**10. Metacognitive modeling by the teacher**

Effective metacognitive skills teaching is done through modeling as the expert learner (teacher) shows the thought processes [4, 9]. Modeling by the teacher is a cornerstone of effective teaching. The metacognitive thinking processes are verbalized by the teacher who is the expert learner in terms of metacognitive learning [4]. A question on the topic concentration is presented to the learners to solve: What is the concentration in mol dm−3 of a solution made from 7.31 g sodium chloride in 250 cm3 of distilled water? The teacher models metacognitive thinking by thinking out loudly (verbalization) in the three phases of metacognitive learning (planning phase, monitoring phase and evaluation phase). This done through the expert metacognitive learner asking himself/herself questions loudly for the learners to observe metacognitive thinking processes [9].

### **10.1 Planning phase**

Teacher as expert metacognitive learner verbalizing thinking process: What is it that l am expected to learn? [4, 9].

Definition of concentration. Convert a given mass into mol and a given volume into dm3 . Calculate concentration.

Teacher as expert metacognitive learner verbalizing thinking process: What is the relevant prior knowledge that can assist me with this learning task? [4, 9]. At home, we add various amount of table salt to soup, the saltiness changes, increasing with the amount of salt added. When we add teaspoons of sugar into tea/coffee the sweetness depends on the number of teaspoons added per fixed volume of tea. Also dried fruits such as mango or sweet reeds or sugar cane are sweeter than fresh mango, sweet reeds/sugar.

Teacher as expert metacognitive learner verbalizing thinking process: What is it that l should do first? [4, 9]. From my relevant prior knowledge of sugar dissolving in tea/coffee and the changes of sweetness from dried and fresh mango/sweet reeds/ sugarcane, l know that concentration is the mass of a substance per unit volume. That means l have an idea from my relevant prior knowledge and know what concentration is though l did not know the chemistry technical term "concentration"?

Teacher as expert metacognitive learner verbalizing thinking process: What direction should I be thinking? [4, 9]. The mass and volume are given but not in the required units, so l should first convert the given mass and volume into the required units before doing anything.

Teacher as expert metacognitive learner verbalizing thinking process: How long should take to complete this? [4, 9]. The thinking, definition and calculation should take me 6 minutes at most.

### **10.2 Monitoring phase**

Teacher as expert metacognitive learner verbalizing thinking process: In terms of the learning task, what is my progress? [4, 9].

I am doing well at the moment as it clear what l should do next.

Teacher as expert metacognitive learner verbalizing thinking process: Am I in the right direction? [4, 9] Yes, l am in the right direction as the conversion of the given mass and volume into mol and dm3 units will give me the appropriate units in mol dm−3.

Teacher as expert metacognitive learner verbalizing thinking process: How should I go on from here? [4, 9]. I should know the relative atomic masses of Na and Cl for me to convert the mass of NaCl into mol. I should also know how to convert of cm3 into dm3 .

> ( ) =+ = = = = = 3 3 3 3 Molar mass NaCl 23 g / 35.5 g / 58.5 g / 7.31 g Number of of NaCl in 7.31 g of NaCl 0.125 58.5 g / <sup>250</sup> Volume of 250 in 0.25 1000 *mol mol mol mol mol mol dm cm dm dm*

Teacher as expert metacognitive learner verbalizing thinking process: What is the important information l should remember?

= = <sup>3</sup> 3 0.125 The concentration of the NaCl solution is 0.5 / 0.25 *mol mol dm dm*

Teacher as expert metacognitive learner verbalizing thinking process: Must I do things in a different direction? [4, 9]. No, I think l am in the right direction so far.

Teacher as expert metacognitive learner verbalizing thinking process: Must I do some adjustment to my pace due to some minor challenges? [4, 9]. Yes, l need to slow down a bit to make sure l do not end up having serious.

Teacher as expert metacognitive learner verbalizing thinking process: What should if I am not understanding what l am doing? [4, 9]. I have to go back to my relevant prior knowledge that will assist me with coming up with the definition of concentration from which l can proceed.

### **10.3 Evaluation phase**

Teacher as expert metacognitive learner verbalizing thinking process: How did I perform? [4, 9]. I think l did well.

Teacher as expert metacognitive learner verbalizing thinking process: What is it that l learned? [4, 9]. I learned how to arrive at the definition of concentration and how to use the definition to calculate the concentration of a solution without having to cram a formula demonstrating a deep understanding of the concept of concentration of solutions.

Teacher as expert metacognitive learner verbalizing thinking process: Where the results l got the expected results? [4, 9].

Yes, l got the expected results as l proved it by working backwards.

Teacher as expert metacognitive learner verbalizing thinking process: What is it that should have been done in different way by me? [4, 9]. I could have used the formula:

<sup>=</sup> <sup>n</sup> <sup>C</sup> V

where C—concentration, n—number of moles and V—the volume to calculate the contraction of the NaCl solution, however changes of getting a deeper understanding are very slim as it is just substitution mechanically into the formula to calculate the concentration.

Teacher as expert metacognitive learner verbalizing thinking process: Is it possible for me to use this type of thinking in other situations or problems as well as in other subjects? [4, 9]. Yes, this type of thing can be used in other situations or problems as well as in other subjects.

Teacher as expert metacognitive learner verbalizing thinking process: Might there be something I do not understand, any knowledge gaps in my understanding? [4, 9]. As far as the definition of concentration and calculation of concentration task is concerned, there is no knowledge gap. The only knowledge gap could be on the calculation a of a new concentration after adding a certain amount of distilled water (dilution) the 0.5 mol/dm3 NaCl solution.

Teacher as expert metacognitive learner verbalizing thinking process: Is there any need for me to fill the gap in knowledge by going back from the beginning to the end of the definition and calculation of concentration task? Yes, l needed to back to the original task, and use my understanding of the definition and calculation of concentration and which l got from my relevant prior knowledge to come up with some sort of equation. This is because the number of moles of NaCl remains constant in the original solution and the diluted solution.

Teacher as expert metacognitive learner verbalizing thinking process: How can l use this type of thinking in other learning situations or problems as well as subjects? This type of thinking can be used in other learning situations or problems as well as subjects by first identifying the relevant prior knowledge to use in that new learning situation or problem as well as subjects [4, 9].

As the teacher model's metacognition through verbalization of metacognitive thinking by asking these types of questions, there is an increase in the metacognitive knowledge, skills, and attitudes of learners. It happens by moving those learners who were tacit and aware learners to learners who are strategic and reflective. This gives learners the metacognitive tools they require to manage and benefit a lot from their learning. In turn, this will have a huge impact on the success and achievement beyond the school-based learning environment.

Worked examples are type of scaffold-ed tasks which enable learners to develop their cognitive and metacognitive skills by avoiding having a lot of demands on learners' mental resources.
