## How Higher Order Questioning Supports Understanding of Mathematics

Question:

How can i use higher order questioning more effectively to support young children in developing their understanding of problem-solving in mathematics?

In educational institutes, questioning helps the practitioners to check the understanding level of the children (Suggate, 2010). It also encourages the young children to engage and focus their thinking on various diverse concepts and ideas (Terezinha and Bryant, 1996). According to Smidt(2009), the teachers probes questioning and discussion to assess the effectiveness of their teaching approaches and promote deeper understanding in pupil progress. High order questioning also stimulates thinking and often generates more questions among the children in order to clarify the process of understanding (Carruthers and Worthington, 2011). However, Haylock and Cockburn (2013) argued that the process of high order questioning might fail due to use of inappropriate questioning techniques and framing of excessive difficult or easy questions. The learners may not be able to reciprocate the correct answer or may not make any further query in the peer fear or pressure to answer a question (Smith, 2007)

Bloom’s taxonomy is a way of distinguishing the fundamental questions within the education system (Frangenheim, 2005). The aim of high order questioning within the primary classroom is not to determine the learning progress of children rather the questions are used to teach the students. The hierarchy in using high order questions from lowest level of thinking to highest level of thinking is knowledge, comprehension, application, analysis, synthesis and evaluative questions (Frangenheim, 2005). In the practical scenario, the teachers make storyboard displaying the main elements to create a mind map of the topic in the mind of the children. In the understanding stage the teacher draw pictures and illustrate the process. In the application stage, the teachers will construct a model to demonstrate the working of the process. In the analyzing part, the teacher makes questionnaire in order to evaluate the progress of the pupils. Finally in the evaluative stage the teachers will be able to evaluate the progress of the pupils based on the process report.

The use of correct high order questions can stimulate mathematical thinking in the early years. (Wallace, 2002) Some of the high order questions like “can you group these… in some way?”,”How can this pattern help you find an answer?”, “Can you see a pattern ?”, “ Is there a way to record what you’ve found that might help us see more patterns?” will help the children to build strong conceptual framework. In addition to these questions McAteer (2012) commented that assessment questions like asking the children to explain what they are doing or how they arrived at a solution may help the practitioner to assess the learning progress of the children. Finally the use of final discussion questions like “Who has the same answer?”, “Who has a different solution?”, “Are everybody’s results same?”provides further opportunity for reflection and realization of the mathematical ideas and relationships established by the children (Terezinha and Bryant, 1996).

High order thinking involves creating and evaluating of the information and on the contrary low order thinking involves remembering of the facts and processing of the information accordingly (Muthivhi, 2012). Low effort thinking may be inefficient however it saves time in comparison to high order thinking. However Simmons (2012) has argued that high order thinking promotes knowledge and hence it is more effective than low order thinking.

## The Bloom’s Taxonomy and Its Application in High Order Questioning

The implementation of higher order thinking can be effectively done within the students with the help of scaffolding (Muthivhi, 2012).This process involves providing the children with necessary support at the beginning of the task and then allows working independently. Some of the other learning schemas include trial, elaboration, organisation and Meta cognition. The trial includes attempting to solve critical numerical problems. The other schema, which is also known as Meta cognition, involves activities such as planning how to approach a task, monitoring and evaluating the progress of a task. Moreover constructive feedback providing immediate specific information should inform the learners of their progress(Marshall and Horton, 2011).

Relational thinking may be defined as the technique of seeing the equal sign as an indication of equivalence or balance and not as a direction to find an answer (Siraj-Blatchford and Nah, 2014). The use relational thinking helps the children to establish an equivalent relationship between the different numerical terms. Marshall and Horton (2011) stresses that high order thinking which is commonly known as highorder thinking skills teaches the children to be critical thinkers. The use of the critical thinking skills is required for the implementation of high order thinking (Haylock and Cockburn. 2013).According to Simmons (2012), the individuals who have the ability to think on a level higher than memorising of facts or copying the actions or thoughts of theoryare said to able to implement high thinking abilities.

The use of thinking Hats concept introduced by Edward De Bono is a useful tool to analyze the decisions from a number of perspectives (Muthivhi, 2012). This forces the learner to move out of their habitual thinking style and helps to get a more rounded view of the situation (Bjorklund, 1990). According to Edward De Bono the white hat may help the learners to be rational in their thinking approach. The red hat may make the learners emotional about their decisions on the contrary the blue hat will make the learner cautious and defensive in their decision approach. The yellow and the green hat help the learners to think positively and creatively respectively. Finally the blue hat stands for process control (Suggate, 2010). A relational connection is seen between the concepts of thinking hat and the Bloom’s taxonomy. The rationality showed by the white hat thinkers can be connected with Bloom’s stage of knowledge acquiring. The red hat thinkers however uses emotions and intuition to evaluate the decisions hence these thinkers can be found in the evaluative stage of Bloom’s taxonomy. In cases of both black hat thinkers and yellow hat thinkers, the assessment of strengths and weaknesses of the individual is noticed hence these types of thinkers are majorly found in the analysis and evaluation stage of the taxonomy. The green hat thinkers are the individuals concerned with the creativity of thoughts and hence can be identified in the comprehension and application stage of taxonomy.

The problem solving process involves a series of decisions each of which depends on the outcomes of the preceding decisions (Williams, 2008). Majority of the schools in UK focuses on the use of nursery rhymes and songs to help the children develop problem solving skills and early mathematical language and concepts in a fun and interactive manner (Wallace, 2002). Bjorklund (1990), highlights that the learners must be provided with initial guidance in order to define the numerical problems and help them in finding appropriate solutions to the numerical problems. On defining the problem, the children will be able to understand the complexity of the problems and will be able to evaluate the type of approach they should consider for solving of the problem (GB. DfE, 2012). The non statutory curriculums were concerned about reasoning on the contrary the statutory curriculum has introduced a single strand on reasoning alone in the field of mathematics (GB. Department for Education and Skills, 2003).

## Effective High Order Questions for Mathematics

The national curriculum sets the standards in all subjects so that all children in all types of educational institutions can learn the same standard of tasks. The complexity of the problem will help the children to use their critical thinking ability to generate simpler alternatives in solving the problems(Geary, 2012). The extensive use of research analytical skills and logical thinking capabilities are required for generating the alternative solutions (GB. DfE, 2013).Finally the learner will be able to judge the problem based on the alternative solutions GB. (Department for Education and Skills, 2003). The uses of creative learning sessions might be helpful in this stage for the learners to ascertain the alternatives and evaluate them(Muthivhi, 2012). Then the children will give preference on the solution which is easier to understand(Wallace, 2002). The child then in the final step of the process might implement the chosen alternative(Anghileri, 1995). The logical implementation of the solution will benefit the children in understanding the whole process and effective in solving the problem(Watchorn, 2014).

The Early years Foundation Stage (EYFS) sets the standards for learning, development and care of children from birth to 5 years old (Koshy, 2011). The formulation of development matters in EYFS sets out the non statutory guidelines for the practitioners for implementing the statutory requirements in early foundation stages. The document shows how the three themes namely a unique child, positive relationship and enabling environments help in learning and development of children. All the schools are required to follow the guidelines of the EYFS in order to nurture the thinking skills and develop the reasoning skills of the children. In the year 2012 various developments took place within the system guidelines (GB. EE, 2012). The unique child develops and learns through positive interaction in positive relationships and enabling environments (Askew Wiliam, 1995). The regulation further states that the practitioners should use development matters as a part of their daily observation, assessment and planning. These regulations are stated in the non-statutory curriculum (GB. Department for Education, 2013).

The Statutory Curriculum provides the necessary guidelines for the practitioners outlining the teaching requirements for mathematics. The teaching requirements need the practitioners to teach how to use and apply numbers, problem solving, communicating, reasoning, counting, understand number patterns and sequences, the number system etc. This helps the children to develop mathematical skills for the early years (GB. Department for Education, 2013). The development of the numerical problem solving ability in the early stage might help the individual child to foster effective logical reasoning skills in the later stages of educational and holistic development (GB. Department for Education, 2013). The use of the critical thinking concepts might help the children in their early foundation years to seek patterns, make connections and recognize relationships between the numerical in order to solve numerical problems __(__Montague-Smith 2014).

With the advancement in the field of educational techniques the pupils are now made to learn the basic counting skills with the help of real life objects (Carruthers and Worthington, 2011). The use of the number lines stimulates discussion about numbers and children learn about the easy numerical problems while exploring with the number lines. Cockburn (1999) suggested that all children might be able to succeed in generating numerical problem solving ability if the practitioners provide them the opportunity to explore the mathematical ideas in ways that would make sense to them and opportunities to develop mathematical concepts and understanding.

## The Benefits of High Order Thinking in Mathematics

In the schools, mathematics is used as an opportunity for communication so that the students can reflect on and clarify their thinking about mathematical ideas and situations (Watson & Mason, 1998). Williams (2008) suggested that mathematics can be regarded as an important language if the students are able to use the language to communicate productively. For example, Use of mathematics as a communicative language will help the children to become logical thinkers. Geary *et al.* (2012) added that communication plays an important role in helping children construct links between their mathematical symbols and help them to realize ways of representing mathematical problems. Young children can learn mathematics with the help of verbal communication hence it is important for them to “talk mathematics.” (Bjorklund, 1990) Interaction with classmates of the same age helps children to construct knowledge, learn thinking ways and clarify individual thoughts. (Smith, 2007)

Children mathematical graphics is the term which refers to the visual marks, representations and graphics that the young children in primary schools are seen to make or choose to use or explore mathematical meanings and communicate their thinking (GB. DfES, 2003). The visual representations found in the nurseries including scribbles, drawings, writing, iconic marks and standard symbols forms a part of the children mathematical graphics (Terezinha and Bryant. 1996). Graphical representation shows that the children are comfortable in usage of informal methods in order to communicate with each other about the mathematical and numerical problems (Carruthers and Worthington, 2011). The graphics are vital for the development of the numerical skills because with the use of their own graphics the children are able to represent their mental mathematics on paper (Haylock and Cockburn, 2013 and Anghileri, 1995). Moreover Smidt(2009) added that children makes or generates standard graphics for the process of the numerical problem solving with the help of the graphics and they create their own layout for solving and understanding of the numerical problems.

A child generally uses the graphical drawings and pointing outs in interpreting mathematical reasoning skills. The Reggio Emilia approach introduced by Loris Malaguzzi focused on preschool and primary education language development (Wien *et al*. 2011). Malaguzzi believed that there are around 100 languages and the aim of this approach is to teach the students in primary schools to communicate using those languages (Anghileri, 1995). The term hundred languages in this approach refer to the numerous ways that children have of expressing themselves The use of the drawing and graphics by children to understand mathematical reasoning is a philosophy of this approach. The Regio Emilia approach states that children must have a control over the direction of learning and must be able to learn through experiences of touching, moving, drawing and observing (Koshy and Muurray, 2011). Hence, children with the help of symbolic depiction, drawing, sculpture, dramatic plays and writing will be able to communicate their reasoning thoughts with each other as well as with the practitioners (Wien *et al*. 2011).

It is seen that the children’s development can be done with the help of various outdoor learning activities. The use of high order questioning, bloom’s taxonomy and mathematical graphics can help the practitioners to develop the reasoning skills of the children. The chapter highlights the basic concepts of the high order thinking and high order questioning that helps in developing the skills and knowledge level of the learners. With the help of the secondary information gathered from the journals and books the evaluation on the learning of the children can be done.

Reference list

Books

1. Bjorklund, D. F. (2013). *Children’s strategies: Contemporary views of cognitive development*. Psychology Press.

2. Montague-Smith, A. (2014). *Mathematics in nursery education*. Routledge.

3. Carruthers, E., and Worthington, M. (2011). *Understanding Children’S Mathematical Graphics: Beginnings In Play: Beginnings in Play*. McGraw-Hill International.

4. McAteer, M. (2012). *Improving Primary Mathematics Teaching and Learning*. McGraw-Hill Education (UK).

5. Roberts-Holmes, G., (2014). *Doing Your Early Years Research Project. *2^{nd}London: PCP.

6. Terezinha N. and Bryant. P. (1996) Children doing Mathematics. Oxford: Blackwell Publishers.

7. Smith, A. M. (2007) Mathematics in Nursery Education. 2^{nd} Ed Oxon: Rotledge.

8. J. (2010) *Mathematical Knowledge for Primary Teachers*. 4^{th} edition Andrew Davis and Maria Goulding. London: Routledge.

9. Fulton, D. (2002)*Teaching Thinking Skills Across the Early Years- a practical approach for children aged 4-7.* Edited by Belle Wallace. 2002.London:

10. S(2009)*Key Issues in Early Years Education: A Guide for Students and Practitioners.*

11. Williams, P. (2008) *Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools*, London: DCSF.

12. The Early Years Mathematics Group (1997) *Learning Mathematics in the Nursery: Desirable Approaches, *Malton: BEAM.

Journals

1. Muthivhi, A. (2012). Schooling and the Development of Verbal Thinking: Tshivenda-Speaking Children’s Reasoning and Classification Skills. *South African Journal of Psychology*, 42(1), pp.82-92

2. Marshall, J. and Horton, R. (2011). The Relationship of Teacher-Facilitated, Inquiry-Based Instruction to Student Higher-Order Thinking. *School Science and Mathematics*, 111(3), pp.93-101

3. Geary, D. C., Hoard, M. K., Nugent, L., and Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. *Journal of Educational Psychology*,*104*(1), pp- 206.

4. Simmons, F. R., Willis, C., and Adams, A. M. (2012). Different components of working memory have different relationships with different mathematical skills.*Journal of experimental child psychology*, *111*(2), pp-139-155.

5. Wien, C.A.; Guyevskey, V.; Berdoussis, N. (2011). “Learning to Document in Reggio-inspired Education”. *Early Childhood Research and Practice*.