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Vinod K. Kanvaria
Department of Education
   University of Delhi
vinodpr111@gmail.com
Mathematics Teaching and Learning

 This talk will cover the following:


   Semantics of Mathematics
   Pragmatics of Mathematics
   Two Daily Life Experiences
   How does it matter for teaching-
   learning of Mathematics?
   Conclusion
What is Semantics ?

     Semantics !
      What is it ?
What is Semantics?
Study of meaning associated with a
language (Syafrinaldi, 2012, p. 88)

Kisno (2012, p.2), Semantics is study
of meanings that can be expressed

Conceptual meaning, connotative
meaning, social/contextual meaning,
emotive meaning, reflected meaning,
collocative meaning and thematic
meaning
Objects
      Meaning                   and Events



                  Semantics



                Relationships


 Knowledge of Semantics is expected to enhance
the quality of Mathematics teaching and learning
What is Pragmatics ?

     Pragmatics !
      What is it ?
Pragmatics
         Deals with the Rules guiding
          the implications of things
            (Rubinstein, 2012, p. 189)


             Sees the world with an
            image, not merely a text
                 (Doam, 2001)

Deals with the intent of communication or speaker
 meaning (Leech, 1983; Sperber & Wilson, 1986a;
             Sperber & Wilson, 1986b)
Why should we keep in mind
       Pragmatics?

   Knowledge of Pragmatics is
    expected to enhance the
     quality of Mathematics
     teaching and learning
Case 1


   Event
Here is the Event

   Child        1 Samosa
 goes to            for
Shopkeeper         Rs. 5



       Rs. 100 note,
    Shopkeeper REFUSES
Case 1


   Event
Here is the Event

   Child            1 Samosa
 goes to                for
Shopkeeper             Rs. 5



 Rs. 5 note then Rs. 100 note,
    Shopkeeper ACCEPTS
Case 2


   Event
Here is the Event

  Child               1 Tea
 goes to                for
 Vender               Rs. 5



Throws the Tea saying ‘not good’,
  Shopkeeper CHARGES Rs. 5
           not Rs. 10
Case 2


   Event
Here is the Event

     Child              1 Tea
    goes to               for
    Vender              Rs. 5


Doesn’t throw Tea saying ‘not good’,
   Shopkeeper CHARGES Rs. 10
             not Rs. 5
?


Do all draw
 the same
inferences?
?


Do all see
the same
  uses?
?


  Whose
 views are
   more
important?
Four Events
              Four See it
              Differently



Child as a                     Shopkeeper /
  buyer                           Vender

                           Teacher or
 Learner in the class   Facilitator in the
                               class
Analysis
           Event’s Semantics and
                Pragmatics

        Discussed at length w.r.t.
         Context, Situations and
               Emotions


Child as the Learner   Shopkeeper as the Learner
Challenges for Mathematics

                  Challenges for
             Learning of Mathematics
           from Daily Life Experiences



Natural Sciences                 Social Sciences
   Context                       Emotions



  Situation                    Perceptions
Output for
         Teaching & Learning
       Facilitator                   Learner

Directed by                  Directed by


        Situation    related with     Context




Situated Learning and Contextualized Learning
Output for
         Teaching & Learning
       Facilitator                    Learner

Directed by                  Directed by


       Perception    related with     Emotion




          Perception based Learning
Conclusion

 It is the rapport, relationship, trust and
It is the rapport, relationship, trust and
   confidence between the learner and
   confidence between the learner and
     the facilitator, in addition to simple
    the facilitator, in addition to simple
       interaction and utilitarian value,
      interaction and utilitarian value,
   which plays a vital role in perceiving
  which plays a vital role in perceiving
          mathematical concepts and
          mathematical concepts and
        which gives a different meaning
       which gives a different meaning
           and interpretations to the
           and interpretations to the
         concepts and the relationship
        concepts and the relationship
  between the people and the concepts,
 between the people and the concepts,
            as they are perceived.
            as they are perceived.
Conclusion
Situation, context and
emotions must be given
exhaustive emphasis while
teaching and facilitating
learning of the
mathematical concepts as
most of the concepts are
perceived in context by the
learners.
What does it have for Teaching
 and Learning of Mathematics?
             Major Areas of
            Concern for better
              Teaching and
               Learning


Situation                     Emotions
                            Social Sciences



               Context
Mathematics Teaching and Learning




  Our success will depend upon
       the extent to which
           we are able
    to make learning better
         for our learners.
Let us all join hands to
 achieve excellence in
 teaching and learning
    of mathematics
   through daily life
      experiences
-to entire Teaching
fraternity, its students,
   Organizations and
         All……
NCERT Meet: Semantics & Pragmatics of Mathematical Events

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NCERT Meet: Semantics & Pragmatics of Mathematical Events

  • 1. Vinod K. Kanvaria Department of Education University of Delhi vinodpr111@gmail.com
  • 2. Mathematics Teaching and Learning This talk will cover the following: Semantics of Mathematics Pragmatics of Mathematics Two Daily Life Experiences How does it matter for teaching- learning of Mathematics? Conclusion
  • 3. What is Semantics ? Semantics ! What is it ?
  • 4. What is Semantics? Study of meaning associated with a language (Syafrinaldi, 2012, p. 88) Kisno (2012, p.2), Semantics is study of meanings that can be expressed Conceptual meaning, connotative meaning, social/contextual meaning, emotive meaning, reflected meaning, collocative meaning and thematic meaning
  • 5. Objects Meaning and Events Semantics Relationships Knowledge of Semantics is expected to enhance the quality of Mathematics teaching and learning
  • 6. What is Pragmatics ? Pragmatics ! What is it ?
  • 7. Pragmatics Deals with the Rules guiding the implications of things (Rubinstein, 2012, p. 189) Sees the world with an image, not merely a text (Doam, 2001) Deals with the intent of communication or speaker meaning (Leech, 1983; Sperber & Wilson, 1986a; Sperber & Wilson, 1986b)
  • 8. Why should we keep in mind Pragmatics? Knowledge of Pragmatics is expected to enhance the quality of Mathematics teaching and learning
  • 9. Case 1 Event
  • 10. Here is the Event Child 1 Samosa goes to for Shopkeeper Rs. 5 Rs. 100 note, Shopkeeper REFUSES
  • 11. Case 1 Event
  • 12. Here is the Event Child 1 Samosa goes to for Shopkeeper Rs. 5 Rs. 5 note then Rs. 100 note, Shopkeeper ACCEPTS
  • 13. Case 2 Event
  • 14. Here is the Event Child 1 Tea goes to for Vender Rs. 5 Throws the Tea saying ‘not good’, Shopkeeper CHARGES Rs. 5 not Rs. 10
  • 15. Case 2 Event
  • 16. Here is the Event Child 1 Tea goes to for Vender Rs. 5 Doesn’t throw Tea saying ‘not good’, Shopkeeper CHARGES Rs. 10 not Rs. 5
  • 17. ? Do all draw the same inferences?
  • 18. ? Do all see the same uses?
  • 19. ? Whose views are more important?
  • 20. Four Events Four See it Differently Child as a Shopkeeper / buyer Vender Teacher or Learner in the class Facilitator in the class
  • 21. Analysis Event’s Semantics and Pragmatics Discussed at length w.r.t. Context, Situations and Emotions Child as the Learner Shopkeeper as the Learner
  • 22. Challenges for Mathematics Challenges for Learning of Mathematics from Daily Life Experiences Natural Sciences Social Sciences Context Emotions Situation Perceptions
  • 23. Output for Teaching & Learning Facilitator Learner Directed by Directed by Situation related with Context Situated Learning and Contextualized Learning
  • 24. Output for Teaching & Learning Facilitator Learner Directed by Directed by Perception related with Emotion Perception based Learning
  • 25. Conclusion It is the rapport, relationship, trust and It is the rapport, relationship, trust and confidence between the learner and confidence between the learner and the facilitator, in addition to simple the facilitator, in addition to simple interaction and utilitarian value, interaction and utilitarian value, which plays a vital role in perceiving which plays a vital role in perceiving mathematical concepts and mathematical concepts and which gives a different meaning which gives a different meaning and interpretations to the and interpretations to the concepts and the relationship concepts and the relationship between the people and the concepts, between the people and the concepts, as they are perceived. as they are perceived.
  • 26. Conclusion Situation, context and emotions must be given exhaustive emphasis while teaching and facilitating learning of the mathematical concepts as most of the concepts are perceived in context by the learners.
  • 27. What does it have for Teaching and Learning of Mathematics? Major Areas of Concern for better Teaching and Learning Situation Emotions Social Sciences Context
  • 28. Mathematics Teaching and Learning Our success will depend upon the extent to which we are able to make learning better for our learners.
  • 29. Let us all join hands to achieve excellence in teaching and learning of mathematics through daily life experiences
  • 30. -to entire Teaching fraternity, its students, Organizations and All……