TMS3725 Assignment 2 solutions 2026
UNISA
ASSIGNMENT 2
Due date: 17 June 2026
Unique assignment number: 114871
All the graphs are drawn
, QUESTION 1
1.1 Difference between problem solving and routine exercises in mathematics
Routine exercises are mathematical activities where learners already know the
method or formula needed to obtain the answer. These exercises usually involve
repeated practice of procedures and rules. Learners follow familiar steps to solve the
problem, for example solving simple equations using previously learned rules.
Problem solving, on the other hand, involves situations where the method is not
immediately clear to the learner. Learners must think critically, analyse the situation,
and decide which mathematical strategies to apply. Problem solving encourages
reasoning, exploration, and understanding rather than memorisation.
Routine exercises mainly develop procedural fluency, while problem solving
develops deeper conceptual understanding and mathematical thinking skills.
1.2 Why Nicholson argues that problem solving requires finding a solution that
is “not immediately obvious”
Nicholson explains that problem solving involves situations where learners cannot
instantly recognise the solution process. The learner must first explore the problem,
identify relationships, and think about possible strategies before solving it.
If the solution method is immediately known, the activity becomes a routine exercise
rather than genuine problem solving. Therefore, problem solving requires learners to
reason, investigate, and make decisions independently.
1.3 How problem solving helps learners develop important mathematical
thinking compared to routine practice
Problem solving helps learners develop critical thinking, reasoning, creativity, and
decision-making skills. Learners learn how to analyse situations, test different
methods, and justify their answers mathematically.
Unlike routine practice, which often focuses on memorising procedures, problem
solving encourages learners to understand mathematical concepts deeply and apply
them in real-life contexts. It also improves learners’ confidence, communication, and
ability to connect different mathematical ideas.
UNISA
ASSIGNMENT 2
Due date: 17 June 2026
Unique assignment number: 114871
All the graphs are drawn
, QUESTION 1
1.1 Difference between problem solving and routine exercises in mathematics
Routine exercises are mathematical activities where learners already know the
method or formula needed to obtain the answer. These exercises usually involve
repeated practice of procedures and rules. Learners follow familiar steps to solve the
problem, for example solving simple equations using previously learned rules.
Problem solving, on the other hand, involves situations where the method is not
immediately clear to the learner. Learners must think critically, analyse the situation,
and decide which mathematical strategies to apply. Problem solving encourages
reasoning, exploration, and understanding rather than memorisation.
Routine exercises mainly develop procedural fluency, while problem solving
develops deeper conceptual understanding and mathematical thinking skills.
1.2 Why Nicholson argues that problem solving requires finding a solution that
is “not immediately obvious”
Nicholson explains that problem solving involves situations where learners cannot
instantly recognise the solution process. The learner must first explore the problem,
identify relationships, and think about possible strategies before solving it.
If the solution method is immediately known, the activity becomes a routine exercise
rather than genuine problem solving. Therefore, problem solving requires learners to
reason, investigate, and make decisions independently.
1.3 How problem solving helps learners develop important mathematical
thinking compared to routine practice
Problem solving helps learners develop critical thinking, reasoning, creativity, and
decision-making skills. Learners learn how to analyse situations, test different
methods, and justify their answers mathematically.
Unlike routine practice, which often focuses on memorising procedures, problem
solving encourages learners to understand mathematical concepts deeply and apply
them in real-life contexts. It also improves learners’ confidence, communication, and
ability to connect different mathematical ideas.
