In problem-based learning, students study by solving problems and reflecting on their experiences. Students also work in mutual groups to discover what they require to learn in order to solve the problem. They engage in self-directed learning (SDL) and then apply their new knowledge to the problem and reproduce on what they learned and the effectiveness of the strategies employed (Hmelo-silver, 2004). For example, instead of having pre-defined outcomes as in so much project based learning (we build a bridge), students have to think more about real life outcomes associated with the problem (where should the bridge be built, what kind of bridge should go there?) Besides that, students work collectively with the classmates to solve the complex and real problem that help develop content knowledge (Hirca, 2011) as well as problem-solving, logic, communication, and self-assessment skills.
Shininger (2006) embarked on a study to determine the benefits of using the STAD technique in a middle school mathematics classroom. He found that Students Teams Achievement Divisions (STAD) increases academic achievement and improves students' self-esteem as learners and their social interactions with their peers. Weaver (2006) investigated the benefits of cooperative learning in the mathematics classroom in secondary school. He found that cooperative learning is useful for learning mathematics in high school. The students who were exposed to cooperative learning seemed to have higher score on the tests and have positive attitude towards mathematics.
In one of simply five process standards, they state “Instructional programs from pre- kindergarten through grade 12 should enable all students to organize and consolidate their mathematical thinking through communication, and communicate their mathematical thinking coherently and clearly to peers, teachers, and others ...” (PSSM, 2000, p. 348). in spite of the National Council of Teachers of Mathematics’ thrust to prepare students to commune mathematics clearly, it is quite a challenge because of the lack of oral usage by mathematical teachers. For example, majority of schools in Jordan begin English Language Teaching by the age of 10-11 and certainly this has major affects on learning how to communicate and comprehend mathematical equations presented in English. Whereas, in many private schools in Jordan mathematics is taught in both languages, English and Arabic, where there is a great emphasis placed on reading and listening skills, leaving aural-oral communication skills out of the picture. Moreover, according to Wood(2012), it is frequently assumed students learning mathematics will automatically pick up on and “absorb” the discourse used to explain it, and thus, be able to commune the mathematical concepts and ideas being learned.
In order to attain the national goals related to scientific literacy, it is necessary to determine what factors influence achievement of students in mathematics. In short, there is a need to analyze all related research, make appropriate policies and develop effective educational methods to improve science and mathematics education. In order to promote greater student achievement and meet increased expectations, Mathematics teacher will need a battery of instructional materials to fulfill students’ needs. Students will more likely see the value of the lesson if the instructional materials and student-assigned tasks reflect the worth of the content. The choice of instructional
Exploring and problem solving to create, integrate, and generalize knowledge, 2. Students driven, interest based activities in which the student determines the sequence and frequency, and 3. Activities to encourage integration of new knowledge into the learner’s existing knowledge base. The first attribute of Discovery Learning is a very important one. Through exploring and problem solving, students take on an active role to create, integrate, and generalize knowledge.
should be coherent; furthermore, the different topical strands of mathematics are highly interconnected. Last, knowledge of instructional strategies are representations for teaching a concept or topic allows teachers to possess a collection of various explanations, metaphors, analogies, and activities. Similarly, Smith and Neale (1989) characterized pedagogical content knowledge as consisting of four components: knowledge of students’ concepts, including students typical errors and developmental paths; knowledge of strategies for teaching content that enable students to conceptually understand a concept by eliciting students’ preconceptions, asking for clarification and explanation, encouraging debate, and discussion, and clearly presenting
The learners understand mathematical ideas, and have the ability to transfer their knowledge into new situations and apply it to new contexts. Conceptual understanding is one of the five strands of mathematical proficiency, set out by the National Research Council’s 1999-2000 Mathematics Learning Study Committee in their report titled Adding It Up: Helping Children Learn Mathematics, published by the National Academy Press in 2001. Conceptual mathematics understanding as knowledge, involves comprehensive understanding of fundamental and foundational concepts behind the algorithms performed in Mathematics (Rille-Johnson,et al, 2001). When developing conceptual understanding, it’s essential to give students freedom of choice in how might potentially respond. Lessening to one representation too often causes students to try to find the one correct path towards a solution, rather than thinking expansively and for them.
Math, and science curriculum should emphasize on critical and higher order thinking and problem solving skills that promotes active involvement of students in the learning process that includes opportunities for them to explore application of higher order of thinking skills and investigate new approached to applying their learning. Math and science curriculum should challenge each student to excel, reflect a commitment of equity and demonstrates and appreciation of diversity. Implementing this curriculum should involve active involvement of students in the learning process to ensure by ways of engaging strategies like understanding the objectives for learning and how the learning relates to everyday life in useful applications and innovations and discoveries. This also can be achieved through classroom activities, homework assignments and other projects base learning (Science fair, research projects) that enable students to apply their learning. Teachers should be
Inquiry: Inquiry is a method in which a learner tries to solve the problem by investigating the problem and finding out the issues. In inquiry method a problem is given to the learner and they have to find out the solution of the problem. It is a student-centered approach in which a child tries to solve a problem by asking questions, researching and gathering data from multiple resources. Examples of inquiry method: Problem based learning, project work are common examples of inquiry method Guided inquiry: It is a student-centered approach in which the student tries to find out the solutions of the problem in the guidance of the teacher. In guided inquiry the teacher provide the problem statement and research questions to the students and the students can formulate their own procedure.