**ABSTRACT**

The purpose of this study is to determine the effects of Mathematical Investigation (Mat In) as a teaching strategy on the achievement and critical thinking skills of the students in mathematics. It utilized the single group pretest – posttest pre-experimental design with one intact class of 54 grade eight students in Poblacion National High School (PNHS). The research was carried out in the fourth quarter of the 2016-2017 academic year. The Mathematics Achievement Test (MAT) for pretest and posttest, Lesson Guides, the Critical Thinking Test (CTT) and its Scoring Rubrics, Classroom Observation Guide, an open-ended Experiences Survey Questionnaire, Mathematical Investigation Activities, and Mathematical Investigation rubrics were the instruments used in this study. The result showed that the students have significant higher posttest scores in the mathematics achievement test and critical thinking test after their exposure to Mat In. The three cognitive domains, content, application and procedural were improved after students’ exposure to Mat In. The students’ group performance in the Mat In activities were scored using three indicators in the Mat In rubrics, foundational knowledge, investigative process, and communication. According to the students, Mat In enabled them to better understand the lessons and helped them to easily recall the topic. This indicates that using Mat In gave positive experiences in the learning of the students. The study concluded that Mat In strategy tends to enhance the achievement in mathematics and critical thinking skills of the students.

**INTRODUCTION**

Mathematics plays a vital role in everyday life. Its application is very important in all fields of endeavour such as science and technology, medicine and business, and it is also used in making decisions. Mathematics has its mental and social values. It works as a powerful filter throughout the threshold of success. It embraces high prestige tools that facilitate students to understanding, model, and manipulate the natural and social worlds around them. Despite its importance, many students dislike mathematics. They do not possess mathematical skills and cannot perform well in school, which lead to poor performance. Students generally perceive that mathematics is a difficult subject. The students who have not mastered the previous learning may not gain enough understanding in higher mathematics which can be a disadvantage later on. Many studies that focused on improving students’ performance in Mathematics have been conducted through the years but results showed that many students still have negative attitude and tend to perform poorly in the subject. Mathematics ranked last out of five subjects in the 2014 - 2015 result of the National Achievement Test (NAT) in Poblacion National High School (PNHS). PNHS is one of the public school participants in the NAT examination. Its Grade 10 students gained 38.60% in NAT in the field of mathematics during the said school year. In the last five years, they obtained an average of 36.81%. A mean percentage score of 75% is currently set as the goal of the Department of Education (DepEd). This indicates that students have low mastery level in mathematics. NAT also measures the critical thinking of Grade 10 students, they obtained 42.25% in the same school year. In the one international comparative survey test, Trends in International Mathematics and Science study (TIMSS) which was first conducted in 1995 among 42 participating countries, the Philippines was placed at the 41st spot in science and at the 38th spot in Mathematics. Sample scores of the latest TIMSS administered test in 2013 have revealed low achievement in science and mathematics of the selected grade 8 students. The Philippines ranked 42nd in science and 41st in mathematics among 45 participating countries for grade 8 students. Notable was the preparation of Filipino students for the TIMSS in 2013 similar to that in 1999. The Philippines ranked lowest among 10 countries in 2008, even with only science high schools participating in the Advance Mathematics category. Parallel to the result of one global survey by World Economic Forum’s (WEF) Global Competitiveness Report for 2011-2012, the Philippines ranked 115th out of 142 countries in perceived quality of Math and Science education. The survey asked the business executives around the world to rate the quality of education, among other things, in their respective countries.

The results of the said assessment and survey are alarming for science and mathematics teachers. The teacher on his/her part should recognize the important factors in determining how to teach a particular concept effectively. He or she should adopt innovative teaching strategies to make the teaching-learning process more meaningful.

Teachers must not stop in searching and enriching new ideas to help in coping up with the learner’s generation. Also, teachers may adopt methods and strategies that may promote the critical thinking skills and may improve the students’ achievements for after all, students are the indicators that measure the effectiveness of the teaching-learning process. Mathematics learning should be imparted through activities from the very beginning of school education that is, from the primary stage itself. Concrete objects, models, maps, patterns, photographs, posters, games, puzzles, and experiments can be used in these activities. It is important to stress the importance of using learning aids. This can be accomplished by engaging students and teachers, as well as mobilizing community resources (National Council of Educational Research and Training, 2000).

Similarly, Grouws & Cebulla (2000) emphasize that research studies show that when students discover mathematical ideas and invent mathematical methods, they have a better conceptual understanding of mathematical relations. Students may construct and discover their own easy way of understanding mathematics According to Flewelling and Higginson (2005), inquiry, inquiries, and problem solving enable students to use their imagination and develop the habit of doing so. Traditional text-based activities, on the other hand, give the student little to no opportunity to do so.

According to Diezmann (2005) rich learning opportunities stem from students’ engagement in challenging task. Classroom tasks can be broadly categorized into those that have the potential for learning and those that provide opportunities for students to practice applying their previously learnt knowledge or skills. Linking ideas and knowledge to students’ prior knowledge help them to understand more when they see connections. The learning in that way becomes meaningful.

Devlin (2000), defined mathematics as the science of order, patterns, structure, and logical relationships. Hence, Mathematical investigations involve a search for pattern and structure. Students may collect related examples of functions, numbers, shapes, or other mathematical objects at the start of an exploration. Discovering is an idea that helps the students to generate their own knowledge that they may connect to the previous knowledge.

Thus, inquiries are at the heart of international reforms aimed at improving mathematical learning and developing children's mathematical abilities (Baroody & Coslick, 1998 as cited in Diezmann, 2005, p. 4). For instance, Laviña’s (2000) study resulting to the positive influence of mathematical investigation in teaching Mathematics and it also helped develop the HOTS of the students in Mathematics against the traditional lecture and drill method. Critical thinking skill to Chukwuyenum (2013), is considered a factor in students’ success in mathematics. In order to draw a credible and valid conclusion, critical thinking involves an effort to gather, interpret, analyze and assess information. Critical thinking must be embedded and stressed in the curriculum when teaching mathematics in schools so that students can develop the skills and use them to enhance their success and reasoning abilities. To prove the relevance of mathematical investigation in coping with the problems mentioned, the study attempted to use mathematical investigation as a teaching strategy to improve students’ achievement in mathematics and critical thinking skills

Knowing the usefulness of Mathematics in real – life situations, the result of this study will be beneficial to all those who believe in the importance of mathematical competence for lifelong learning. Further, outcome of this study may help students who struggle in mathematics to improve their performance and enhance their higher order thinking skills. This will redound to learners who are equipped with the 21st century skills thus, making them successful in their workplace.

see PDF attachment for more information