Change, constancy, and measurement Concepts
Initial perceptual naive misconceptions (any age)
Misconceptions
Beginning (preschool - 7 years)
Concepts
Change
- Clouds, birds, and airplanes all have properties, locations, and movements that can be observed and described.
- There are more stars in the sky than can be easily counted.
- They are not scattered evenly and are not the same brightness or color.
- The sun can be seen only in the day time.
- The moon can be seen sometimes at day and sometimes at night.
- The sun, moon, and stars all appear to move in the sky.
- The moon looks a little different every day and the same again about every four weeks.
- Earth is a planet.
- Gravity pulls objects toward the Earth.
Constancy
- Somethings stay the same and some things change.
Measurement
- Properties can be counted.
- Conservation of number- the number of objects does not change with the position of the objects.
- Length of an object does not change when its position is changed or its shape is altered by bending.
- Conservation of length.
- Objects can be used to compare other objects.
- Measurement is a way of detecting change.
- Time is the measurement of years divided into seconds, minutes, hours, days, weeks, months, decades, centuries.
- Linear measurement is the distance between two points.
- Volume is the measurement of space an object occupies.
- Area measures the surface of an object.
- A standard unit of measurement helps communication.
- When the thermometer goes up the temperature is hotter.
- Measurement helps in making better observations.
- Scales measure mass and weight.
- Measuring cups measure volume.
- Measurements can be compared.
- Measurement is used in everyday life (recipes, plans, designing, building).
- Time is communicated in standard units.
- The duration of an event from the beginning to the end is measured in time.
- Time represents past, present, and future events.
Intermediate (7 years - 11 years)
Concepts
Change
- Some things may have properties that change and properties that don't change.
- Properties of matter, position of objects, motion, form, function of systems all change.
- Change varies in rate, scale, and pattern.
- Some changes occur in patterns when the changes are looked at in different directions, flipped, or reflected.
- Things change in steady repetitive or irregular ways.
- Sometimes in more than one way at a time.
- Drawing pictures, making charts, graphs, or taking measurements helps to see change.
- Observed changes in properties can be attributed to changes of other variables and used to exlplain cause and effect for the observed change.
Constancy
- Objects, properties, and events stay the same or happen in similar ways.
- Constancy enables people to understand the universe.
- Almost anything has limits on how big or small it can be.
Measurement
- Properties and change of properties can be quantified.
- All measurement is relative to a unit, usually a standard unit.
- Scale is proportional.
- Measurement helps in making more accurate observations.
- Quantitative estimates of familiar lengths, weights, and time intervals can be confirmed by measurement.
- Mass does not change when the shape or position of an object is changed.
- Conservation of mass.
- Volume of a substance does not change when its shape does.
- Conservation of volume.
- Measurement helps in making better observations.
- Rulers are used to measure linear measurement.
- Scales measure mass and weight.
- Measuring cups measure volume.
- Measurements can be compared.
- Measurement is used in everyday life (recipes, plans, designing, building).
- Rate is based on time Standard units include: Time is measure in units of seconds, minutes, hours, days, weeks, months, years, decades, centuries.
- Time is used to order events.
- Twenty-four hours in a day, about 30 days in a month, 365 days in a year, 52 weeks in a year, 12 months in a year.
- Calendar is used to measure time.
- Clocks are used to measure time.
- Clocks can be analog and digital.
- A day is divided into daytime and nighttime.
- Time is determined by Earth's movement.
- Time is cyclic (seasons, days of weeks, months).
- Volume standard units are ml, liter, cup, pint, quart, gallon.
- Mass standard units are g, kg, pounds, ounces, tons.
- Linear measurement standard units are cm, m, km, inch, foot, yard, mile.
- Temperature measures hot and cold.
- Degrees in Celsius and Fahrenheit are standard units of temperature.
Literate (11+)
Concepts
Change
- Properties of systems that depend on volume, such as weight and capacity, change proportionally according to area and surface tension.
- Physical and biological systems often change until they become stable and then they remain the same unless the environment changes.
- Finding out how big or small something can be is sometimes as revealing as knowing what the usual value is.
- Many systems contain feedback mechanisms that limit changes to specific ranges.
- Equations can be used to summarize how the quantity of something changes over time in response to other changes.
- Change can include trends and cycles.
- Energy can be transferred and matter can be changed, however the sum of the matter and energy in systems remains the same.
Constancy
- Objects, properties, and events may change but much about them remains constant.
- Constancy makes the universe understandable.
- A system may stay the same because nothing is happening or because things are happening to counterbalance each other.
- Symmetry or lack of it may determine properties of many objects (molecules, crystals, organisms, and designed structures).
- Things that change in cycles (seasons, body temperature) can be described by the cycle length, frequency, highest and lowest value, and when the occur.
- Cycles can range from thousands of years to billionths of a second.
- As a system get more complicated we can gain understanding by using summaries of average, range, and describing the typical properties of the system.
Measurement
- All measurement has error.
- Scale is a proportional relationship of characteristics, properties, or relationships within a system as its dimensions are increased or decreased.
- Rate involves a measure of change for a part relative to a whole (birth rate as part of population growth and comparing one measured quantity to another measured quantity (km per hour).
Dr. Robert Sweetland's notes
homeofbob.com