Active Learning Reflection

Another idea to improve mathematics performance in elementary level is to encourage the student to link the existing knowledge and the new knowledge effectively while working math problems/examples. A worked example is “a step-by-step demonstration of how to perform a problem” (Clark, Nguyen, & Sweller, 2006, p. 190). This will prepare the students for similar problems in the future as they bridge the connection between the problems and the examples. In many cases, students are encouraged to link the informal ideas with the formal mathematics ideas that are presented by the teacher to be able to solve problems. When students examine their own ideas, they are encouraged to build functional understanding through interaction in the classroom. When students share among themselves on differences and similarities in arithmetic procedures, they construct the relationship between themselves hence making it the foundation for achieving better grades in mathematics. Teachers can also encourage students to learn concepts and skills by solving problems (Mitchell et al 2000). Students do perform successfully after they acquire good conceptual understanding because they develop skills and procedures, which are necessary for their better performance. However, slow learning students should engage in more practice

This is why I also employ the constructivism technique of collaborative groups in my classroom to give students the opportunity to discuss ideas with their peers and make reasonable conclusions about what they are learning. My classroom is arranged with student desks placed in small groups, which allows students to direct their attention to the front of the room when needed, yet they can turn and collaborate with their peers during group work.

Small groups require active teaching with much teacher guidance or involvement. Small groups can teach the context better than a larger group, allowing for no child to be struggling and left behind. Reading, math and science can benefit from small group interaction. Each student has a chance to be heard, voice his opinion or conclusion, get a response from the teacher and the other group participants, and close the gap for error. The key for successful learning is when the teacher involves himself and gets excited about what the children are to be taught. This is also true in group study as

Students in second grade when comparing two containers of equal volume may consider a tall thin container having a capacity greater than that of a short wide container. Allowing students to use standard measuring tools to record the volume provides the context for accomodation of conservation of volume. Additionally, students may use concrete manipulatives to accommodate conservation of numbers when solving problems involving addition and subtraction with regrouping employing base ten blocks. Subsequently, students are guided in the assimilating a semiotic function as they transfer to the use of representative symbols in place of using concrete manipulatives. An activity where students use nonstandard units of measure, such as cut outs of their foot shape, to measure identical objects creates tension when students compare their findings and discover that they are not in agreement. This activity prepares students for asimilating and accomodating seriation using standard units of measure such as inches and centimeters. In fact, best practices in second grade math instruction always begin in the concrete and upon mastery of this schema assimilate and accommodate into the representational or semiotic. However, these schema may be developed across the curriculum. Second grade students are

Manipulatives and Models to teach Algebra Concepts (6 points) Identify and explain how specific (by name) manipulatives, mathematical and physical models, and/or technology can be used to teach Algebra concepts for the following strands for a total of 3 tools. See Section 2 directions for more detail. Remember to include references and represent at least one concept from the following strand with a minimum of one of each tool (manipulative, model, and technology) represented in the section.

“Helping students develop mathematical dispositions in which they share their ideas, discuss others’ ideas, and so on, is always a challenge,” (The National Council of Teachers Mathematics, 2003, P. 151). I found this quote and reading to be very relatable, in the sense that students can often struggle to come up with their own ideas. This was definitely true for me and my group when we were working on the locker problem in class. In the book and in class, discussions can really benefit students and keep them engaged. “To encourage all students to contribute to discussions, the teacher should ask other students to explain their classmates ideas,” (The National Council of Teachers Mathematics, 2003, P. 153) this statement made me think of dialogic teaching. Dialogic teaching is students having a rich discussion amongst each other while being guided by the teacher. The students find out the answer on their own and the teacher does not tell them. So social norms and classroom management plays a big role when students problem solve.

Using hands-on resources and manipulatives in mathematics is important for student’s development of mathematical content knowledge. Knaus & Featherstone (2014. p. 12) state that through the manipulation of objects in a mathematically rich environment children are able to achieve an understanding providing a bridge between everyday concepts and abstract concepts. Furthermore, manipulatives and play are linked. During play with manipulatives such as an age appropriately fill treasure basket children are able to explore a range of objects shapes, sizes, textures, weights, lengths and the mathematical language that is related to the objects (Knaus & Featherstone, 2014). According to, Connell, Shearer, Tobin and Harrod (2006) exploratory manipulatives provide students with the opportunity to explore their

With the heterogeneous groups the level of discussion and cooperative work is increased, providing benefits for every student partaking. According to Paul Burden and David Byrd (2012), “Having students work in groups generally has a positive effect on their achievement when compared to their work as individuals.” Small-group work and discussions allows for students to improve their communication skill, cooperation skills, and gain new insight and understanding from their peers in a way that could not be achieved working alone.

When I become a teacher I plan to have my students work in cooperative groups because this allows them a chance to share their knowledge and ideas with their peers. Due to the fact that most students are on different developmental levels, those students who are of higher developmental levels can provide the other students with their ideas and perception of their knowledge. I feel that teachers should not be scared to let their students participate in group work because I think it is a great method of learning.

Middle school is the time for exploration and identity development. This age is defined by two periods of cognitive development that Jean Piaget called the concrete operational age and the formal operations stage. For this very reason, lessons and activities in the middle school need to be varied and unique. Students develop at different rates, and for this reason some of my students maybe concrete thinkers while others could be abstract thinkers. It all boils down to that individual student. Therefore, it is important to understand that not every student learns at the same pace from the same activity. What may work for one will not work for all. This is why in my math classes I will incorporate problem-solving tasks and questions. I believe in groupwork when it comes to these types of problems because it gives students a chance to listen to multiple ways of thinking to come to a solution. I cannot think of a job today where someone will always work alone. Our society is built on cooperation between different types of peoples to achieve one goal, to improve our world. Teaching students these lessons early on, increases their abilities to work together to come to a solution for a problem, and to embrace the diversity of learning in those

Seeing what these students struggled with has inspired me to teach and try to incorporate into my future classroom the educational skills students will need. These skills include learning to think critically, efficiently reading and writing, and developing arguments with backed up evidence. When students are exposed to these skills, they will enter the university level, and their future career paths prepared. Also, in my classroom, I want to challenge students and watch them grow to their full potential. I want to take students at different levels and see them develop together for the betterment of each individual. Therefore, group work is essential to having a thriving class. The impact of group work, when students help fellow students, changes each person and transforms the atmosphere of the class as a whole. Thus, I believe it is crucial to help students develop their social and interaction skills through group work and

In the education world of today, it is understood that one can only be effective in teaching by taking into consideration the different learning styles of students. In a classroom, it is expected that teachers would want their students to acquire a meaningful knowledge base, become proficient problem solvers and learn how to work productively with others (Biehler and Snowman, 2006, p. 370). If this is the case, teachers need to know how to be able to develop this situation in the classroom and make it more conducive to learning. Therefore, it would seem that they need to encourage students to converse with each other with group discussions and assignments, to make sure they are active in

“Group work is a teaching strategy that promotes academic achievement and socialization”(Frykedal, Chiriac, 2011). This method is often used since allow individuals to combine their skills with the intention to achieve a mutual goal. To be efficient when working with a group, individuals have the responsibility to understand and respect others preferences and

Based on several studies, one of the best ways to understand mathematical ideas and apply these ideas is through the use of manipulatives. Students explore these manipulatives, however, it is important that they make their own observations. The teacher then should model and show how to use the materials and explain the link of these materials to the mathematical concept being taught. Schweyer (2000) stated that students learn best when they are active participants in the learning process where they are given the opportunity to explore, assimilate knowledge and discuss their discoveries.

With knowledge gained from previous experience, I knew that the students I would be teaching were comfortable with a variety of learning methods, but work more effectively when a practical or group task is set. I shall therefore tailor my resources to promote this type of learning within my teaching group.