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Students and teachers form relationships in the classroom to help the student learn. The relationships help facilitate social interaction and activate participation in the learning tasks. Students learn through observation, listening, and talking through their tasks.

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Parents and teachers usually interact with children to guide their learning. Students learn best when working collaboratively with those whose proficiency level is higher than their own. This allows them to complete tasks they are not yet able to do independently.

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Vygotsky states that the environment in which children grow up will influence how they think and what they think about.

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This theory is based on the concept that people will make their own thoughts and knowledge, and their reality is defined by the experiences that they may have and what knowledge they acquire out of those experiences.

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Teachers who uphold these theories will pair students who perform on or above grade level with students who are performing under grade level. This allows for students to interact and discuss what they have learned/acquired from a specific lesson. When integrating this theory into Math, we can use it in a group setting. This allows students to work out problems together and discuss their theories as to how an answer was achieved. An example of an activity is when students are learning to measure. The teacher is able to put students into groups and give them specific sets of things to measure. This will allow students to speak with one another and find proper measuring through the activity. They can log their and answers, and then discuss how they reached their conclusion.

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The Constructivism Learning Theory is based on the idea that people actively construct or make their own knowledge, and that reality is determined by your experiences as a learner. Knowledge is constructed and built upon other knowledge. Learning involves constructing meaning and systems of meaning. Learning is an active process which involves sensory input to construct meaning. Learning is a social activity. People learn in ways connected to things they already know and believe to be true. Knowledge is personal and based on your own experiences and beliefs. Hands-on experiences and physical actions are necessary for learning. Lastly, Constructivists believe motivation is key to learning.

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Sociocultural theory focuses not only how adults and peers influence individual learning, but also on how cultural beliefs and attitudes affect how learning takes place.

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An important concept in sociocultural theory is known as the zone of proximal development. This is the distance between the actual development level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers.

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The Sociocultural Learning Theory is about the concept that a learner's environment plays a pivotal role in his or her learning development. Vygotsky stated that the learning process actually involves three key themes: culture, language, and the zone of proximal development. It is important for instructors to understand the human mind from a historical point of view as well as a cultural one. Language is a direct result of symbols and tools that emerge within a culture. The zone of proximal development is the gap or distance that exists between a learner's possible educational development, which is determined through problem solving activities, and the development that actually takes place.

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Learning is active rather than passive meaning that learners construct meaning only through active engagement with the world, such as experiments and real-world problem solving.

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The constructivist theory posits that knowledge can only exist within the human mind, and it does not have to match any real world reality. Learners will be constantly trying to develop their own individual mental model of the real world from their perceptions of that world.

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When integrating sociocultural and constructivist learning theories in a math classroom, scaffolding and inquiry-based learning can be combined for an activity. For example, the students can work in pairs of two and predict and ask questions on the lesson. While predicting the students can tap into their prior knowledge and transfer what they have learned. For example, use a guessing game for an activity. Ask the students to think of two numbers and write down their sum, difference, quotient, and product with their partner. For instance, if your two numbers are 3 and 9, then the sum will be 12; the difference will be 6; the quotient will be 3 and the product will be 27. The students must then figure out the two numbers you used.

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Sociocultural theory influence students to play as part of the learning. Different types of playing in the classroom such as songs, imaginary play, role-playing, acting games, and games.

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Sociocultural theory adults reactions and interpretations transform the children emerging behaviors in social interaction. Communication is a key of experience in this theory. Teachers promote learning by planning their lessons where interactions will develop skills on children. Eg (Group in pairs)

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Constructivist theory use prior knowledge can influence in knowledge it can be new or modified knowledge. All students construct their knowledge through experiences.

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This theory emphasizes as well in communication between teacher and students, influencing on learning activities. It's important to encourage students to use critical thinking skills and ask questions to other students to evaluate their knowledge.

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Including sociocultural theory and constructivist in a classroom as an activity can be perform in pairs or group. To apply this in math classroom we can do an activity called "Measurement Man". In this activity students will learn how to identify how measurement works. Measurements concepts will be how many cups in a gallon and how many quarts in a gallon. Students will have one sheet of colored paper to measure the body into "gallons". They will fold and cut the sheet into quarts, then into eighths for pints and folding the sheet into sixteenths for cups. By creating a measurement man, students can learn the measurements as well to socialize with their classmates on the step by step in this activity.