The Effect of Mathematical Habits of Mind and Early Mathematical Ability on Modeling Ability of High School Students

Modeling mathematics serves as a bridge between the processes of translating real-world problems into mathematics. In reality, however, students' mathematical modeling skills, including their knowledge of derivative applications, remain subpar. This study is intended to determine the relationship between mathematical modeling skills, mathematical habits of mind (MHoM), and early mathematical ability (EMA). This research employed a quantitative methodology with mix method sequential explanatory design. The method used a quantitative and qualitative approach. The first quantitative phase is used, then explained more deeply through the qualitative phase. Sample in this study were 36 eleventh-grade students from one of Tasikmalaya's senior high schools. In this investigation, the EMA was the previous semester's math report card grade. A mathematical modeling ability test question and an MHoM questionnaire were administered to students, and the quantitative analysis of the results followed. This study demonstrates that the relationship between MHoM and EMA has a 31.2% modeling capability. In addition, a one-point increase in MHoM and EMA increases the average mathematical modeling ability of pupils by 1,570 and 2,241. Therefore, it can be concluded that MHoM and EMA have a positive effect on mathematical modeling ability

RUANG LIPSCHITZ

ABSTRAK. Diberikan ruang metrik  dan lapangan  (real atau kompleks). Suatu fungsi dikatakan fungsi Lipschitz bernilai skalar jika terdapat konstanta  sedemikian sehingga Ruang Lipschitz  adalah ruang dari semua fungsi Lipschitz terbatas bernilai skalar pada . Didefinisikan penjumlahan dan perkalian skalar pada  dengan aturan                  dan , .Ruang Lipschitz dilengkapi dengan norm Lipschitz yang didefinisikan sebagai.Kajian ini mengkaji sifat-sifat dari fungsi Lipschitz bernilai skalar dan hubungannya  dengan ruang Banach. Kata kunci: fungsi Lipschitz, fungsi Lipschitz bernilai skalar, ruang Lipschitz, ruang Banach, norm Lipschitz. ABSTRACT. Given a metric space  and a field  (real or complex). A function is said to be scalar-valued Lipschitz function if there exists a constant  such that Lipschitz space is the space of all bounded scalar valued Lipschitz function on . Addition and scalar multiplication defined on  with                      and ,  .Lipschitz space equipped with norm Lipschitz which is defined by.This study observes the properties of scalar valued Lipschitz function and its relationship with Banach Space. Keywords: Lipschitz function, scalar valued Lipschitz function, Lipschitz space, Banach space, Lipschitz norm