• Use the numbers 0, 1, 2, or 3 to alert the teacher of their level of understanding simultaneously with the class.

• Can also be done while the students put their heads down.

• Students who are language learners may benefit from this.

• Having a unique way to answer may increase student engagement.

• Students can either write these numbers down and hold them up or put a number in the air to indicate their level of understanding.

  • 0 = did not understand

  • 1 = understood a bit

  • 2 = mostly understood

  • 3 = fully understood

• Encouraging students with confidence boosters like, "The Not Yet" phrase to help students understand that they may not yet know the correct answer but with further learning, they will be able to get it with practice.

• This encourages them to believe that with hard work and dedication, understanding of complex ideas is possible and promotes a growth mindset.

8 Mathematics Training Practices have been determined by the National Council of Teachers of Mathematics as important.

• show significant improvement in their test scores

• improves problem-solving skills, drive, and confidence

• can narrow gaps in performance, grade level, or gender

• These 8 principals have been proven to be consistent with providing concept-based curriculum and instruction with respect to these world education systems and their goal to increase student thinking.

Student discussion and collaboration is important when working with multiple students but must be done carefully.

Allowing the students to participate and work with others improves engagement, opens others to alternative ways of thinking, and increases social and academic skills.

For example, activities helpful in gaining and providing feedback while simultaneously promoting student engagement increases student communication, collaboration, and feedback both amongst peers and the teacher.

• An "agree, disagree, and depend" activity is helpful for getting the students up and working together.

• A sign is posted around the classroom, and students stand by the sign that best represents their understanding of the objective or skill being taught.

• Having students work in stations stimulates the mind.

• Having students work with multiple students is also helpful for finding which students work well together.

• Lastly, group work is very effective when done correctly.

• Sets expectations for what is required at the end of each assignment, broken down into 3 stages: opening, during, and closing.

• Activity is started with no clear directions to engage students' minds.

Objective is stated at start of lesson.

• Generalized overview of lesson being taught.

• Encourages synergetic thinking, collaboration, engagement, and thinking.

• Connects/extends prior knowledge.

• Is measurable and fair for all.

• This can be done in a number of ways in the form of an assessment.

• This information acts as evidence of learning and analyzes the students learning, knowledge, and skills.

• Students are given the opportunity to rate their learning.

• "Teacher and student reflect on and analyze the success of the learning." (Wathall Ch 8).

• Students are guided to where the lesson will lead next.

Concept-based learning was chosen because of its use world-wide and its successful use with models like the I Do, We Do, You Do model. Having a teacher with mastery deliver the content utilizing teaching strategies and then guiding the students and promoting engagement within the students and in the class and then closing with a strong conclusion and reflection of the objective, is how I plan on teaching when I am a teacher. Using pedagogical principles to ensure I am hitting all of the important elements to foster a positive learning environment and learning experience will help to keep my lessons aligned and consistent. Lastly, promoting alternative ways for students to share their answers, participate, and feel welcome will improve the learning environment, improve confidence, and foster a growth mindset full of collaboration, feedback, and learning.