At Timestamp 5, the teacher waited on the learners to realize that there is something wrong. No one said a word. She continued to work with them to hopefully make them see that something is wrong. Sometimes we as teachers need to let go and work with the learners. We need to "guide" them to see the mistake and communicate with them. We need to listen and work with them.

The teacher gives the learners the opportunity to communicate their thoughts. Everyone shared something else - how they calculate to get to the number in the green block.

Timestamp 1- The educator tries to use social knowledge, it can be said that posing a question that seeks to attain your personal undestanding of the block. Learners should be aware of grids and that a shaded block indicates a place or a specific number. This social knowledge is part of the learner's prior knowledge that is then built on to make concrete meaning.

Time stamp 5

The educator follows the learner's thinking- following their steps they follow when deducing what x value would be, the reasoning is that since all knowledge must be scaffolded educators need to know where the learner's are conceptually. If the educator follows their thinking pattern the educator is able to understand the misconceptions learners have as well as clear them up when explaining or engaging with these types of questions.

Logico-mathematical thinking is displayed when the learner tried to ascertain which number is placed on the green block- when learners used the grid and counted or interpreted the grid based on their understanding of 5x10+4. The educator gets learners to use mathematical language

Ms. F. Arendse

The learner that say you do bot start from the 1, so 1 is the first position and then you count from the next block.

Timestamp 5 - The teacher allows the error to continue to show the learners how to think critically about their answers. Not only to figure out that their initial thought process might be incorrect, but also how to correct that thinking. Basically, how to work through their thought process logically.

Example - when the learner states that you do not need to add the one, but that you are counting FROM the one and continue in the next block.

The learners use their conventional knowledge of grids and number grids to establish what the green block represents. The class also establishes a convention for what the grid represents for the rest of the lesson.

One could also say it is Logico-mathematical because they are creating relationships between the blocks and the number system, so that each block now represents a value or a number.

Time Stamp 5

Teacher wants to encourage critical thinking. The teacher wanted the learners to figure out the error for themselves. If they are engaging critically they would ask themselves is this right? does this make sense? If i follow my thinking and understanding does this answer make sense.

A. Waterboer

Timestamp 5 - The teachers wanted the learners to think critical about their answers. She also wanted them to figure out their mistakes they maked themself.

Example - the learners was given the opportunity to communicate their thoughts.

Timestamp 5 - learners was giving the wrong answer but could explain how they got to the answer. The teacher allowed time for learners to think and realise the error.

The logico-mathematical thinking happened when the learner realised that she should start counting from 702 and not 701.

Individuals are leveraging the norms and rules previously instilled in them. They are establishing a connection between the grid example and concepts previously taught, such as counting and grid referencing.

Timestamp 5: Logico-mathematical knowledge

The educator’s purpose in presenting the error was to enable learners to recognize their misunderstandings. This approach promotes learning from errors and enhances conceptual understanding. Additionally, the educator fosters critical thinking and cultivates a positive learning environment.  

Timestamp 5 - Help learners understand their mistake and guide them in correcting it.

Learners showed Logico-mathematical thinking when they discovered that it would be easier to group the rows in groups of 10 and work out their answer from there.

Linzey Joorst

Timestamp 1 - Social knowledge

Timestamp 2 - Logico-mathematical thinking.

In TS5, the teacher used logico-mathematical knowledge to take place. The children had to use their social knowledge to inform their logico-mathematical knowledge when the problem became more complex. She did not intervene and correct, she allowed the learners to critically think about the problem and make connections so that they can find the answer by themselves. When one learner finally made the correct connections, she allowed the others to think about it, she didn't immediately correct but she helped them to use that one connection to build a deeper understanding until everyone arrived at the correct place and had a shared understanding.

Time stamp 5 - Tamsyn

To see the learners thinking everyone sees their own way of doing things. Their thinking is clever and out of the box

Where learners show logical mathematical knowledge - tamsyn

Learners counted in 10’s for each row. They counted in ones when they cou ted to the right where they get to the green thing. Some learners removed the one and added it again aftee 700. They assume they know the number.

Learners' prior knowledge and how they were taught also some logical thinking was revealed.

Learners was never told that they were right or wrong. they should learn and understand their mistakes.

It was easier to group the rows and to count in 10's.

The learners were allowed to carry on with the mistake so that they learn to speak up when they do not understand an answer, and so that they can better understand how they came to making the mistake onve it is corrected.

The learners show logico-mathematical thinking when the girl explains that the first block is counted as 1. Her prior knowledge of counting whole numbers allows her to notice that there is no need to subtract one, but count the first block as block number 1.

Mona I.L

Prior knowledge came out when the learner recalled the grid and her social understanding of what was previously taught on grid work (Letter on top and numbers on the side) BUT on timestamp 5, the educator tested the whole classes understanding and logico-mathematical thinking when she created a 3 digit number (701) compared to a 1 digit number (1). It is here that learners had to reason and count to make logical sense of what the green card could be.

Time Stamp 5- Logico-Mathematical thinking is taking place here. Learners started using logical thinking and reasoning to answer the question.

Lastly, Logico-mathematical thinking is evident when learners start thinking of the rows as groups of 10 (tens) and each block as a unit (1).

At time stamp 1, we see that the learners are using prior knowledge - bring us to understand that they are aware of the rules of society. Showing that they have social knowledge.

timestamp 5 - The teacher uses this opportunity to engage with the learners critically - ensuring that they use their critical thinking and understanding.

Logico - thinking is displayed when learners demonstrate the ability to see the rows not just as a unit but in logical patterns.

Making Mathematical Sense

Timestamp 5: The teacher wanted the the learners to use their loco-mathematical knowledge to get to the answer, but she also wanted them to use social knowledge to help eachother.

After timestamp 5, and 6 learners were reasoning their own calculations and were using loco-mathematical knowledge.

Timestamp 1: It seems that the teacher is emphasizing the importance of collaborative learning and consensus-building within the class. By inviting learners to share their ideas about what the green block could mean, the teacher is encouraging active participation and diverse perspectives. However, the statement "We have to agree what this block will mean" suggests that the teacher is also highlighting the need for the class to reach a collective understanding or consensus regarding the interpretation of the green block. This emphasizes social interaction, communication, and the development of shared knowledge and meanings within the learning community.

Timestamp 5:

The teacher's purpose in allowing the learners to continue with the error for quite some time might be to promote a process of exploration, critical thinking, and self-correction within the class. Allowing learners to make mistakes and work through them can be an effective teaching strategy. It encourages students to actively engage with the material, question their own assumptions, and collaborate with peers to arrive at the correct answer. By not immediately correcting the learners, the teacher may be fostering a classroom environment where learners feel comfortable expressing their ideas, discussing different perspectives, and learning from both correct and incorrect responses. This approach can contribute to the development of problem-solving skills, resilience, and a deeper understanding of the subject matter. The teacher may eventually intervene to guide the class toward the correct solution or to facilitate a discussion about the process and the importance of double-checking answers.

Example: Pattern Recognition: The learners are recognizing a pattern or rule within the given problem. They seem to be observing that the number placed in the green block is related to the other numbers in a specific way.

learners thought the green block meant, despite the fact that the number grid had no visible numbers. The teacher facilitated a discussion with the learners, provoking them to use critical thinking skills,

about the function of the green block and how it related to the number grid. The activity therefore assisted the learners to improve their logical reasoning skills and have an improved understanding of

mathematical ideas[ Logico Mathematical Knowledge]. She then encouraged her learners to justify their ideas in order

to foster critical thinking and reasoning skills . She also gave her learners the opportunity to analyse and

explore ideas to determine what the green block represents on the grid. The teacher also allows learners to devise their own methods of problem solving. In this way, learners are encouraged to experiment, investigate, and look for patterns to support their critical thinking.

Both learners and teacher were engaged throughout the lesson to promote active

involvement and collaboration. The teacher promoted open discussions and provided guidance when needed( guided approach), promoting a positive learning environment. Both instructor and the students were actively involved.

S.M NZUZA

TS5: They need to share their thoughts and that can later be rectified to come to the correct answer. This is to enhance critical thinking.

The girl that realised that the 1 should not be added because they started counting at 701 thus the 1 is already in the calculation.

TS 5 & 6: Logical thinking, learners' own calculations.