Hands on and Concrete Activities
Which of the following are hands on concrete activities?
- Making an analog clock from a paper plate, brass fastener, and two strips of oak tag cut as a minute hand and hour hand.
- Using money to count change.
- Rolling spheres of different masses down hot wheels ramps.
- Using base ten blocks to add double digit numbers.
- Cutting out fraction strips.
- pour vinegar onto baking soda
- sorting rocks into categories
- taking apart a flower and drawing the different parts
- looking at one celled organisms in a magnified viewer.
An important part of the definition of hands on has to include the idea -> that the manipulatives or realistic concrete representations in the hands on activity helps the student construct the concept or to explain the concept in a meaningful way.
Hands on is more than just an activity. In fact it is more than just a process, it is a way of teaching and learning with meaningful representations.
The conditions that are necessary for an experience to be hands on include:
- It must focus the students attention on both the present activity and connect that information to information from the students past experiences in their own lives. Without this the information will not be connected and a fragile memory at best.
- Mental reflection on the full power of what the representations mean conceptually. The thinking isn't situated in their hands it must be in their minds. The must construct a mental representation that accurately represents the ideas.
- The teacher must have a clearly defined conceptual goal and operational definition of a range of possible student outcomes.
- The use of the processes of mathematics and science are required to identify, manipulate, organize, imagine, and reason to conceptualization and communication.
- There must be a communication process that convinces each person of another person's understanding when they desire to know.
When we observe students using a manipulative in a hands on activity we can literally see how their external representations mirror their internal representation. A great way to assess and infer their conceptualizations more accurately.
Last, it has enormous emotional benefits: increased self-confidence, satisfaction, understand - because they are concrete and all of our understanding begins at the concrete level. Manipulatives are more easily changed than on paper. Objects can be moved without erasing. Students are more comfortable with them and feel they help them understand, therefore empower them to solve problems.
I certainly encourage the use of concrete manipulatives, but drawings, or notes that might include symbols are just as concrete for students that are concrete operational.
Is money concrete? It doesn't represent the value in a concrete manner. In fact this is supported by the fact that children have a difficult time learning the value of pennies, nickels, dimes, and quarters.
Is touch math? Maybe. Is counting hands on? If it is, then touch math is hands on. If counting isn't, then touch math isn't. The worst thing about it is once students begin to use counting as a strategy for solving problems, they will continue to use it. It becomes very difficult to change to something better and they won't until an alternative is found more useful, easier, and comfortable.
See the example of ODD + ODD = EVEN represented with three different examples: concrete, semiconcrete or iconic, and formal operational. I would imagine that if a sixth grade class were challenged to prove this, there would be examples from each of the three, but mostly concrete with most students not not needing to actually manipulate physical objects, but choosing and needing to represent them with drawings. Visual concrete representations of odd and even in setting up the problem and throughout the procedure used to achieve the solution. Concrete and visual meaning a picture or drawing that illustrates concretely the property of odd and the property of even as groupings of physical objects. Unlike a symbol O = odd and E = even. I would also imagine there would be students that would solve some examples with numbers and then argue that it’s true, but since they didn’t check every number, it does’t prove it. Therefore, they would have to move to using objects, or drawings of objects, or using symbols to present an example that could be used to represent every number.
Manipulatives for upper grades is most often paper to draw write and notes, paper grids to make more accurate representations, photo copies of different shapes and objects, and drawings that fit with an activity or problem. Concrete manipulatives more appropriate for middle grades are Cuisenaire rods. However, a ruler and colored pencils can be used for most any problem.
Robert Sweetland's Notes ©