The traditional 'isms' and pedagogy by Jack Stothard https://padlet.com/jstothard/f19jljq5dfyicuda Contribute any thoughts you had surrounding these four epistemological areas relating to pedagogy. These can be any thoughts or ideas or how they may relate to practice. en-us 2020-10-12 12:47:37 UTC 2026-03-17 22:02:45 UTC hello@padlet.com Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/821842870    Pupils should not be guided solely by extrinsic motivation. Instead, learners should be supported in developing an intrinsic motivation to mathematics learning. Those who are limited to extrinsic motives are, in experience, more likely to be unwilling to develop their mathematical knowledge and skills beyond the compulsory.
The inclusion of ‘drilling’ maths facts could adversely affect pupil confidence and motivation, and promote an ingrained loathing of mathematics.
]]> 2020-10-12 14:56:47 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/821842870 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/821851302 2020-10-12 14:59:15 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/821851302 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/821853007 2020-10-12 14:59:46 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/821853007 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/821854088 2020-10-12 15:00:06 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/821854088 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822005448 This theory is considered one of the most traditional learning theories, however most teachers nowadays continue to apply a behaviourist view of learning to their teaching. This emphasises on behaviour that can be observed and leads itself naturally to the rote learning method. 
The learning environment should focus on hierarchical procedures and outcomes so that mastery of basic skills provides a scaffold to more advanced mathematical concepts. ]]> 2020-10-12 15:43:58 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822005448 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822044752 Cognitivism arose mainly in response to behaviourism and learning is seen as an adaptive process. It stresses on the mental processing activities such as thinking, knowing and problem solving. It is vital that teachers organise their teaching practice that is appropriate and effective for pupils cognitive structure. 
In relation to mathematics, cognitivism places an emphasis on learning through problem solving. A mathematical problem will be interpreted by using existing knowledge and transferring this to new concepts. ]]> 2020-10-12 15:55:27 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822044752 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822078939 Constructivism is vital in teaching and learning mathematics. This is a process where individuals will construct their own knowledge and understanding through active learning in the classroom. Constructivism allows pupils to find a variety of different ways in searching for new knowledge and ensuring this learning is meaningful. 
Although constructivism is the most favoured pedagogy, there are still problems in the context of mathematics and numeracy. Teachers tend to have the assumption that learners already have extensive prior knowledge which enables them to engage with their learning activities. However, this is not the case, and a lot of mathematical concepts need to be learned, which leads the children to be having misconceptions around some aspects in maths. ]]> 2020-10-12 16:05:59 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822078939 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822105051 Connectivism is seen as a teaching and learning theory which is used in the 21st century. By using group knowledge, teachers and students can gain experience and action. 
The role of the teacher has altered from being the expert within the classroom, to becoming the facilitator, listener, observer and organiser for the collaborative classroom. ]]> 2020-10-12 16:13:42 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822105051 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822118110 The 'ideal' learning environment focuses on outcomes so that a mastery of more basic skills moves forward as a scaffold into more advanced concepts in Maths. ]]> 2020-10-12 16:17:38 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822118110 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822125217 Knowledge may be transferred between individuals in this way (perhaps through group/collaborative work), but is stored as internal knowledge. ]]> 2020-10-12 16:19:47 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822125217 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822270941 Cognitivism is based on mental processes such as; thinking and problem solving. Cognitivism looks at how the mind receives and stores knew information and how this is processed based on prior knowledge (Schemas). According to cognitivism, maths learning should be adaptive and shared between individuals. Learning is observational and should include problem solving, where children can compare their own learning with others' ideas (Social cognitivsm).]]> 2020-10-12 17:03:22 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822270941 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822281868 Maths is learnt through active learning activities where children have the opportunity to work at their own speed. Cognitivism looks at children 'doing' rather than being instructed. This because this theory promotes the idea that information cannot be transmitted, instead learner have to build their own understanding. Therefore, instead of taking a didactic approach, teachers become a facilitator of learning, who encourage mathematical learning through talk and offering opportunities to discover through real life scenarios.]]> 2020-10-12 17:06:32 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822281868 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822295936 Connectivist learning promotes gaining knowledge through interaction with groups and encourages a collaborative classroom. This theory encourages the use of digital tools in mathematical teaching and learning. The main aim is to create links between mathematical language and the actual meanings of these. This allows children to access questions and apply processes through thorough understanding of mathematical language.]]> 2020-10-12 17:10:29 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822295936 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822322988 Mathematical learning is based on observation and a stimulus-response process. This includes motivations, rewards and punishments. In the context of mathematics learning; mastery of fundamental skills becomes a scaffold for future more complex work. Teaching within the behaviourist approach is mostly didactic, with the teacher transmitting information.]]> 2020-10-12 17:18:29 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/822322988 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824242801 This approach to the teaching of mathematics involves teachers using positive reinforcement to encourage children to use correct, taught methods in their own mathematics. Children do not get the opportunity to explore their own methods when this approach is used. A lot of practise of the correct methods is needed in order for children to have a chance at remembering what they have been taught.]]> 2020-10-13 09:37:57 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824242801 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824248695 I believe this approach is an effective and more classroom friendly approach to behaviourism. It allows for social learning and discussion around the topic meaning children can explore ideas together and build their confidence by embedding learning as they teach each other. This approach also focuses on the mental processes involved in learning mathematics such as problem-solving and the process behind remembering what they have been taught. ]]> 2020-10-13 09:41:03 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824248695 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824255369 I really like this approach as it emphasises the use of real life examples in order to help children learn. Through my reading I have learnt that real life examples help children to have meaningful experiences, which in turn, allow children to remember what they have learnt for longer. It also allows them to become more engaged in their learning as they see that what they are learning is going to be relevant at some point in the future. ]]> 2020-10-13 09:45:00 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824255369 Behaviourism allows the pupil to be conditioned into behaving or doing something in a certain way without much need for thinking, something Klinger referred to as 'skill and drill' the paragraph clearly shows the writers prejudice against the method of teaching. However, the National Curriculum (2013) requires children to, 'Recall and apply knowledge rapidly and accurately'. To be able to recall times tables for example the act of 'skill and drill' is necessary for the child to do so. This does not need to be in the form of learning by wrote but simply by celebrating achievements in times tables rock stars. https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824309765 2020-10-13 10:19:49 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824309765 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824315430 2020-10-13 10:23:39 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824315430 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824316134 2020-10-13 10:24:05 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824316134 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824316465 2020-10-13 10:24:18 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824316465 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824316761 Connectivism – the idea that pupils can learn and deepen their understanding and experiences through interaction with groups and encourages a collaborative working environment. The pupils are active learners in their education and the teacher becomes the facilitator. ]]> 2020-10-13 10:24:30 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824316761 Behaviourism eleanor_knapton https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824324196 Behaviourism is one of the more tradditional learning theories as is commonly used in schools today as it aligns well with the curriculum design and outcomes. However, it relies on there being extrinsic motivation for the pupil. This also means pupils do not develop intrinsic motivation for learning maths. ]]> 2020-10-13 10:29:52 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824324196 Cognitivism eleanor_knapton https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824328362 Cognitivism takes into account on individuals mental process and putting the suitable teaching methods in place. By using this learning theory it allows for the pupil to link in new concepts with their existing knowledge.]]> 2020-10-13 10:32:49 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824328362 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824329274 Connectivism- This allows collaborate learning ideas. It allows children to make links between each other, using maths language. This allows there to be less confusion in the classroom.]]> 2020-10-13 10:33:31 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824329274 Cognitivism is described by Kashefi et al (2017) as a learning theory that encourages learning through real life examples . The theory suggests that leaners build on previous knowledge and experiences which must be accommodated by the teacher. The theory suggest that learning through connections allows the learner to develop cognitively. Piaget's theory suggests that children learn through schemas which supports this theory. However, in order to support this careful planning and assessment must be done in order to teach a lesson that is inclusive for all. https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824330585 2020-10-13 10:34:31 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824330585 Constructivism eleanor_knapton https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824330863 In constructivism the pupil is an active participant within their own learning. This encourages children to work at their own speed which will promote participation as children feel comfortable within their knowledge.]]> 2020-10-13 10:34:44 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824330863 connectivism eleanor_knapton https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824336395 Connectivism follows the idea as the teachers as facillitators / catalysts for learning. It focuses on building group knowledge and our individual minds understanding with the outside world. This learning theory provides students with opportunities to form their own links, therefore making them more confident in the knowledge they have. This is good for anxious learners.]]> 2020-10-13 10:38:47 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824336395 Connectivism theory suggests that learners develop a better understanding of a subject area through collaboratively working in groups. Social interactions have been found to improve learners attainment, MOHAMMAD SALEH, ARD W. LAZONDER & TON DE JONG (2004) supporting the theory. However, children could reply on their class and therefor struggle to work independently later in life e.g. online learning at university. https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824353731 2020-10-13 10:50:48 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824353731 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824455529 Behaviourism is considered to be the traditional learning theory that is used by most teachers. An ideal learning environment for behaviourism focuses on the hierarchical procedures and outcomes so that children can progress to more advanced activities. However, this needs to be positively reinforced. For example, using rewards and praise. 

On the other hand, children still might not respond to the praise as they might still have the 'I can't do' attitude and this might come as a result of past experiences. Therefore, in order for teachers to be effective they need to build the pupils' passion in mathematics by giving interesting examples of day to day real life activities.]]> 2020-10-13 11:58:48 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824455529 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824489835 Cognitivism focuses on the mental processing activities such as knowing, thinking and problem solving. In order for this to be effective to children teachers' need to make this meaningful and relate the new information to previous knowledge already learnt. A way in which teachers can achieve this is to make use of social activities within their lessons. This fuses together both the elements of behaviourism and cognitivism together.]]> 2020-10-13 12:13:34 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824489835 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824505407 Constructivism is a process where pupils become active learners; they begin to construct their own knowledge and learning in the classroom. As a result of this teachers let go of the didactic authority and become more of a facilitator of the learning process enabling children with opportunities to discover, explore and apply ideas that will fulfil their learning objectives.

However, in order for pupils to be able to do this teachers need to have good subject knowledge and a deep pedagogical understanding of mathematics. ]]> 2020-10-13 12:19:30 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824505407 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824523991 The idea of connectivism is that the connectivity attained by linking mathematical know-how language and other skills from the student's existing knowledge serves as a bases to build understanding, which will then lead to fluency. In order to facilitate this theory within the classroom, teachers need to take a step back and become more of a listener, observer and organiser for the collaborate classroom. However, teachers need to be aware and have the understanding to know when the appropriate time is to intervene, in order to support the child's development further.]]> 2020-10-13 12:26:34 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824523991 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824670677 The paradigm of behaviourism advocates that behaviour can be observed, thus leading to rote learning via the stimulus eliciting a response. Although behaviourism is the oldest and most traditional of these paradigms, it is still widely used today in the primary classroom, despite criticism. It relies on extrinsic motivation, and although this can prove effective in the short-term, intrinsic motivation is much more important in terms of developing life-long learners of mathematics]]> 2020-10-13 13:07:59 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824670677 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824686269 Cognitivism focuses primarily on the mental processes, such as thinking, knowing and problem solving. In relation to maths, cognitivism places an emphasis on learning by problem solving as a recursive process (an outcome actualised by the national curriculum) which can prove detrimental to students mathematical understanding as it suggests that applying one set algorithm to problems will garner the correct answer, failing to explore alternative solutions. ]]> 2020-10-13 13:11:40 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824686269 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824705875 Constructivism has dominated education for a considerable amount of time, suggesting that knowledge cannot be transmitted because it is a construct of the mind with the teacher being viewed as a facilitator of the learning, rather than the all-knowledgeable didactic figure. Due to mathematics’ need for active learning in order to foster children’s interest and enthusiasm in the discipline, constructivism is essential to high quality teaching and learning in maths, although teachers often assume children have sufficient prior knowledge, enabling them to participate in the active learning, which is not always the case]]> 2020-10-13 13:16:22 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824705875 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824707007 Connectivism offers a new perspective of high quality teaching and learning in mathematics in that it approaches the subject from a technological perspective, advocating knowledge is attained via a collaborative process, encouraging the use of digital tools within the classroom, despite an apparent lack of practitioner confidence in utilising such technology.]]> 2020-10-13 13:16:40 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824707007 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824832574 Behaviourism is thought to be one of the traditional learning theories used by teachers. The approach to learning is based on a stimulus and a desired response. It argues that giving motivation, punishment and rewards will make the teaching more efficient. The article referred Behaviourism as 'skill and drill'. I believe this is an approach that should be used in Mathematics especially with timetables. The National Curriculum (2013) states that all children in year 4 should be able to recall multiplication and division facts to 12x12. Therefore it can be argued that this is the best way for children to learn their times tables. On my placement, the children used 'Times tables rockstar' where they would practice their timetables. If the children answered correctly, they would win rewards. They enjoyed this way of learning. ]]> 2020-10-13 13:43:57 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824832574 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824882234 Cognitivism focuses on relating new information to existing knowledge the children already have. The approach emphasises the importance of making knowledge more meaningful, for example using problem solving to use their mathematical understanding in a meaningful approach. ]]> 2020-10-13 13:55:28 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824882234 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824930893 Behaviourism is considered to be one of the most traditional methods of learning, and can still be found in most schools (whether this is right or wrong is un for debate?). It includes the process of 'drilling' children with knowledge and the constant repetition of worked examples, such as reeling off the timetables. It relies heavily on the children responding to the stimulus given by the teacher, such as positive praise. ]]> 2020-10-13 14:06:32 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824930893 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824953733 Cognitivism is arguably a more meaningful approach to helping children learn as it encourages them to search for new knowledge and relating it to any current knowledge they may have. Learning through problem solving is a key strand to adapting a cognitive approach to learning. ]]> 2020-10-13 14:11:38 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/824953733 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825007276 Behaviourism is considered to be a traditional learning theory in which the vast majority of teachers use in their current daily teaching routines. It explores changes in behaviour where a stimulus response occurs. Motivating students to perform to their best through the use of rewards and positive reinforcement. ]]> 2020-10-13 14:22:57 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825007276 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825024522 Cognitivism highlights the importance of using activities in mathematics that promote skills such as thinking and problem solving. Teachers need to ensure that the information that they portray is meaningful and assists the child/individual to organise the new information to already existing prior knowledge. Therefore, it explains that teachers need to find an organised manner in which assists children to relate to their prior knowledge and existing experiences. ]]> 2020-10-13 14:26:44 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825024522 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825038691 Constructivism is perceived as a process of which individuals construct their knowledge and understanding through being active within the classroom. Therefore, active learning taking place assists their knowledge and understanding of a topic through for example class discussions. Another example of active learning is the recent changes in textbooks as they are now more colourful, engaging, inviting, the use of diagrams as explanations instead of text, real life scenarios which enables the learner to relate and engage with the information better. ]]> 2020-10-13 14:29:55 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825038691 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825061440 The idea that learners learn through the interaction with other peers and being apart of a collaborative learning environment and classroom. Linking mathematical language and skills that students already have from their existing knowledge and building upon their mathematical understanding. ]]> 2020-10-13 14:34:47 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825061440 katy461 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825463804 Constructivism central idea is that knowledge cannot be transmitted, it is built through active engagement with the environment. The teacher should facilitate opportunities for the children to develop their mathematical understanding through discovery, exploration and application of their knowledge. This not only develops children's understanding in maths, it can foster interest and passion for the subject. Contrastingly, constructivism assumes that children have the sufficient knowledge and understanding to engage effectively in the exploration of mathematical concept (active learning). Therefore, when children who have a lack of prior knowledge, take part in constructivist activities, they may embed a variety of misconceptions in their knowledge and thus the activity is not effective. 
Therefore, the article suggests that children need to develop their understanding of the basic aspects of a mathematics topic, prior to active learning opportunities.

]]> 2020-10-13 16:00:27 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825463804 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825589263 Behaviourism incorporates ideas of didactic teaching and rote learning, aspects which contrasts with ideas of mastery that are encouraged in maths learning today, as this focuses on factual learning and understanding rather than conceptual understanding. This approach also links to positive reinforcement by using rewards, which can be affective and was something experienced on placement as the Dojo system was used.]]> 2020-10-13 16:27:07 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825589263 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825609080 The Cognitivist approach involves learning through observation. This may be seen in maths when a teacher models a method or an answer to a particular question on the board, for pupils to observe and then develop an understanding of. As mentioned in one of the articles, this approach also involves teachers recognising different experiences learners will have, something which is important for a teacher to consider as all pupils will have different learning needs, prior knowledge and understanding, and respond differently to stimulus. ]]> 2020-10-13 16:31:26 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825609080 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825615314 Constructivism centres around ideas of active learning, involving elements such as talk. This was something experienced on placement, as pupils would have opportunities to discuss questions with their partner before working through the solutions as a class. Khalid (2014) suggestion of meaningful learning is referenced in one of the articles, and this is important in maths, as activities can be incorporated to show pupils how their maths learning could be applied and used in real life contexts, for example money.]]> 2020-10-13 16:32:46 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825615314 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825626922 Connectivism is a more recent theory of learning. Here, there is a movement away from depending on rules that have been identified and learnt and instead focuses on mathematical language. Additionally, a focus on developing links between maths learning is incorporated into this approach. This links to mastery approaches, as pupils are supported in developing conceptual understanding and will be able to apply this to a range of questions.]]> 2020-10-13 16:34:37 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825626922 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825858927 The behaviourist approach to teaching maths as using the correct application of a skill to achieve correct results, with teachers using positive or negative reinforcement to achieve them. 
Skills can be taught and often re-taught in order for children to remember them, showing a need for practising them a lot. ]]> 2020-10-13 17:24:58 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825858927 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825864744 Behaviourism is believed to be one of the traditional learning theories used by teachers. This approach is based on using positive reinforcement, by rewards of success approval or negatively by failure and disapproval. This may be seen as more of a challenge if a child already has a negative attitude towards learning mathematics as there is an automatic loss of interest/drive to want to learn, therefore may affect these strategies. Teachers have recognised that although some traditional approaches may still be used, they are seen to be less effective. This highlights the importance of pedagogy choice to suite different learning styles. ]]> 2020-10-13 17:26:18 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/825864744 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828541787 It accounts for children being able to learn through experiences and linking past experiences to their current learning. The cognitivist approach allows for teachers to understand that not all pupils learn the same and are the same, enabling them to adapt different pedagogical approaches which results in an inclusive classroom.]]> 2020-10-14 13:30:26 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828541787 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828560860 Despite this theory of teaching and learning being traditional, it is still highly popular teaching approach in mathematics. This theory focuseses on the changes in student behaviour whereby stimulus-response occurs. This theory is categorised by providing rewards or punishments in order to increase or decrease the likelihood of the behaviour reoccuring. ]]> 2020-10-14 13:35:01 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828560860 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828583159 This learning theory views learning as an active process whereby knowledge can be transmitted from individuals and stored in the working memory. The cognitivism theory suggests that teachers should arrange activities that a suitable to the children's cognitive structure. ]]> 2020-10-14 13:40:23 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828583159 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828596940 The constructivist theory suggest that children are responsible for their own learning. Active learning allows children to construct their own knowledge and understanding. This theory proposes that teachers play a passive role to guide the children to make progress. ]]> 2020-10-14 13:43:37 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828596940 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828605143 The most traditional learning theory which is based on positive and negative reinforcements. With it being a traditional theory, teachers can be reluctant to embedding this into their lessons but from personal experience, I have found that this works well and keeps the engagement of the children. ]]> 2020-10-14 13:45:31 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828605143 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828621962 This is a more modern approach to learning, proposed by Siemens (2005) as a 'learning theory for a digital age'. Connectivism suggests that learning should be done by forming connections with others and recognising patterns ]]> 2020-10-14 13:49:24 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828621962 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828631187 A theory that enables children to become their own learners by using their own ways of learning. These learning techniques are often constructed by things they see around the classroom, hence why a lot more classrooms and schools have maths working walls. Teachers play passive roles in this theory where the children take full credit and responsibility for their own learning, hence being active learners.]]> 2020-10-14 13:51:29 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828631187 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828644640 A newer theory that is increasingly being adapted in the 21st century. It incorporates the digital era that we find ourselves in, something that the other theories do not.]]> 2020-10-14 13:54:52 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828644640 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828884777 Behaviourism emphasises on behaviour that can be observed and leads itself naturally to rote learning method. Behaviourism also focuses on the changes in the student behaviour whereby stimulus-response occurs. Learning occurs when pupils respond to the stimulus given by the teacher. In supporting mathematics development in the effective classroom, the teacher also needs to build the pupils’ passion in mathematics by giving interesting examples of daily life activities. ]]> 2020-10-14 14:48:54 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828884777 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828894729 Constructivism is a process whereby pupils construct their knowledge and understanding through active learning in the classroom. According to Scrivener, the main role of a teacher is to help students to learn to work at their own speed, by encouraging them to participate and talk. Constructivism leads the pupils to find many ways in searching for new knowledge and it makes the learning meaningful.]]> 2020-10-14 14:51:07 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/828894729 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/829064295 The articles highlight that concept that Behaviourism within mathematics is linked to the idea that children learning through didactic teaching and that in order for children to obtain the answers to the solutions there are specific algorithms that are used in order to gain the results. However, within the articles they discuss research from Orton (2004) who highlights that skills and techniques utilised within mathematics can often be forgotten and that employing a behaviourist approach could encourage the teacher to disapprove of using strategies that are used within different subjects. 

]]> 2020-10-14 15:29:02 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/829064295 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/829065690 Due to the believes within the behaviourist approach, the concept of Cognitivism arose and these two concepts were blended together by Bandura to create the concept of social cognitivism. Firstly, Cognitivism is linked to the idea that individuals are able to share their knowledge with others and when this knowledge it shared those individuals receiving this are able to store this. This is why the concept of social cognitivism was formed, as it highlights that learning is not only behavioural and cognitive but further, due to the social activity, is presents social elements. Therefore, the idea of learning with “elements of behaviourism and cognitivism with social aspects” arose. ]]> 2020-10-14 15:29:19 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/829065690 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/829067061 For many years Constructivism is a key concept within the learning of mathematics and science. It juxtaposes Social Cognitivism as it is the idea that an individuals builds their own knowledge of the concepts within these subjects, and it is highlighted that within this theory, knowledge cannot be transmitted, highlighting its difference to Social Cognitivism. The ideas within this theory are related to children being exposed to opportunities that will allow them to enhance their learning through methods, such as; discovery, application and exploration. ]]> 2020-10-14 15:29:37 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/829067061 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/829068672 The concept of Connectivism is about the role change for the teacher, they change from being didactic and instead become facilitators for the children’s learning and scaffold this. Likewise, it is linked to the use of collaborative learning and the idea although you may develop knowledge within a group setting, the children are still able to hold that knowledge for their individual self and use it to make sense of the world around them.]]> 2020-10-14 15:29:57 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/829068672 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/831478977 Applying cognitivism to mathematics will help make the knowledge meaningful to the child and help them to organise and related it too existing knowledge that is already in the memory. It will also help focus on the mental processes such as problem solving. However, it is important that teacher remain aware that students have different learning experiences that could impact the learning outcome.]]> 2020-10-15 07:49:56 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/831478977 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/831480594 Using constructivism means the children will construct their knowledge and understanding through active learning. This can be done through collaborative learning and linking to cognitivism it is about making the learning meaningful.]]> 2020-10-15 07:50:32 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/831480594 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/831747934 Teaching Mathematics using behaviourism approach relies on the teacher using positive reinforcement methods to encourage the pupils to engage and apply the methods they are taught. A positive response such as rewards and motivations support behaviourism. There appears to be less freedom to apply their own methods when this strategy is used. This approach also relies on the children remembering what they have been taught which means practise and consolidation of their knowledge must happen in order for them to remember. When teaching Maths this method may hinder teaching Mastery as children learn in a multitude of ways and not solely from the teacher relaying information. 

]]> 2020-10-15 10:09:35 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/831747934 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832361447 Within an effective classroom to aid and support mathematics development it is important to build on the pupils passions by incorporating interesting examples of daily life activities. 

]]> 2020-10-15 13:59:51 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832361447 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832370560 Is focused on the mental processing and the thinking, knowing and problem solving and it is the teacher's duty to find the most effective method to organise mew information by linking back to previous learning.]]> 2020-10-15 14:02:05 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832370560 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832378147 Constructivism plays a vital role in the teaching and learning of mathematics, collaborative learning can take place to aid their knowledge and understanding through active learning.

]]> 2020-10-15 14:03:50 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832378147 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832387834 Connectivism is a theory which has become popular within the 21st century. It is based around the idea that learning should take place by forming connections with other people and their knowledge.]]> 2020-10-15 14:06:03 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832387834 c_craigie1 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832433148 Focuses on the stimulus-response that occur during student behaviour change. Teachers provide extrinsic motivation to progress learning through rewards. It is a traditionally learning theory that many teachers still rely on today. ]]> 2020-10-15 14:16:07 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832433148 c_craigie1 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832454297 Focuses on the processing information, such as problem solving. Cognitive theories emphasise the importance of making information relatable and building on prior knowledge with new knowledge. ]]> 2020-10-15 14:20:44 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832454297 c_craigie1 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832469538 Teachers act as a scaffold in an active learning environment, encouraging pupils to participate, discuss and have a go on their own. Constructivism focuses on pupils 'constructing' their own knowledge and understanding. ]]> 2020-10-15 14:24:09 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832469538 c_craigie1 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832485158 Focuses on collaboration and learning that takes place from forming connections with others. Teachers are facilitators rather than 'answer givers'. ]]> 2020-10-15 14:27:47 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832485158 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832825627 2020-10-15 15:41:34 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832825627 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832825758 I like the behaviourism approach to learning as like cognitivism it makes learning more relatable by using examples of daily life activities in order to build a passion for mathematics and motivate children to learn. ]]> 2020-10-15 15:41:36 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832825758 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832827318 I agree with the cognitive learning theory in that making knowledge meaningful results in more effective learning. It makes learning more relatable meaning knowledge can be used in different situations. Cognitivism also focuses on problem solving which is also an effective skill for children to transfer to different situations. ]]> 2020-10-15 15:41:58 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832827318 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832831914  I like the constructivist approach as it allows children to work at a pace, they are comfortable with and also learn by working stuff out for themselves. This also allows teachers to provide more support/scaffolding to those children who need it and give little support to those who don’t/ need challenging further. ]]> 2020-10-15 15:43:01 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832831914 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832833750 Behaviourism is based on positive reinforcement (e.g. rewards such as stickers) and negative reinforcement (e.g. losing some of their break time). I personally like positive reinforcement because from my experience it can be a very effective approach. However, a downside to using reinforcement is that it needs to be consistent in order for it to be effective so e.g. if a supply teacher comes in and uses different methods, the children won't respond as well. ]]> 2020-10-15 15:43:27 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832833750 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832834063 I like the connectivism theory as it like constructivism allows children to work at their own pace. It also means teachers aren’t spoon feeding children the answers, they are supported to work it out themselves meaning the learning taking place is more likely to stick. ]]> 2020-10-15 15:43:31 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832834063 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832856088 Cognitivism stresses on the mental processing activities such as thinking, knowing and problem solving and how information is received, organised, stored and retrieved by the mind. Therefore, teachers have to consider student's prior knowledge before hand and take into account that not all children will have had the same experiences. ]]> 2020-10-15 15:48:37 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832856088 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832880251 Constructivism involves children building their knowledge and understanding through active learning in the classroom. I personally feel that active learning is essential when it comes to remembering information (schemas). Constructivism also prefers the children's participation over the teachers long explanations- which is good in most cases but not if the minimal information being relayed isn't clear. ]]> 2020-10-15 15:54:19 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832880251 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832898321 Connectivism is considered the most used theory in the 21st century, whereby the teachers role has shifted from expert (e.g. spoon feeder) to facilitator (e.g. observer), which allows children to be the drivers in their own education. Even though this is a good idea because it'll mean the children will be paying closer attention, there's also the possibility that some will fall behind easier without the extra support. ]]> 2020-10-15 15:58:26 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/832898321 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833730715 2020-10-15 19:20:33 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833730715 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833730866 Behaviourism is a stimulus-response approach. This approach is still used today without some teachers being aware they are incorporating it into their lessons. Certainly positive reinforcement has its place, however, on it’s own does not provide lasting learning/results. We are fortunate today to understand negative reinforcement can have adverse effects. Children need to have intrinsic motivation to allow deeper understanding which will not be achieved by positive and negative reinforcement alone.

]]> 2020-10-15 19:20:36 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833730866 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833778448 Social cognitivism in particular recognises the importance of observation. Teachers adapt lessons to meet the needs of learners' cognitive thinking. With a focus on process skills and prior learning children are able to build upon their schemas.



]]> 2020-10-15 19:34:31 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833778448 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833786134 Connectivism promotes intrinsic learning by allowing children ownership of their learning and encouraging teachers to scaffold the children. Teachers acting as facilitators ensures children are making deeper connections within mathematics at their own pace. This approach may well reduce anxiety surrounding mathematics due to a learn together approach rather than the teacher giving direct instruction.

]]> 2020-10-15 19:37:18 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833786134 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833796662 Behaviourism is one of the most popular approaches used in the teaching of mathematics. This particularly involves 'skill and drill' strategies which includes repetition of concepts in order for children to gain an understanding and then move onto to the next level of learning.]]> 2020-10-15 19:41:14 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833796662 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833813150 Constructivism has links with both connectivism and cognitivism. It promotes teachers having a facilitative role which can be seen in connectivism. Children construct their own knowledge through participation, discussion and independently. Similar to cognitivism, active learning is a key aspect within constructivism ensuring knowledge is meaningful. ]]> 2020-10-15 19:47:19 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833813150 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833817112 Cognitivism is a collaborative approach that blends both behaviourism and social cognitivism, particularly through observations. It is particularly founded upon mental constructs and representations.]]> 2020-10-15 19:48:35 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833817112 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833826558 The idea that children make sense of the world mathematical concepts by constructing their own understanding through hypothesising and reflection. Even though this seems an individualised learning approach, the teacher offers a variety of opportunities for the child to discover.]]> 2020-10-15 19:52:05 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/833826558 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/834382430 Behaviourism is the ‘ideal’ learning environment which focuses on the hierarchical procedures so that the mastery of basic skills creates a scaffold into more advanced mathematical concepts. This approach within mathematics involves the teacher conditioning behaviour and using positive reinforcement to motivate children to use taught methods within their own work. However, this means that children are not able to explore their own methods.  ]]> 2020-10-16 00:58:56 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/834382430 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/834384291 Cognitivism links learning to the students existing knowledge and allows children to build on this by applying this knowledge to new concepts. It focuses on the mental processes such as; knowing, thinking and problem solving. Observational learning should include problem solving and should allow children to compare their own learning with other pupils ideas. ]]> 2020-10-16 00:59:50 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/834384291 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/834388051 Constructivism focuses on pupils constructing their own knowledge and understanding through active learning in the classroom. It aims to make children be in control of their own learning and then they can reflect on this. Teachers provide scaffolding for the learners in their active learning environment to ensure misconceptions do not arise.]]> 2020-10-16 01:01:38 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/834388051 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/834394991 Connectivism uses the idea that the teacher is the facilitator of learning and not the deliverer of knowledge. It focuses on working in groups and encourages a collaborative working environment to allow children to make their own links and become more confident within themselves and their own knowledge. However, teachers must intervene when necessary to address any misconceptions. ]]> 2020-10-16 01:05:05 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/834394991 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835016868 Behaviourism is the 'ideal' learning environment, which many teacher still apply within the classroom. The nature focuses on procedures and outcomes so that mastery of basic skills provides a scaffold to more advanced tasks. Behaviourism emphasises on behaviour which can be observed and leads itself naturally into different learning methods.]]> 2020-10-16 08:25:33 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835016868 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835022371 Cognitivism 'arose' in response to behaviourism. It emphasises on making knowledge meaningful, and to help relate new information to existing knowledge. It focuses on the mental constructs and representations.]]> 2020-10-16 08:30:34 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835022371 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835028445 Constructivism leads the children to find ways in searching for new knowledge and making the learning meaningful. It allows curriculum outcomes and demonstrates ability to apply different procedures in mathematics.]]> 2020-10-16 08:36:26 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835028445 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835031612 Connectivism focuses on working in groups. Working in groups allows children to make connections with their learning through interacting with others. Connectivism allows teachers to scaffold children's knowledge, which creates an enquiry-based approach to their learning. ]]> 2020-10-16 08:39:36 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835031612 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835240275 Connectivism acknowledges the important of forming connections and recognising patterns within all aspects of learning. It recognises that making links helps to build a better understanding of the world and key mathematical concepts and skills, as maths is understood to be a language in itself. Student’s prior knowledge is seen to be very important as new ideas are linked and connected based on what is already known, this helps to develop mathematical fluency across various aspects of math. The learning process is child-led with lots of individual and collaborative working, this helps to foster children’s intrinsic motivation to achieve in maths and moments of understanding may help to build a child’s confidence in the subject.]]> 2020-10-16 11:47:01 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835240275 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835240927 Constructivism focusses on children being able to construct and form their own knowledge based on experiences. One key aspect of the constructivist learning theory is the role of the teacher changing from the provider of information to the facilitator. The learning should be child-led as they take an active role in their understanding of various concepts. It is the teacher’s responsibility to scaffolding and support the child’s learning through use of things like questioning and provision of resources. However, a challenge of this approach is that without proper support misconceptions can occur as children are exploring math concepts more independently. Learning will often be supported with concrete resources to help clarify mathematical concepts (deeper conceptual understanding) and to engage learners with active and practical exercises. The use of resources can be really beneficial to support deeper understanding however children can sometimes struggle to convey answers into written form, again highlighting the importance of scaffolding and teacher support to build an understanding of maths as a language.]]> 2020-10-16 11:47:33 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835240927 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835241340 The cognitive approach to learning is based around the idea that learning is a social activity. It suggests that individuals are active participants in the learning process and that they use experiences with others to help process and construct understanding of a topic. 
Maths teaching tends to be focused around problem solving, where new concepts and ideas are matched to an existing schema (assimilation), eventually through experience and interaction known information can be changed to accommodate new learning. A challenge with this approach is all children will have differing amounts of mathematical experience and therefore some children may find it easier to relate mathematical concepts to prior knowledge and experience. However, the approach does attempt to make knowledge meaningful to help the student organise information and remember it.
]]> 2020-10-16 11:47:54 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835241340 Behaviourism t_darwood11 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835260712 Behaviourism focuses on what can be observed and learnt through interaction with the environment. It is one of the most common approaches to teaching maths and relies heavily on didactic teaching. This means it is more teacher-led learning than child-led. The behaviourist approach lend itself well to rote learning and a moreprocedural and factual understanding of maths to obtain the correct answers. This gives the impression that maths knowledge is external and that the key to success is through correct application of algorithms. However, this approach may neglect the conceptual understanding required to be able to apply methods and techniques to different areas of maths and unfamiliar problems. There is also a focus on the use of a rewards system. Some may believe that this encourages children to work and succeed however for those who struggle with maths this could damage self-esteem and confidence levels and possibly contribute to negative attitudes in math lessons. ]]> 2020-10-16 12:01:15 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835260712 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835559545 Most of the primary school teachers are still comfortable using behaviour as their teacher approach in mathematics.
Behaviourism highlights the changes in student behaviour, meaning without this approach children’s learning could be hindered due to distractions in the classroom. Teachers need to build the pupils love for mathematics; this can be done by giving interesting examples relating to real life sceneries. 
However, theories only help analyse or explain the way of teaching, they rarely provide the direct guidance for teacher’s practices. 
There is a long tradition of teachers adopting a behaviourist approach in their mathematics. However, sometimes these are inexpert teachers, by their lack of awareness of the actual complexity of their expertise can make them think what they are teaching it ‘obvious’ knowledge. 

]]> 2020-10-16 13:46:12 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835559545 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835562758 2020-10-16 13:47:06 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835562758 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835565572 Constructivism is a process whereby students construct their knowledge and understanding through active learning. 
The central principle is that knowledge cannot be transmitted because it is a construct of the mind and learners have an active role in building understanding, so they can make sense of the world.
Social constructivism adds the further proposition that there can be no definition of knowledge that ignores its social context.
However, learning mathematics through constructivism involves several factors, pedagogical, individual factors. 
]]> 2020-10-16 13:47:53 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835565572 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835566712 2020-10-16 13:48:09 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835566712 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835566838 2020-10-16 13:48:11 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/835566838 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/837715925 Behaviourism is described as being absolute in that it involves the correct application of algorithms which are either positively reinforced through approval or negatively reinforced by failure or disapproval. The learning method is often seen as rote with a stimulus response.  

I dislike the Behaviourist style of teaching Mathematics because, the use of negative reinforcement can be detrimental to children's confidence within mathematics and may cause them to be discouraged and affect their learning and progress as they may no longer want to take part within mathematics lessons through the fear of getting the answers wrong. Alongside this, children may forget knowledge taught within this way as there is no chance for them to gain meaningful experiences within mathematics causing children to gain procedural understanding but not conceptual.]]> 2020-10-17 15:19:57 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/837715925 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/837719633 Cognitivism is described as being a mental process of learning whereby children use the skills of thinking, knowing and problem solving with a strong focus on how information is received, organised, stored and retrieved by the mind. 

I like the idea of cognitivism because, it works to support children in finding knowledge meaningful by relating new information to already existing knowledge. This can help children to gain a deeper understanding of concepts because children have a foundation of knowledge to already build on. Although, this does require teachers to be aware of children's prior knowledge and experiences so, assessment may need to support teachers understanding of this.]]> 2020-10-17 15:24:31 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/837719633 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/837722730 Constructivism is the idea that children construct their own learning through active learning whilst, the teacher becomes the facilitator of children's learning by providing the resources and content for children to explore and apply their ideas. Social constructivism further expands on this working towards the idea that socialisation can extend knowledge.

I like the constructivist approach to mathematics because, I feel as if it gives children the chance to problem solve and discuss their ideas with their peers to gain a deeper understanding of concepts as well as creating a more memorable experience as children are actively involved within the task. However, an issue with constructivism is that some children may not have enough prior knowledge to construct their own learning within this way which could cause children to develop misconceptions. To improve this, I think that children will need a blended approach whereby teachers provide some input and teach misconceptions before letting children explore to ensure that all children have sufficient prior knowledge.]]> 2020-10-17 15:28:10 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/837722730 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/837732588 Connectivism is the idea that teachers are the facilitator of a collaborative classroom within the digital age. It focuses on the idea that knowledge is distributed across networks by forming diverse connections and recognising patterns. 

I like the connectivism approach as I think that the approach aligns well with the mastery approach to mathematics. This is because, the approach focuses on children forming links between mathematical concepts and their own skills and understanding of the world to build their understanding and fluency. This is beneficial because, children are able to relate to maths and find the subject less daunting and easier to conceptualise when they can easily connect ideas.]]> 2020-10-17 15:40:02 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/837732588 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/838738851 Behavioursism is one of the most traditional learning theories. Teaching is didactic and a downside to this is that it might lead to passive rather than active learners. It focuses more on individual work and I personally think that children need to work in groups/pairs have those interaction in order to expand their knowledge and build that deep understanding. It is also based on positive and negative reinforcement which if used correctly might be really beneficial for a classroom. With positive reinforcement children increase their motivation levels and feel good in general. On the other hand, with negative reinforcement some children might not react well and not change- improve their behavior. This approach is not going to work with every single child. ]]> 2020-10-18 12:03:30 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/838738851 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/838770688 Cognitivism focuses on how information is retrieved by the mind. An advantage of this theory is that children need to communicate what they already know about the given topic (prior knowledge) and then link the learning with children's experiences. I believe that by sharing their experiences it will help to associate them with their understanding of the world and the learning that will take place throughout the lesson. It also focuses on memorization for learning which if not used properly, will result on children placing borders in their minds and not being able to build that deep understanding and expand their thoughts.]]> 2020-10-18 12:46:55 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/838770688 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/838776805 I really like Constructivism because with this approach children are able to communicate their personal experiences, be active learners, and work in groups (collaborate learning) which I believe is essential to deepen their understanding and develop mastery in Mathematics. In addition, I really like it because the role of the teacher is to be the facilitator which allows the children to be in control of their learning, to make sense of the world, to discover, explore and apply ideas that will satisfy the learning objectives without having the teacher to do their work for them. This approach, when used correctly result in higher levels of achievement and engagement as well. A disadvantage might be that not all group talks are going to be effective which means that the teacher needs to observe the children while having those discussions. ]]> 2020-10-18 12:55:34 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/838776805 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/838791080 It is based on forming a diverse network of connections and recognizing attendant patterns. A benefit of Connectivism is that children can work collaboratively as interactions are key to learning. Another benefit is that it focuses on what the child already knows, and then enables the children to make those links-connections between mathematical concepts, various skills and their understanding of the world. ]]> 2020-10-18 13:13:34 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/838791080 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/839074467 Behaviourism is seen as one of the most established learning theories. 
This focuses on an 'ideal' learning environment and this therefore helps with the progression of basic skills to more advanced activities. 
Behaviourism in history has focussed almost entirely on behaviour being conditioned. For example, when a child succeeds giving them a reward and oppositely when a child 'fails' providing negativity. This however, has been criticised in recent years as this can create great anxiety for children and therefore produces a negative stigma towards certain lessons e.g mathematics. ]]> 2020-10-18 18:07:46 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/839074467 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/840671651 Behaviourism is seen as the traditional approach to teaching but using a 'skill and drill' approach to maths possibly only leads to surface learning and not mastery as the curriculum defines maths to be taught. 
With the introduction of a Year 4 times table test, it could be considered that this goes against mastery and focuses on behaviourism and the right and wrong of maths and the ability to recall facts quickly and accurately instead of the intrinsic learning of how and why 3x3 equals 9.

]]> 2020-10-19 12:16:31 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/840671651 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/840684755 This theory suggests that you need to develop a schema by problem solving. The mastery approach of concrete, pictorial and abstract supports this as through progression of those steps children are building upon a schema (prior knowledge) and deepening their understanding of the concept.]]> 2020-10-19 12:21:06 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/840684755 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/842659026 Behaviourism is based conditioning and stimulus response bonds. Rewards are used when a positive response is shown, for example, getting a question right. This behaviour will then be repeated through the use of rewards. However, this is extrinsic motivation so is normally short lived and the children will then always expect a reward when they do anything right.]]> 2020-10-19 19:59:22 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/842659026 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/842678593 Cognitivism states that learning is an adaptive process where knowledge is shared between individuals and stored as internal mental constructs. Learning is through collaboration with others and observations. This is useful as children direct their own learning, find things out for themselves and learning is more intrinsic as nothing physical is needed. Children sharing ideas means that they can find out new things from eachother and ask eachother questions and this way of learning lasts longer compared to behavourism. ]]> 2020-10-19 20:06:17 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/842678593 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/842692237 The teacher is the learning facilitator by giving students objectives to work towards. This is through the use of social interaction. Children need to know which procedures they need to know use for different things. Collaborative learning and group work are an essential part of children's learning.]]> 2020-10-19 20:11:05 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/842692237 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/842712729 Connectivism states that knowledge is distributed across a network of connections and patterns. Children use what they have learnt and find ways of how it all connects together. The have a deeper understanding meaning that they are more empowered to undertake self-directed learning. This also develops their fluency. I believe that this approach is most effective as children understand what they are learning so are more likely to remember it and are able to apply it to different scenarios.]]> 2020-10-19 20:18:27 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/842712729 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844114341 2020-10-20 09:05:06 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844114341 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844115646 Cognitivism rose in response to behaviourism and although still rather traditional, it is less contentious, however, both are usually combined. This theory, with social-cognitivism aspects, advocates that knowledge should be shared which may translate in the classroom as group or paired work. Mental processing, thinking skills and problem solving are crucial, but so is exploration and meaningful learning experiences.
The classroom may appear more inclusive than that of a behaviourist. Individual differences, and therefore pedagogical strategies, are recognised and learning is seen as an adaptive process. This theory acknowledges how the mind stores information and how previous knowledge underpins future knowledge development. Connections with existing knowledge has been shown to develop a deeper conceptual understanding which is vital in mathematics. However, teachers may assume all children have had the same life experiences and have therefore developed the appropriate schema, which can be argued as not-so inclusive. The child may therefore fail to interpret problems which is fundamental in mathematical fluency.
]]> 2020-10-20 09:05:46 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844115646 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844116509 2020-10-20 09:06:15 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844116509 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844117388 Considered a theory for the 21st century and the technological age, connectivism was adapted from the science of complexity in 2005. Connectivism recognises that linking mathematical language and know-how to other skills develops fluency through using the knowledge base as leverage. Group/peer interaction leads to sharing knowledge, creates links and an individual’s understanding of the world. With maths being seen as a language in itself, this helps build understanding which may lead to children being less perturbed of maths in the present and into adulthood. With less emphasis on the “rules of maths”, teaching is focussed around broadening a deeper mathematical language, leading to increased understanding and fluency. This provides more opportunities for “Ah-ha!” moments which may be rare for children to discover alone, especially in early maths. The teacher is therefore seen as a catalyst for learning and are much less didactic in their approaches. This promotes intrinsic motivation development, essential when developing self-esteem and confidence in the subject. However, research has shown many teachers lack understanding and training in technological areas of teaching so therefore the quality may be undermined. Teachers must also act immediately upon misconceptions individuals may have by observing and guiding where appropriate.]]> 2020-10-20 09:06:43 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844117388 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844393038 Cognitivism - Learning being seen as an adaptive process, where knowledge can be shared (such as; through group work) and highlights the importance of mental processes. 

]]> 2020-10-20 11:48:15 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844393038 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844831512 2020-10-20 13:51:46 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844831512 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844846084 Cognitivism
Knowledge can be passed on through pupils to other pupils. This can be through group/ collaborative work. According to cognitivism, maths learning should be adaptive and shared between pupils in order to help children progress in maths. However, this can have limitations as some children won't contribute to the group learning.]]> 2020-10-20 13:54:48 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844846084 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844863591 Constructivism
Children will create their own learning environment and construct their own knowledge through active learning within the classroom. It allows the children to find a different ways to search for new knowledge, it works in the way that children should be learning through doing something rather than being told to do something.]]> 2020-10-20 13:58:31 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844863591 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844876701 Connectivism
This reduces confusion in the classroom as children can learn through collaborative learning and allows them to make links between each other. It focuses on teachers as being facillitators of learning rather than a deliverer of knowledge.]]> 2020-10-20 14:01:11 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/844876701 Behaviourism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/848109425 Behaviourism is one of the most traditional learning theories that focuses on routine, methodology and ‘skill and drill’. Behaviourist believe that the learning environment should focus on hierarchical procedures and outcomes in order to provide scaffolds to progress children further. Conditioning and reinforcement through rewards or disapproval leads to more successful teaching and learning and it is suggested that through the didactic method of teaching (teaching that is content orientated and requires instruction giving) learning can become more consolidated. This approach may be one of the best approaches that will enable 'mastery' within maths.]]> 2020-10-21 10:08:04 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/848109425 Cognitivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/848140066 The theory of cognitivism grew as a result of the behaviourist approach. The theory believes that learning is adaptive and can be shared between individuals. This sharing can be done through collaborative tasks. A lot of emphasis is also placed on observational learning and problem solving through interpretation. ]]> 2020-10-21 10:27:29 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/848140066 Constructivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/848153605 Constructivism has dominated as a learning theory within science and maths. The theories central principle states that children must play an active role in constructing their own knowledge through rule creating and reflection. Opportunities need to be provided for the children to discover and explore in order to satisfy their own ideas and thinking. Social constructivism which is a brand within the constructivist theory states that within maths teaching and learning social values and standards is necessary for understanding to occur. One way in which this can be done is by providing children with a range of different scenarios within lessons that can replicate ‘real life’. Practical exercises and experiments will also help children to construct their own knowledge. ]]> 2020-10-21 10:36:26 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/848153605 Connectivism https://padlet.com/jstothard/f19jljq5dfyicuda/wish/848166281 Connectivism is one of the more recent theories within maths that states that through collaboration and teacher facilitation children can start to make strong connections in their learning. This approach is known as the ‘learning theory for the digital age’ and requires children to be self-organised and confident within their learning. This approach is becoming more important within classrooms and so needs due consideration of.  ]]> 2020-10-21 10:44:46 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/848166281 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/849834354 Behaviourism is thought to be one of the traditional learning theories to teach.
It’s about stimuli and response to achieve a desired outcome, thus making teaching/learning more effective 
]]> 2020-10-21 17:58:27 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/849834354 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/849851193 Cognitivism is about connecting previous knowledge to new learning, using cognitive processes to solve problems and link learning and knowledge and allows for collaborative sharing (Vygotsky’s MKO, ZPD)]]> 2020-10-21 18:02:15 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/849851193 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/849866399 Constructivism is about hands on learning, theory leading to practice and learning at their own pace. Bringing in prior knowledge to build and increase their knowledge further ]]> 2020-10-21 18:05:36 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/849866399 https://padlet.com/jstothard/f19jljq5dfyicuda/wish/849878051 Connectivism is a more modern construct and assumes the teacher is the facilitator for learning, guiding the children to and through the knowledge to reach their own understanding ]]> 2020-10-21 18:08:11 UTC https://padlet.com/jstothard/f19jljq5dfyicuda/wish/849878051