higher-order-thinking-skills

Technology and Design

DiScoro writes about inquiry-based learning, digital resources, and ways to encourage higher-order thinking. We focus on STEM education and the use of technology.

This time we write about Technology & Design as a school subject or project for students (grade 6 to 10). In several countries Technology and Design has become a school subject.
Most commonly students work on a task during more than one hour. The tasks are interdisciplinary and require many different skills: planning, sketching, creativity, safety, use of tools, research , construction, experimentation etc.
Technology is not limited to the use of digital technology. Technology & Design tasks have a strong practical component and aim at problem solving skills. By nature the tasks are often low floor-high ceiling tasks. This implies that it is clearly understandable what the goal is, all students are able to get started (low floor). At the same time the tasks offer enough challenges and opportunities to dive deeper both in creativity as well as in complexity (high ceiling).

To make a plan is usually a step in the process. It is up to the teacher to ask for a report of the process or not. This can be written, visual, oral, with the use of multi-media (photos, video) or a combination.

Topics that could be part of Technology & Design are

    • design and create a rocking horse for children age 2-3
    • make a piece of household furniture using recycled materials
    • make a gripper stick for waste picking, or for elderly people at their homes
  • engineering (using concepts from chemistry and physics)

Technology and Design will certainly focus on the new economy where circular design and production, and no or minimal waste, are the ultimate challenges and goals.

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DaVinci Kindergarten

DaVinci Kindergarten is a pilot project in which we design, develop and try-out inquiry-based activities for children in the age 4-8. We have worked with children age 4-5 at two kindergartens in Norway. The activities focus on concepts from science, and technology and foster mathematical thinking.

We present some of the activities that have been developped. Contact us if you wish a complete description of the activity.

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  1. Show-box– sight lines and mirroring.
  2. How big is the panther? – measuring, human-based measuring units e.g. foot, thumb(=duym/inch), span (=fathom), step.
  3. How do you get the light on? – electricity, battery, light, lightbulb, lamp, electrical wire, curcuit.
  4. What weighs most/least? – experimenting with balance scales and different materials with the same volume and different weight.
  5. Discover more about your toys. What kind of materials are they made of? – Categorise, recognise, examine the different materials and discover their characteristics.
  6. Bee-bot – programming a robot.

Effective talk in the classroom

The Edutopia.org website offers great examples on pedagogy and didactics that build on concepts like growth mindset, ownership, effective learning, social and emotional learning, collaboration.

One topic is on Strategies for Effective Talk in the Classroom. This is not about the teacher talking, but about pupils/students talking and communicating. The approach supports learning in all subjects. It shows clearly how important it is that all pupils learn to communicate and express themselves clearly in different settings. The guidelines provided can be applied by any teacher.

Design math tasks

In the previous blogpost on how to Change math task so that they become more challenging, we wrote about guidelines on how to change existing tasks. In this blogpost we discuss how to design new math tasks. Challenging maths tasks give students the opportunity to learn, think, explore, discuss, be creative and learn (about) different strategies and respresentations or visualisations in the process.

The guidelines below are particularly useful when you design new, challenging tasks.

  1. Can you make it into an activity?

  2. Can you make it hands-on: use materials, equipment and tools?

  3. Can you make it into an experiment?

  4. Can you use problems from the real world?

  5. Can you integrate it with other subjects?

H) Fold an air-plane from and A4 piece of paper and measure whose air-plane gets farthest. Pupils work in groups. (They decide how many tries they are allowed, how they can measure in a fair way, how they can improve their paper plane etc.)

I) Use polydron squares. See the blogpost Cube 3D-2D and Make a cube and fold it out into a nett. How many different netts can you find?

J) Let the students measure the schools playground using ‘steps’ (or a rope). What is the shortest way to cross the playground? Ask them to draw the playground and their shortest route on cm2 grid paper.

K) Plan a trip from your home town to Oslo. Work out and compare different options.
When is the trip fastest? Which means of transport is cheapest? Depending of how much time you want to spend on the project, you can decide how much information you give: timetables, maps, pricelists.

L) The task in the blogpost on Balancing Act is both physics and maths. It offers students the opportunity to investigation, experiment, and to find the rule. The last step is generalisation and (early) algebra. Instead of using a computerprogram you can also use a real balance/scales or have the students construct their own.

weegschaal met schaal

Change maths tasks

A headmaster of a primary school asked us if we had some good maths tasks for the lower grades.

fishingrodReminding the expression:
Give someone a fish, and they’ll eat for a day. Give them a fishing rod, and they’ll eat for life.’
we decided to give some tools in order to be able to:

(1) change existing tasks into better tasks, and
(2) design challenging math tasks.

But what are criteria for a challenging math task? We refer to Prof. Jo Boaler and use her criteria and add some of our own ideas based on experience with realistic mathematics education (Freudenthal Institute) and other resources.

We strongly advocate Inquiry-based learning. Note that we do not write ‘teaching’, we write ‘learning‘, because the goal is not teaching, but learning. More about inquiry-based learning can be found in earlier blogposts: Research on inquiry-based learning and Inquiry-based learning in practice. Inquiry-based learning uses more open tasks. Closed tasks with more scaffolding are less exciting and challenging. If students get step-by-step instructions (cooking-book practices), they stop thinking.

Challenging maths tasks give students the opportunity to learn, think, explore, discuss, be creative and learn (about) different strategies and respresentations or visualisations in the process.

Jo Boaler (‘Mathematical Mindsets’, 2015) offers the following rules to open up an existing task, thus making it more challenging:

  1. Can you open up the task to encourage multiple methods, pathways and representations?

  2. Can up make it into and inquiry task?

  3. Can you ask the problem before teaching?

  4. Can you add a visual component?

  5. Can you make it low floor and high ceiling?

  6. Can you add the requirement to convince and reason?

A) If you take a simple task from a textbook such as  5 + 7   Ask the students how they came to their answer (before even asking what the answer is). This way you encourage pupils to think about their strategy, to express their strategy in words or visually, to use mathematical vocabulary, to see and learn different strategies from each other.

B) Take the simple task  24 x 3  Students have already learned different strategies, such as swop the numbers  3 x 12 which is probably easier for some. Or they have used the strategy to double one number and half the other number 12 x 6. Now ask the students why 24 x 3 is equal to 3 x 24. Can they prove that this is true? They could for example use rectangles on a grid.

C) Take a task like  28 :  4   Do not teach the way to check the answer, but first ask: How could you check your answer  yourself?

D) Take the following task  1/4  x  5 . First offer visualisation and ask: How much is 1/4 of the 5 circles? Or instead of asking for an answer, ask: How could you divide the 5 circles in four?

vijf cirkels

E) Take the topic average. Do not teach the different averages, but let the pupils work on average without specifying what it is. They will have a basic notion of what average is. Let them for example measure their own height and register this for all students in class. Let them come up with the class average. Discuss which ‘average’ they think is best/fairest.

F) Take a task about measuring. This task deals already with understanding, namely of units of measurement. We can change the task so that it becomes ‘low floor, high ceiling’ (accessible and challenging for all).

multi 5b measurement

  • Estimate height or length and write this down using a unit of measurement.
  • Measure the objects (except for e).
  • If the students in your group came up with different results, discuss how this may have occured.
  • Try to write the height/length in a different unit of measument.

Another task on measurement. Instead og asking What is the circumference of a given rectangle? ask: Draw different rectangles with a circumference of 12 cm.

Multi 5b circumference

G) See the task Beads on a string from FI-rekenweb. See also the blogpost Early Algebra on Beads on a string.

kralen applet

 

 

Concept Cartoons

concept ice in waterConcept Cartoon is a relatively new approach to teaching, learning and assessment in science. Concept Cartoons were first developed and created by Brenda Keogh and Stuart Naylor in 1991. Concept Cartoons feature cartoon-style drawings showing different characters arguing about an everyday situation. They are designed to intrigue, to provoke to encourage discussion, and to stimulate scientific thinking. The problems or questions posed may not have a single “right answer”.

The characters in the Concept Cartoons offer the students a role model they can identify with. This encourages students to choose a character and thus discuss freely. It does not become too personal what the student expresses about the concept. The cartoons can be used with pupils from 6 to 14.

Concept Cartoons can be an introduction to a more practical and hands-on experiment, a summary after experimenting, or just a discussion in class.

concept cave dark light

More on Concept Cartoons-2 and Concept Cartoons_3.

HOT Math-3

In the HOT Math series we publish a number of Hands-On Tasks for Mathematics. The practical activities link mathematics to other school subjects or to students’ experiences. Students’ age group: ± 12-14 yrs. No lesson plans are offered, as each idea will need adaptation to class level.

The students discover and learn to discover. Mathematics is not merely reproducing, but actively producing. The manipulative materials in this HOT Math series are learners’ materials and not demonstration aids for the teachers.

Activity: Rubber band

In this activity students will investigate how a rubber band stretches linearily (physics).

rubberband

Required material/equipment:

Clipboard, a paper clip, a cut rubberband, a white sheet, 30 cm ruler, graphing paper, 10 big washers (bought at a hardware store).

Task-1:

– Find out how the rubberband stretches further with each washer.
– Make a table/graph.

Additional task:

– Predict how much further the rubber band will stretch with more washers than available.

Task-2:
Discuss how the starting point (zero washers) can be measured in different ways and how this will affect the ensuing measurements.
How will the measurements be if we reduce the rubber band to half its length?
– Make a table/graph.

rubbrings
What can be learnt:
  • measuring
  • making tables and graphs
  • extrapolation
  • reasoning on the y-intercept of the graph
  • how a rubber band stretches linearily (physics)

Additional remarks from classroom experience:
as a start some students will need to be supplied with a table to fill.

number of rings distance in cm

0
1
2
3

 

Assessment criteria:
– quality of table (headers, zero-measurement with 0 rings)
– precision of measuring (no rounding)
– neatness of graph
– logics in extrapolation
– reasoning