Today’s math activities had an element of surprise – card trick, folding triangle and cutting it, story reading. Mathematics has never been this interesting for me. But what was most important, is the skills of observation, infering and generalization that helped to address the outcomes. I was able to relate and make connections especially with the use of my prior knowledge.
It’s all about ANGLES today!
The five learning concepts are further emphasized in today’s lessons.
It was rather difficult and very challenging for me and all the other classmates to derive the answer in solving the measurement of an angle given in the drawing. After many tries and critical thinking, the result was achieved. I conclude that there is a huge need for visualization and having meta-cognition in this multi step process to solution.
Nonetheless, I am so pleased and glad to explore possibilities when solving problems instead of merely concern about one specific step or equation and concentrating on the ‘end product’. Also, I am looking forward to looking at the inter-disciplinary connection of art in relation to mathematics.
I felt intrigued with today’s mathematical learning. The materials used highlighted the elements of fun learning with a component of creativity or innovation. Challenging students to think and try of ways to manipulate the materials. The CPA approach – concrete, pictorial and abstarct, is further elaborated and enhanced. I realized that it applies to our daily encounters of trying to figure out solutions.
However, a problem story as the final activity of the day was mentally stimulating which required a lot of thinking skills on my part. It was not easy for me to conclude the answer but there is a need to dig deep into our mental/intellectual capacity to understand what is required to solve such problems.
Today’s activities (pictures above) discussed variations of getting a solution or solving a problem which was insightful and mentally stimulating. Having a number sense – flexibility to compute numbers helps children to decipher better when they think of possible answers to questions. Knowledge of number bonds, whether or not, with manipulation of concrete materials, is a required arithmetic concept for children to grasp for further extension of mathematical skills.
Tasks with specific constrains/requirements (e.g. only using certain digits, no repetitions of numerals, etc.) challenges students to think and develops their metacognition. Consequently, the appropriate use of math language/terms, is crucial for teachers to ensure understanding instead of causing confusion.
On a separate note, I do strongly believe in incidental learning – telling time, graph, patterning, etc. Such mathematics topics ought to be introduced on a daily basis as children go about doing other activities and it need not be enforced in a structured manner within the confines of a curriculum.
“How you teach is more important than what you teach.” ~Anonymous
The three activities – making rectangle with tangrams, 99th letter of your name, dividing rectangle into 4 equal parts, helped me developed confidence and a sense of curiosity especially with the way it was presented. A student will definitely respond positively to the encouragement, open-ended questions and teacher’s disposition.
Apparently, each of the tasks involved problem solving hence the three ways of teaching – exploration, scaffolding and teacher/role modelling were clearly displayed to emphasize the need for them in the classroom.
Though I am used to teaching children how to derive at answers by getting them to learn, practice and apply (the way in which I was being taught in the 1980s) but I seldom provide opportunities for them to enrich their learning with my approach of being very instructional which I’ve learnt to avoid at this point. It’s enlightening to ask a student “how many different ways” can a task be done. I think it develops a two-way learning process (teacher and student).
In addition, the approach by which concrete, pictorial and abstract learning is carried out to cultivate teaching mathematics has been proven successful.
“Mathematics is the science of concepts and processes that have a pattern of regularity and logical order. Finding exploring this regularity or order, and then making sense of it, is what doing mathematics is all about.” Van, . W. J. A., & Bay-Williams, J., Karp, S., 2013, p. 13)
We know that there may be more than one solution to resolve a problem, similarly in a mathematical context. Students need to be given proper tools and experience to enhace their thinking skills and possess the motivation, drive and determination to get answers. Therefore, providing grounded understanding, necessary language aquisition which is important and the required manupulatives/materials would propel students and empower them to engage in math activities.
At the same time, giving children opportunities to explore and learn while making mistakes will provide a chance for reflection and learning. Building new knowledge from prior knowledge helps teachers to scaffold and facilitate learning mathematics.
Beisdes the specific details in technical explanation and emphasis of mathematical principles, standards, strands and contents, being proficient in the subject requires appropriate learning dispositions to be developed.
Mathematics is not all just about numbers, formulas and equations (as seen in my earlier post) but it also involves thinking skills, concepts and applications.
Principles and Standards for School Mathematics (NCTM), 2000) provides guidance and direction for teachers and other leaders in pre-K-2 mathematics education.
Equity, Curriculum, Teaching, Learning, Assessment, Technology are the six principles fundamental to high-quality mathematics education. There are also five content standards – number, algrebra, geometry, measurement, data analysis and probability with a set of goals applicable to all grad bands.
Teachers need to acquire standards too and know process to support their teaching
Children need to develop mathematical understanding. Thus, teachers must ensure that components of mathematics are present within the children’s environment (contact) and concepts are clearly delivered or taught.
1, 2, 4 ,7 ,11, 16, 22, 29, 37, 46, …
What is the 2011th number?