Using Effective Lesson Observations to Deepen Subject Knowledge


The development of instructor cognition is greatly enhanced by attempts within the wider educational community. Teachers need the support of others—particularly stuff, systems, and human and emotional support. While instructors can larn a great trade by working together with a group of supportive mathematics co-workers, professional development enterprises are frequently a necessary accelerator for major alteration ( Anthony & A ; Walshaw, 2009 ) p26.

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This assignment will try to show my turning accomplishments in placing good pattern in mathematics, in the signifier of a lesson observation. I will see the teacher’s capable cognition, the suitableness of his tools and representations, the extent to which he make connexions within and beyond the lesson subject of venn diagrams, and analyze how effectively mistakes and misconceptions are addressed. Further to my contemplations on the lesson, I will be offering and warranting future develop points for the instructor.

I structured my lesson utilizing the cognition four, a tool developed by Tim Rowland and his co-workers ( Rowland, et al. , 2003 ) , pulling on the earlier work of Lee Schulman ( Schulman, 1986 ) . Schulman claimed that the accents on instructors ‘ capable cognition and teaching method were being treated as reciprocally sole. He argued that the two cognition Fieldss should be combined. Rowlandet Altook Schulman’s thoughts one measure further and looked at four dimensions of state of affairss that may originate during a mathematics lesson, as opposed to types of cognition. The first being foundation, which consists of both mathematical content cognition and theoretical cognition of mathematics learning and larning. The 2nd dimension, transmutation, is the dimension most similar to Shulman’s ( 1986 ) conceptualization of pedagogical content cognition, that is, how a instructor takes their ain content cognition and transforms it into lessons that are accessible and ‘pedagogically powerful’ to pupils ( Schulman, 1986 ) . This class includes the teacher’s usage of representations, illustrations, accounts, and analogies. A 3rd dimension is connexion, which is whether a instructor makes determinations with an consciousness of connexions both within and outside the topic of mathematics. This class besides includes the demand to sequence activities for students, expecting what student will probably happen ‘hard’ or ‘easy’ , and understand typical student misconceptions. Eventuality is the dimension concerned with a teacher’s demand to believe on their pess in unplanned and unexpected minutes, for illustration, reacting to children’s statements, replies, and inquiries ( Weston, 2013 ) .


The instructor was confident in his presentation and clearly had strong capable cognition, both in the starting motor and the chief lesson. The right vocabulary was used, for illustration breakdown, figure facts and screening. Other footings that could hold been used include, intersection and classifying, and the word ‘data’ was used by the instructor merely one time, right at the terminal of the lesson, something which I found surprising as the lesson was centred around informations managing. One kid, when asked near the beginning of the lesson, did in fact say that a Carroll diagram could be used to ‘interpret data’ .

This reply was non praised, or even acknowledged. Some chances for broadening mathematical vocabulary nevertheless were identified through inquiring:

C ; ’18 and-a-half plus 18 and a half is 37’

T ; So 18 and-a-half is half of 37?

This type of state of affairs could be handled more efficaciously by inquiring the kid if she could believe of a different manner to set it instead than merely stating her.


The instructor was highly expert at utilizing the synergistic whiteboard and used it for a batch of his instruction in an synergistic manner. In add-on to this, practical resources were used, for illustration, figure cards, mundane nutrients and plastics forms.

The kids spent the first 27 proceedingss of the lesson on the rug, which left merely 15 proceedingss of working clip. This, in my sentiment, was an excessively long clip for immature kids to be expected to sit. Although the synergistic usage of the basketballs to stand for a Venn diagram did affect a spot of traveling about, the instructor could hold made this portion of lesson even more kinesthetic by utilizing the kids themselves to make human Carroll or venn diagrams. This would hold gotten the kids off the rug and catered for different acquisition manners.

It was hard to be certain in the picture, but it seemed that a hands up attack was used when inquiring for voluntaries and replying inquiries. The danger with this is that the same kids may be chosen all the clip and others may go ‘invisible’ kids who are non given the chance to happen their voice. An alternate solution would be to utilize lollipop sticks, picking out a stick with a child’s name on at random. This method can even be ‘orchestrated’ by the instructor so that peculiar kids are chosen without it looking that they are being ‘picked on’ . I observed really small congratulations throughout the lesson. Those kids who did volunteer an wrong reply were merely told ‘no’ , perchance impacting self-pride and forestalling that kid from volunteering once more. This is an country where I decidedly feel the instructor could better. In future, possibly he could inquire the kid to state him how they came to that reply.

The category had a instruction helper who spent the lesson with what I assume was the middle-ability group. She used a mini whiteboard to help them with their work, scribing for them. Although she was oppugning the kids before scribing, I saw no ground why they could non each have their ain single whiteboard to guarantee they did non go dependant on the TA.

When screening practical resources into the venn diagram on the rug, the instructor let the kids choose their ain sorting standards, affecting them in the undertaking and giving them ownership. Practical resources were besides used by the lower ability group when the kids returned to their tabular arraies to finish their independent undertakings. Assisted by the instructor, they were asked to screen fictile forms into venn diagrams on a big sheet of paper. I identified two betterment points while detecting this portion of the lesson ; the kids may hold been more occupied if the resources used were more relevant to them, for illustration plaything autos or Lego ; this was an ideal appraisal chance which was non recorded in any manner. If exposure had been taken, this would hold created a lasting record.

During the independent undertaking, the higher ability group were asked to pull 3 venn diagrams. This was rather a repetitive exercising which affected the kids in one of two ways. Some finished the undertaking within seconds and some became disengaged and spent most of their clip pulling their circles, therefore bring forthing deficient work. Some of the misss were still pulling circles merely 1 minute before the plenary. This group of kids needed to be challenged farther, possibly being asked to finish 3-circle venn diagrams or answer inquiries on informations that had already been sorted. This would hold provided them with some assortment. Furthermore, mini-plenaries would work out the job of that peculiar tabular array non being monitored as the kids would be cognizant that any one of them could be picked to portion their work.

Following the plenary, the kids were asked to self-assess their apprehension. This was a positive portion of the lesson, nevertheless, it could hold been made more effectual by inquiring the kids to explicate their apprehension, or deficiency of it.


The starting motor was an activity on figure which the kids had experienced earlier. A batch of treatment was held about times tabular arraies, particularly the 5 tabular array, odd/even Numberss and HTU. This so linked to the standards set for independent work on venn diagrams.

Before the chief instruction began, the instructor recapped on the old lesson, which was on Carroll diagrams. He used the children’s ain names to screen into both the Carroll and venn diagrams, contextualising the activity. He could hold gone even further by speaking to the kids about how this type of informations managing could be used in real-life.

The usage of mundane nutrient provided a good cross-curricular nexus as it linked to mundane life and besides the school’s current subject, calling the nutrient in Spanish added to the cross-curricular nature of this portion of the lesson. The TA, who was fluent in Spanish, was utilised good at this point. The instructor could hold thought through the types of fruit and veggies he used for this activity nevertheless, as some of the kids became confused with which nutrients belonged in which intersections, take awaying from the maths.

Effective instructors take attention that the contexts they choose do non deflect pupils from the task’s mathematical intent. They make the mathematical connexions and ends explicit, to back up those pupils who are inclined to concentrate on context issues at the disbursal of the mathematics ( Anthony & A ; Walshaw, 2009 ) .p15

For the plenary, the usage of animate beings in plenary linked to domestic pets covered earlier in the twenty-four hours, another cross-curricular connexion. A kid was asked to screen the animate beings utilizing her ain standards. Following this, the instructor asked ‘would a Carroll diagram be better? ’ Possibly alternatively he could hold asked for suggestions and allow the kid make the connexion.


I found that there were many little chances throughout the lesson which were non picked up by the instructor. For illustration, when a kid identified that the figure 37 was non in any of the times tabular arraies, there could hold been an interesting treatment about premier Numberss.

One kid had a theory that if they started with 1: 3,5,7 and 9 would be in the 2 times table. This was answered with an disconnected ‘no’ , a word which was used a batch throughout the lesson, along with the words ‘right’ and ‘wrong’ . Alternatively of brushing over an wrong reply, the instructor could hold asked the kid how they had come to that answer alternatively of merely stating ‘no’ and traveling on to following kid.

Not merely were the higher ability group insufficiently challenged during independent work, there besides appeared to be no extension work available. One kid who had completed their undertaking was merely asked to assist kids on other tabular arraies.


By utilizing the cognition four to construction my observation, I have identified many positive points about the lesson. I have besides identified some betterment points, two which, in my function as mathematics specializer, would give me some cause for concern:

Differentiation: Not all kids were sufficiently challenged, ensuing in some detachment and deficient work completed. The instructor needs to guarantee that all kids are challenged at their ain degree within his lessons, guaranting that they all make advancement.

Childs are non being questioned sufficiently about their replies and statements. Therefore, misconceptions could be left undiagnosed and unsolved. Just replying ‘no’ and non turn toing misconceptions, may impact the child’s self-pride and forestall them from taking portion in any farther treatments.

…to disregard them or disregard them as ‘wrong’ , can be construed as a deficiency of involvement in what it is that that kid ( and perchance others ) have come to cognize as a effect, in portion, of the instructor ‘s instruction ( Rowland, et al. , 2003 ) .

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