scientific and humanistic evidence are in agreement that general guidance is needed, but should not come at the expense of student cognitive engagement. The evidence also consistently shows that instruction should emphasize genuine understanding of the underlying reasons for mathematical principles. Skills (such as fluency in computations) are not in opposition to concepts, but rather in mutual support. Solving varied and unexpected problems is essential in good mathematics instruction. Mathematical “rigor” (meaning precision in expression) plays an important role in mathematical thought, but should be carefully balanced with accessibility for children. While such principles give general guidance, knowing them is not enough to create excellent instructional programs: they need to be applied consistently in each moment of each lesson. Getting these details right is challenging, and can only be done through years of trial and error. This helps explain why good instructional traditions in mathematics are so rare.

The neurobiological platform for moral values

Behaviour ◽  
2014 ◽  
Vol 151 (2-3) ◽  
pp. 283-296 ◽  
Author(s):  
Patricia S. Churchland
Keyword(s):  
Prefrontal Cortex ◽  
Social Context ◽  
Negative Reinforcement ◽  
Moral Values ◽  
Social Practices ◽  
Neuroendocrine System ◽  
Trial And Error ◽  
Psychological States ◽  
Human Brains

What we humans call ethics or morality depends on four interlocking brain processes: (1) caring (supported by the neuroendocrine system, and emerging in the young as a function of parental care); (2) learning local social practices and the ways of others — by positive and negative reinforcement, by imitation, by trial and error, by various kinds of conditioning, and by analogy; (3) recognition of others’ psychological states (goals, feelings etc.); (4) problem-solving in a social context. These four broad capacities are not unique to humans, but are probably uniquely developed in human brains by virtue of the expansion of the prefrontal cortex (this formulation is based on Chapter 1 of my book, Braintrust: What neuroscience tells us about morality).

Brief Reports: An Annotated Bibliography of Research on Self-Paced Mathematics Instruction (1965-1976)

1977 ◽  
Vol 8 (2) ◽  
pp. 144-145
Author(s):  
Harold L. Schoen ◽  
Gloria L. Drapac
Keyword(s):  
School Children ◽  
Mathematics Instruction ◽  
Annotated Bibliography ◽  
Instructional Programs ◽  
The Past ◽  
Local Schools ◽  
Individually Guided Education

During the past decade, an increased emphasis has been placed on individualizing the instruction of America's school children. Many educational agencies have published materials to be used in self-paced or individualized instructional programs. They include Individually Prescribed Instruction (IPI), Program for Learning in Accordance with Needs (PLAN), and Individually Guided Education (IGE) among others. Teachers in local schools throughout the country have a lso been involved in writing packets for selfpaced instruction. The aim of all these materials is to allow the student to proceed through the content presented at the pace best for him.

scholarly journals English Teachers Assess Instructional Methods Supporting Knowledge Processes

2018 ◽  
Vol 6 (1) ◽  
pp. 68
Author(s):  
Andreas Zendle
Keyword(s):  
General Education ◽  
Instructional Methods ◽  
English Teachers ◽  
Discovery Learning ◽  
Project Work ◽  
Empirical Examination ◽  
Learning By Teaching ◽  
Knowledge Processes ◽  
Learning Tasks ◽  
English Classroom

Answers to the questions of which instructional methods are suitable for school, which instructional methods should be applied in teaching individual subjects and how instructional methods support the act of learning represent challenges to general education and education in individual subjects. This article focuses on the empirical examination of instructional methods supporting knowledge processes in the act of learning. A survey was conducted in which English teachers evaluated 20 instructional methods in regard to the following knowledge processes: build, process, apply, transfer, assess and integrate. The results of the study demonstrate that certain instructional methods are especially predestined for the English classroom: project work, jigsaw, problem-based learning, learning tasks, learning stations, presentation, learning by teaching, discovery learning, and role-play.

Integrating Manipulatives and Computers in Problem-Solving Experiences

1990 ◽  
Vol 38 (2) ◽  
pp. 8-10
Author(s):  
Sue Brown
Keyword(s):  
Problem Solving ◽  
Group Work ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Good Mathematics Instruction ◽  
K 12

In 1980, the National Council of Teachers of Mathematics stated that “problem solving must be the focus of school mathematics.” In 1989 the Council reaffirmed that belief with the Curriculum and Evaluation Standards for School Mathematics (Standards). Standard 1 for grades K–12 is “Mathematics as Problem Solving.” The Standards also asserts that “a computer should be available in every classroom for demonstration purposes, and every student should have access to a computer for individual and group work.” Also according to the Standards, “manipulative materials are necessary for good mathematics instruction.” In a typical classroom, problem solving may be taught, manipulative materials may be used, or students may be working at a computer. These functions, however, are usually completed as disjoint activities. Integrating these activities is possible, and this article illustrates how it can be done.

scholarly journals PENGGUNAAN EMODUL INTERAKTIF MENGGUNAKAN METODE DISCOVERY LEARNING UNTUK MENINGKATKAN PERFORMA AKADEMIK SISWA PADA MATA PELAJARAN BAHASA INGGRIS DI KELAS X MIPA 7 SMAN 1 GARUT

2021 ◽  
Vol 1 (2) ◽  
pp. 119-129
Author(s):  
RINA AGUSTINA
Keyword(s):  
Student Engagement ◽  
Cognitive Engagement ◽  
Discovery Learning ◽  
Behavioral Engagement ◽  
Past Tense ◽  
Present Perfect

Penelitian ini bertujuan untuk meningkatkan keterlibatan siswa dalam Pembelajaran Bahasa Inggris dengan menggunakan  Emodul Interaktif dengan metode  Discovery learning. Subjek penelitian terdiri dari 32 siswa SMA dengan fokus pada siswa Berprestasi Rendah (LA) dan Berprestasi Tinggi (HA). Penelitian ini merupakan Penelitian Tindakan Kelas (PTK) dengan 3 Siklus. Prosedur penelitian meliputi tahap refleksi, perencanaan pelaksanaan tindakan dan observasi. Behavioral Engagement (BE) Data diperoleh melalui observasi, data lain berupa Psychologycal Engagement (PE) dan Cognitive Engagement (CE) diperoleh melalui angket student engagement berdasarkan Student engagement Instrument (SEI). Hasil penelitian menunjukan bahwa penggunaan E Modul Interaktif dengan metode  Discovery Learning dapat meningkatkan keterlibatan siswa dalam pembelajaran Bahasa Inggris, khususnya pada materi Past Tense vs Present Perfect Tense. Persentase rata-rata semua aspek BE yang diamati pada siswa LA sebelum diberikan perlakuan. Siklus I, Siklus II dan Siklus III masing-masing sebesar 13,7%, 35, 24%, 48,26% dan 64, 24 &%. Sedangkan hasil BE siswa HA sebelum perlakuan diberikan. Siklus I, Siklus II, dan Siklus III masing-masing sebesar 22,2%, 48,97%, 56,6% dan 64,76%. Hasil PE siswa HA sebelum diberikan perlakuan siklus III meningkat dari 3,75%, hasil LA siswa meningkat sebelum diberikan perlakuan terhadap siklus III yaitu 2,94% sedangkan pada siswa HA meningkat 2,95. %.

scholarly journals PENERAPAN METODE DISCOVERY LEARNING UNTUK MENINGKATKAN KEAKTIFAN BELAJAR SISWA PADA MATA PELAJARAN BAHASA INGGRIS KELAS X.IIS.2 SMA NEGERI 3 MUARO JAMBI TAHUN PELAJARAN 2018/2019

2021 ◽  
Vol 1 (1) ◽  
pp. 64-73
Author(s):  
TOMBANG ARIUS BERTUA SINAGA
Keyword(s):  
Student Engagement ◽  
Cognitive Engagement ◽  
Discovery Learning ◽  
Behavioral Engagement ◽  
Past Tense ◽  
Present Perfect

Tujuan penelitian ini adalah untuk meningkatkan keaktifan siswa dalam Pembelajaran Bahasa Inggris dengan menggunakan metode Discovery Learning. Subjek penelitian terdiri dari 32 siswa kelas X.IIS.2 SMA Negeri 3 Muaro Jambi dengan fokus pada siswa Berprestasi Rendah (LA) dan Berprestasi Tinggi (HA). Penelitian ini merupakan Penelitian Tindakan Kelas (PTK) dengan 2 Siklus. Prosedur penelitian meliputi tahap refleksi, perencanaan pelaksanaan tindakan dan observasi. Behavioral Engagement (BE) Data diperoleh melalui observasi, data lain berupa Psychologycal Engagement (PE) dan Cognitive Engagement (CE) diperoleh melalui angket student engagement berdasarkan Student engagement Instrument (SEI). Hasil penelitian menunjukan bahwa penggunaan metode Discovery Learning dapat meningkatkan keaktifan siswa dalam pembelajaran Bahasa Inggris, khususnya pada materi Past Tense vs Present Perfect Tense. Persentase rata-rata semua aspek BE yang diamati pada siswa LA sebelum diberikan perlakuan. Siklus I dan Siklus II masing-masing sebesar 13,7%, 35, 24%, 48,26% dan 64,24%. Sedangkan hasil BE siswa HA sebelum perlakuan diberikan. Siklus Idan Siklus II, masing-masing sebesar 22,2%, 48,97%, 56,6% dan 64,76%. Hasil PE siswa HA sebelum diberikan perlakuan siklus II meningkat dari 3,75%, hasil LA siswa meningkat sebelum diberikan perlakuan terhadap siklus II yaitu 2,94% sedangkan pada siswa HA meningkat 2,95. %.

Mathematics Teachers Assess Instructional Methods Supporting Knowledge Processes

2019 ◽  
Vol 4 (2) ◽  
pp. 76-86
Author(s):  
Andreas M. Zendler ◽  
Cornelia Seitz ◽  
Dieter Klaudt
Keyword(s):  
Mathematics Education ◽  
General Education ◽  
Mathematics Teachers ◽  
Instructional Methods ◽  
Problem Based Learning ◽  
Discovery Learning ◽  
Project Work ◽  
Empirical Examination ◽  
Knowledge Processes ◽  
Learning Tasks

Answers to the questions of which instructional methods are suitable for school, what instructional methods should be applied in teaching individual subjects and how instructional methods support the act of learning represent challenges to general education and education in individual subjects. This article focuses on the empirical examination of instructional methods supporting knowledge processes in the act of learning. A survey was conducted in which mathematics teachers evaluated 20 instructional methods in regard to the following knowledge processes: build, process, apply, transfer, assess and integrate. The results of the study demonstrate that certain instructional methods are especially predestined for mathematics education: problem-based learning, direct instruction, learning at stations, learning tasks, project work and discovery learning

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