Introduction:
The world in which we live is mathematical. In our everyday activities we need mathematics for instance; there is need in everyone for mathematical thinking as well as problem solving in the workplace, at home, when in a shopping spree, etc. In a world of such kind, you notice that those who comprehend and can operate mathematics will have immense opportunities that others lack. In fact, mathematical proficiency opens avenues to productive prospects. Conversely, lack of mathematical competency closes those doors. Usually, learners have varied abilities, interests and more fundamentally, needs. Yet each learner requires mathematics in his or her individual life, be it at home, in the workplace, and even in further study. All learners deserve a chance to appreciate the power and splendor of mathematics. Students should learn a new collection of mathematics nitty-gritty as well as higher level critical-thinking handiness which are critical to problem solving. These permits them to work out fluently, interpret and to unravel puzzles innovatively and resourcefully.
The objectives of this lesson is to enable instructors establish suitable strategies employable in problem solving and appropriate forms of mathematical assessment and further the correlation between problem solving and learner’s achievement. In the lesson, the standards in mathematics with regard puzzle solving are also looked at, as well as problem solving and assessment in an inclusive setting.
In the lesson, several standards put down by the National Council of Teachers of Mathematics (NCTM) were addressed. The NCTM declares that “students need to develop a range of strategies for solving problems, such as using diagrams, looking for patterns, or trying special values or cases” (NCTM, 2000, p. 7). These teaching strategies allow learners to comprehend with ease abstract mathematical concepts and make these concepts realistic to learners’ perception. According to Hanson et al (2001), if all learners are going to gain knowledge of these strategies, then these strategies should be imbedded in and most importantly be taught across the curriculum. Beside strategies standards, NCTM also establishes the standards for mathematics assessment to help in enhancing learning of mathematics and modeling and shaping teacher instruction. As a result, learners need to use assessments as a part of the reflecting process and work together in partnership with the teachers to determine the direction of learning in mathematics (Hanson et al, 2001).

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The teacher did discriminate instruction within a diverse classroom into mainly high achievers and the low performing learners. In this case, the teacher exposed low achievers to basic skills with limited exposure to operate higher-level problem-solving skills which were left for the higher performers (Grouws & Cebulla, 2000). These low performing learners according to Grouws & Cebulla, (2000) need to be exposed to more challenging curricula which provide first hand experience. For instance, rather than handing learners a worksheet, a more interesting puzzle might relate to an investigation of classmates involving the kinds of pets they have. From that basis, the class could create graphs depicting data, find partial comparisons (introduction to ratios and probability) and percents.
Technology was not used in the instruction of the math lesson. For more effectiveness and probably efficiency, technology can be incorporated into this lesson. For instance, the teacher can make use a graphing calculator. This will offer learners an opportunity to collaborate and discuss the puzzles to establish the solution, as they would in a real world situation.
Teaching mathematics needs a lot of reference lists. Teachers habitually have reference lists posted in their classrooms during lessons to which students can make reference when faced with a problem-solving situation. Mathematical problem solving indeed is a multifaceted cognitive activity which involves numerous processes as well as strategies (Montague, n.d.). Stages involving Problem solving are twofold: representation of the problem and problem execution. In the lesson, the teacher used pictures or manipulative objects. Pictures and objects do help make the problems as well as concepts more real and concrete to students as nearly all mathematics concepts are abstract.
Modern theories on teaching techniques discourage competition and instead promote collaborative learning. Competition as a teaching strategy demotivates and demoralizes the underperformers. As a teacher, I would reorganize the classroom to accommodate more learner-learner interaction. Placing learners into cooperative learning and problem solving situations will promptly increase the interaction between the high-performing and low-performing students with the target of bridging the learning gap. Moreover, I would employ use of alternative assessments like portfolios and hands-on projects in order to improve strengths and weaknesses of each individual mathematics students. I would also include modifications like slowing the pace of instruction, reducing the process of estimation from problem solving, using flip charts of the involved processes and strategies, and finally teaching from known to unknown, concrete to abstract and from simple to complex.
Conclusion:
Mathematical problem solving can best be taught by employing cooperative learning technique. Students should be provided with the processes, stages and strategies that make mathematics problem solving simple to learn. Teachers should also consider providing real life mathematics situations to challenge students, and students will begin to appreciate the necessity and essence to be excellent problem solvers.
References:
Grouws, D. & Cebulla, K. (2000). Improving Student Achievement in Mathematics. Geneva, Switzerland: International Academy of Education International Bureau of Education, Educational Practices Series -4.
Hanson, et al (2001). Should standard calculators be provided in testing situations? An investigation of performance and preference differences. Applied Measurement in Education, 14(1), 59-72.

Montague, M. (n.d.). Math problem solving for middle school students with disabilities. The Access Center.
National Council of Teachers of Mathematics (2000). Principles and standards for
school mathematics.