# 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 manipulatives, or realistic concrete representations, in the activity that helps the student construct the concept and explain the concept with the manipulatives or concrete representation 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 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 will be created at best.
- Encourage 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. They must construct a mental representation that accurately represents the ideas.
- Relate to a clearly defined conceptual goal (concept) that can be defined operationally with a range of possible student outcome levels.
- Use reasoning processes that can be included in critical thinking, mathematical thinking, and scientific thinking. Processes used to physically manipulate, categorize, identify, organize, imagine, and reason to conceptualize and communication understanding.
- 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.

Concrete activities have enormous emotional benefits:

- Increased self-confidence, self-efficacy, satisfaction, and understand as all understanding begins at the concrete level.
- Manipulatives are more easily changed than on paper. Allowing students to make mistakes and change direction more easily as objects can be moved without erasing and leaving signs of mistakes.
- 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 important for students that are concrete as the iconic symbols connect to physical objects and interaction on them.

*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 touch math 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. Touch math is usually used when teachers don't understand better ways to facilitate student's learning. See development of number sense, place value, and operations.

*Concrete, semi concrete or iconic, and formal operational*

See the example of proving that ODD + ODD = EVEN in three ways: concrete, semi concrete or iconic, and formal operational thinking.

If a middle grade class was challenged to prove that when: an *odd* number was added to any *odd* number the answer is always *even*.

There could be examples from each of the three levels, but most would be more concrete than formal operational. however, most students would not need to actually manipulate physical objects, but would choose to represent numbers with drawings and physical actions. Concrete representations of odd and even in setting up the problem and throughout the procedure used to achieve a 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 or as numbers with physical manipulation of moving the value of one from odd to even or even to odd.

Most solutions will probably be argued with specific examples that are true. However, since they didnâ€™t check every number, it isn't a mathematical proof. however, using objects, or drawings of objects, or using symbols can all be used to provide examples that could be used to represent it is true for every number as well as an algebraic proof.

Manipulatives for upper grades are most often paper to draw and write notes, paper grids, photo copies of different shapes and objects, and drawings that fit with an activity or problem.

Concrete manipulatives that are appropriate for middle grades are Cuisenaire rods, multi-colored disks, and geometric manipulatives. However, a ruler and colored pencils can be used for all problems also.