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Our main takeaway was that the authors believe that teachers should have common/specific knowledge when teaching their subjects, in this case, math. They claim that students' assessment scores match their teachers' scores on the test researchers provided. Reflecting on these findings we should keep in mind cultural differences and differences in teaching methods (teacher-centred and student-centred) for these factors will influence how the subject is taught. So though there may be truth to these findings, it is also possible that knowledge of a subject does not equal the ability to teach a subject since students are unique. Some teachers may be great academically but struggle with teaching the subjects.

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Our main takeaways are that mathematical procedures that are automatic to adults are far from obvious to students. With all students being at different developmental levels educators must ensure that their teaching practices are adaptable to all students in a way that all students can understand.

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Our main takeaway is that we as facilitators need to be able to teach math in a way that the students can understand, it needs to be  grade appropriate

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Our main takeaway is that teachers and students are both learners in the classroom. This matters because students' understanding of the content is a reflection of the teacher's teaching.
It's also important to know that teachers will not always have answers for everything and that students can provide various solutions to the problem.

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Our main takeaway was teachers' abiliities in mathematics translate to their practice in teaching students mathematics. Therefore, it is important that there is a focus on increasing the level of teachers' proficiency in math to help them perform and share knowledge to their students more effectively.

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Our main takeaway was that teachers must be responsive to unconventional methods. This matters because methods may not always be valid and teachers must be open to rectifying any potential issues.

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Our main takeaway we took from the reading was that teachers should choose useful models or examples to ensure maximum students’ comprehensions.

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Our main takeaway was teacher needs knowledge of students and content together to help teach math in effective ways and this is important because you do not need a mathematician to teach grade 3 math. Also, teachers are capable of teaching students based on academic level they are at and able to meet grade expectations.

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The main takeaway we took from the reading is that it is more important for the students to be able to understand the answer they are coming to, rather than the teacher to teach memorization and have the knowledge themselves. This is important because students gain number sense and understand the value behind the mathematics they're doing.

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Our main takeaway was that the author believes that teachers should have a high level of proficiency in math to be able to explain to students in depth. Teachers math knowledge may predict students achievement however this can be controversial. This matters because a teachers math knowledge does not necessarily correlate to their teaching ability.

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Our takeaway is that it is important to have teachers equipped with the mathematical knowledge needed for teaching so that every student has opportunity to achieve his/her full learning potential.

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For us to better teach math, it’s not about knowing more advanced or complicated math, but knowing more details and the logic behind those seemingly simple math rules so we can better explain them to students because oftentimes we know how, but don’t know much about why.

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Our main takeaway was that teachers need to be assessed the way that students are in relation to the grade that they are teaching. This matters because a teacher needs to be able to effectively explain the steps of the desired outcome.

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Our main take away from this article is that teachers should have an understanding of what the Math concept that they are teaching in the classroom. This means that teachers should be at least proficient and have a deep understanding of the math skills that they are teaching to their students. This article also goes on to add that when teachers have that foundational knowledge and understanding of math they are able to feel more confident in having their students learn and understand these same concepts.

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Our main takeaway was.... This matters because...

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Article: Knowing Mathematics for Teaching

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Article: Knowing Mathematics for Teaching