This quantitative quasi-experimental research aimed to study the effects of Mathematical Investigation as an approach in teaching Algebra to proof writing and problem solving skills and mathematical habits of mind (HoM). Sixty third year high school students coming from two intact classes with 30 students from each class of Philippine Science High School composed the two treatment groups, the traditional (TI) and the mathematical investigation classes (MI). The comparability of the two groups was tested in terms of their pretest scores in problem solving, proof writing, and pre-intervention evaluation of mathematical HoM and further validated by their logical reasoning ability. Conducted from October to December 2011, this research utilized the researcher-made tests in Problem Solving (multiple choice type and habits of the mind problems) and Proof Writing; three different modified standardized rubrics to evaluate answers for tests in proving, problem solving and mathematical (HoM); and the standardized Purdue Non-Language Test. The statistical tools employed were frequency, percentage, mean, mean gain, rank, and standard deviation for descriptive statistics; t-test for independent and dependent/paired samples, Analysis of Variance (ANOVA), Pearson's r, and Multiple Regression Analysis for Inferential Statistics. Moreover, this study used the 0.05 level of significance. The study revealed that the pretest levels of both the traditional instruction (TI) and mathematical investigation (MI) groups were "novice" in both problem solving and proving; and "slightly developed" mathematical HoM. Generally, the same levels were obtained in the categories of each group when classified according to levels of mathematics achievement, logical reasoning ability,and scholarship status. However, the post test scores of the MI and TI groups in problem solving were "skillful" and "developing", respectively. This was also true in proving by induction. On the other hand, their post-intervention of HoM were "excellently developed" for the MI group, while "strongly developed" for the TI group. Students exposed to MI who were in the lower levelin terms their logical reasoning ability and mathematics achievement test had higher mean gain in all areas tested compared with their counterparts who were exposed to TI. Consequently, when each of the two groups was classified according to categories, the MI group had an edge over the TI group in almost all skills of interest. Meanwhile, there were significant differences between the pretest and post test achievement scores in problem-solving, proving, and evaluated HoM in both groups. Significant differences were also observed between the mean gains of the TI and MI groups in proving and evaluated HoM which further revealed the superiority of MI as an instructional strategy insofar as increase in performance was concerned. However, the two groups were comparable in terms of their mean gains in Problem solving. There were significant differences in the two groups in problem solving and proof writing when classified according to levels of the PSHS mathematics achievement. Moreover, significant difference was also observed in the mean gain in problem solving of the TI group when classified according to level of logical reasoning while in the MI group they are comparable. Significant relationships were likewise observed between the post test scores in problem solving and (a) mathematics achievement, (b) logical reasoning ability; post test in proving and mathematics achievement; and post-evaluation HoM and Mathematics achievement. The scores in the pretest for proving and the PSHS national mathematics achivement test were found to be significant predictors of the scholars' posttest performance in problem solving, proof writing, and post-intervention evaluation of mathematical habits of mind.

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