Research on the relationship betwee

Research on the relationship between teachers’ mathematical knowledge and students’ achievement supports the importance of teachers’ content knowledge in student learning.
—National Mathematics Advisory Panel (2008, p. xxi)

Research on mathematics teaching suggests that many teachers do not possess the equisite subject-matter knowledge to implement high-quality instruction (Ball, 1990; Ball & Bass, 2000; Ball & Cohen, 1999; Hill, Schilling & Ball, 2004; Ma, 1999; National Commission on Teaching and America’s Future, 1996). The National Mathematics Advisory Panel (2008) underscores the need for teachers to know mathematics for teaching in order to teach effectively:

Teachers must know in detail and from a more advanced perspective the mathematical
content they are responsible for teaching and the connections of that content to
other important mathematics, both prior to and beyond the level they are assigned
to teach. (p. 38)

The logic herein is that teachers who possess strong mathematical knowledge at a greater depth and span are more likely to foster students’ ability to reason, conjecture, and problem-solve, while also being able to more accurately diagnose and address students’ mathematical (mis)conceptions and computational (dys)fluencies (Kilpatrick, Swafford, & Findell, 2001). Two challenges have been associated with ensuring that teachers have the adequate content knowledge to teach mathematics effectively. First, because mathematics education research has been fraught with philosophical differences, defining the content or subject matter that teachers should master has been a matter of some debate (National Council of Teachers of Mathematics, 2006; National Mathematics Advisory Panel, 2008). The National Mathematics Advisory Panel Task Group on Teachers and Teacher Education (Ball, Simons, Wu, Whitehurst, & Yun, 2008) commented, TQ Connection Issue Paper
5 “defining a precise body of mathematical knowledge that would effectively serve teachers and would guide teacher education, professional development, and policy has proved challenging” (2008, p. 5-x). Second, the use of indirect indicators or proxies for teacher knowledge, such as teacher certification, coursework, and teacher licensing exams, rather than more robust and direct measures of teachers’ mathematical knowledge, has made the study of content knowledge and its link to student learning difficult (Hill, Rowan, & Ball, 2005).

Results (Indonesian) 1:

Penelitian tentang hubungan antara pengetahuan matematika guru dan siswa prestasi mendukung pentingnya pengetahuan isi guru belajar.-Matematika national Advisory Panel (2008, p. xxi)Penelitian pada pembelajaran Matematika menunjukkan bahwa banyak guru tidak memiliki pengetahuan subjek-materi equisite untuk melaksanakan instruksi berkualitas tinggi (bola, 1990; Bola & Bass, 2000; Bola & Cohen, 1999; Hill, Schilling & bola, 2004; MA, 1999; Komisi Nasional pengajaran dan Amerika masa depan, 1996). Matematika National Advisory Panel (2008) menggarisbawahi kebutuhan bagi guru untuk tahu matematika untuk mengajar untuk mengajar secara efektif:Guru harus mengetahui secara rinci dan yang lain maju perspektif matematikakonten mereka bertanggung jawab untuk mengajar dan koneksi dari konten yangmatematika penting lainnya, baik sebelum dan melampaui tingkat mereka ditugaskanuntuk mengajar. (ms. 38)Logika di sini adalah bahwa guru-guru yang memiliki pengetahuan matematika yang kuat pada kedalaman lebih besar dan rentang lebih mungkin untuk mengembangkan kemampuan siswa untuk alasan, dugaan, dan memecahkan masalah, sementara juga mampu untuk lebih akurat mendiagnosa dan alamat mahasiswa matematika (mis) konsepsi dan komputasi (dys) fluencies (Kilpatrick, Swafford, & Findell, 2001). Dua tantangan telah dikaitkan dengan memastikan bahwa guru memiliki pengetahuan konten yang memadai untuk mengajar matematika secara efektif. Pertama, karena penelitian pendidikan matematika telah penuh dengan perbedaan filosofis, mendefinisikan isi atau materi pokok yang guru harus menguasai telah masalah beberapa perdebatan (Nasional Dewan guru matematika, 2006; Tingkat Nasional National Mathematics Advisory Panel, 2008). Matematika Advisory Panel tugas kelompok nasional guru dan guru pendidikan (bola, Simons, Wu, Whitehurst, & Yun, 2008) berkomentar, TQ koneksi masalah kertas5 "mendefinisikan tubuh pengetahuan matematika yang secara efektif akan melayani guru dan akan membimbing pendidikan guru, pengembangan profesional dan kebijakan yang tepat telah membuktikan menantang" (2008, p. 5-x). Kedua, penggunaan indikator tidak langsung atau proxy untuk pengetahuan guru, sertifikasi guru, kursus dan ujian lisensi guru, daripada lebih kuat dan langsung langkah-langkah guru matematika pengetahuan, telah membuat studi pengetahuan isi dan link untuk pembelajaran sulit (Hill, Rowan, & bola, 2005).