Teaching Mathematics & Science through

Integrated ApproachIntegrated Approach

Dr. Bharti DograReadeReader

School of EducationIGNOU New DelhiIGNOU, New Delhi

22. 12.2012

Why Science need to be yintegrated with Mathematics?

Mathematics is language of science& science of patternspMathematical inquiry shares withscientific methodscientific methodIt focuses on exploration,investigation conjecture evidenceinvestigation, conjecture, evidence,and reasoning.

Math & Science Linear Integration ContinuumIntegration Continuum

(Education Development Centre, 1970)

M         Ms          MS       Sm           S

Math    Math‐ Math     Science‐ ScienceScience & ApplyScience          &        ApplyContext     Science  Math                  

Science & Mathematics Integration Sequence

SMM

SmMs

MS

Berlin-White Berlin White Integrated Science and M th ti Mathematics

ModelModel

Th SIX t i thi There are SIX aspects in this Model

Ways of Learning

Integration can be based on how gstudentsexperienceporganize &think  about Science & Mathematicsstudent must be actively involvedin his learning (Constructivism)g ( )

Ways of Knowing

Integration can reinforce cyclical relationship betweenpinductive‐deductive &qualitative‐quantitative views of q qthe world

In science and mathematics, new,knowledge is often produced through acombination of induction and deduction

Content Knowledge

Science & Mathematics can be integratedin terms of content that is overlapping orpp ganalogous (like change, conservation,models, patterns, scale, symmetry, and, p , , y y,systems)Each discipline has some ideas that are punique and there are some ideas which are analogous/overlap (e.g., the fulcrum g p ( g ,of a lever and the mean of a distribution)

Process and Thinking Process and Thinking Skills

Integration of Science & Mathematics can:

develop processes and skills related toinquiry, problem‐solving, and higher‐q y, p g, gorder thinking skills.focus on ways of collecting and usingy g ginformation gathered by investigation,exploration, experimentation, andp , p ,problem solving.

Attitudes and Attitudes and Perceptions

Integration can be viewed from whatchildren believe about science andmathematics, their involvement, and theirconfidence in their ability to do scienceyand mathematics.Science and Mathematics education sharecertain values, attitudes, and ways ofthinking.g

Teaching Strategies

Integration can be viewed from teachingmethods valued by Science &yMathematics like:

inquiry‐based learningq y gproblem solvinguse of calculators and computerspcooperative learningEmbedding assessment withinginstruction

Contextualizing science and mathematics

integrationintegration

Classroom Examples based Classroom Examples based on BWISM Model

Ratios & Percentages

NCERT Class X Science Book

Chapter 4: Carbon and its Compounds

Topic: Anthracite

Classroom Examples based Classroom Examples based on BWISM Model

Anthracite is composed of theelements carbon hydrogen nitrogenelements carbon, hydrogen, nitrogenand oxygen in the followingproportion by mass: Carbon = 93 3%;proportion by mass: Carbon = 93.3%;hydrogen = 3%; nitrogen = 1.0%,

2 7%oxygen = 2.7%

Classroom Examples based on Classroom Examples based on BWISM Model

Based on the information providedanswer following questions:answer following questions:1. What mass of carbon is contained in

100g of anthracite?100g of anthracite?2. What mass of oxygen was contained in

200g of anthracite?200g of anthracite?3. How many grams of anthracite

contained a combined mass of 12g ofcontained a combined mass of 12g ofhydrogen and nitrogen?

Dil ti f Dilution of Solutions

For example if a 10 cm³ solutions needs to be

diluted ten times, pupils are likely to add 100 cm³ rather than

90 ³ St d t t d t d90 cm³. Students must understandof how dilutions are

formed?formed?

Graphs

L H t B t R tLesson: Heart Beat RateStudents divided into groups and

given a task to record their pulse readings given a task to record their pulse readings before and after the exercise. Students recoded

the first pulse reading after 2 minutes of p gexercise and did this recording for 15

minutes. Students then plotted l results on a

graph.

Two Graphs, using p , gdifferent axes scales, showing the same datashowing the same data

Statistical Errors

Some of the basic statistics,Some of the basic statistics,such as averages and means,median and modes, are lessmedian and modes, are lessunderstood.Science, pupils often find theScie ce, pupi s o e i eterms discrete and continuousdifficult to apply to variablesi i u o app y o a ia e