Parents can help teens connect math they learn in school and their everyday lives. As a parent, you could talk to your teen about how you use math in your daily life. You could also ask family members and friends how they use math in their daily lives. Please talk to your teens about these math connections to real world. Share with your child the examples of everyday math applications, which are listed below. When your teens hear how math can be used every day, they will be more likely to view math as important and valuable. They may also become more interested in mathematics. Remember that you as a parent can greatly influence how your child thinks about mathematics.

Background:  Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions.


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Aims:  The aims were (1) to investigate the mediating role of mathematical self-concept in the relation between mathematics achievement and the achievement emotions of enjoyment and anxiety in a comprehensive model, and (2) to test possible differences in this mediating role between low-, average-, and high-achieving students.

Methods:  Through an online survey including mathematical problems, students were asked to indicate their levels of mathematics enjoyment, anxiety, and self-concept. Structural equation modelling was used to test the mediating role of self-concept in the relation between mathematics achievement and emotions. Multigroup analyses were performed to compare these relations across the three achievement groups.

Results:  Results confirmed full mediation of the relation between mathematics achievement and emotions by mathematical self-concept. Furthermore, we found higher self-concepts, more enjoyment and less math anxiety in high-achieving students compared to their average and low-achieving peers. No differences across these achievement groups were found in the relations in the mediational model.

Conclusions:  Mathematical self-concept plays a pivotal role in students' appraisal of mathematics. Mathematics achievement is only one factor explaining students' self-concept. Likely also classroom instruction and teachers' feedback strategies help to shape students' self-concept.

The ultimate goals of mathematics instruction are students understanding the material presented, applying the skills, and recalling the concepts in the future. There's little benefit in students recalling a formula or procedure to prepare for an assessment tomorrow only to forget the core concept by next week. It's imperative for teachers to focus on making sure that the students understand the material and not just memorize the procedures.

The more types of representations that you can present to students addressing their different learning styles, the more likely they will truly understand the concept being presented. Different representations could include using manipulatives, showing a picture, drawing out the problem, and offering a symbolic representation. For example, when presenting linear relationships with one unknown, illustrate to students the same problem as an equation, on a number line, in words, and with pictures. Students who are exposed to and can recognize the same relationship posed in the different representational modes are more likely to have conceptual understanding of the relationship and perform better on assessments (PDF).

In the best classroom environment, the teacher is able to show different ways to solve the same problem and encourage the students to come up with their own creative ways to solve them. The more strategies and approaches that students are exposed to, the deeper their conceptual understanding of the topic becomes. Empowering students to create their own problem-solving methods can make the teacher nervous. What if we don't follow their logic? What if they're incorrect? However, it's worth the risk to have them explore. After an individual, pair, or small group of students finish solving the class problem using a single method, encourage them to look for alternate ways to come up with the same correct solution. Having students develop their own methods and then share the correct steps with the class is a very powerful learning experience. The video below shows how a teacher encourages students more than one way to solve the same problem on rectangular prisms:

In a perfect world, we would always be able to demonstrate how every concept can be applied to the real world -- and when that's possible, it helps improve the students' understanding. When a concept cannot be applied in that manner, we can still share how it might be applied within mathematics or another subject area. Another option is showing how the concept was developed through the history of math. Consider taking a minute out of each lesson to show your students where or how the math can be seen or used in life outside of the classroom.

Aims:  This study aimed to investigate the role of two possible mediational mechanisms between math anxiety and math performance. Specifically, we sought to test the simultaneous mediating role of working memory and math self-concept.

Methods:  Children completed a set of questionnaires used to assess math and trait anxiety, math self-concept as well as measures of math fluency and math problem-solving. Teachers were asked to rate each student's math achievement. As measures of working memory, two backward span tasks were administered to the children.

Results:  A series of multiple mediation analyses were conducted. Results indicated that both mediators (working memory and math self-concept) contributed to explaining the relationship between math anxiety and math achievement.

Conclusions:  Results suggest that working memory and self-concept could be worth considering when designing interventions aimed at helping students with math anxiety. Longitudinal designs could also be used to better understand the mediational mechanisms that may explain the relationship between math anxiety and math performance.

The concept image consists of all the cognitive structure in the individual's mind that is associated with a given concept. This may not be globally coherent and may have aspects which are quite different from the formal concept definition.

The development of limits and continuity, as taught in secondary school and university, are considered. Various investigations are reported which demonstrate individual concept images differing from the formal theory and containing factors which cause cognitive conflict.

According to Spearman and Watt (2013), there are three possible explanations for the STEM gender gap: (1) differences in ability between boys and girls, (2) differences in attitudes towards STEM and (3) differences in socialisation. In terms of ability, on average, there are no large differences in the mathematics achievements of boys and girls across countries participating in the latest versions of studies such as the Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Assessment (PISA) (Mullis, Martin, Foy & Hooper, 2016; OECD, 2016b). However, a consistent finding in these studies, and in secondary analyses using their data, is that the size and the direction of the gender gap in mathematics achievement vary across countries (Alkhateeb, 2001; Badr, Morrissey & Appleton, 2012; Bedard & Cho, 2010; Guiso, Monte, Sapienza & Zingales, 2008; Mullis, Martin, Foy & Arora, 2012; OECD, 2013, 2016b). The reports from several cycles of TIMSS and PISA show that, in general, in most of the countries, there are no significant gender differences and, when they do exist, it tends to be in favour of boys. Only in a few countries (e.g. Qatar, Kuwait, Thailand), the gender differences are in favour of girls (OECD, 2013; Mullis, Martin, & Foy, 2008; Mullis et al., 2012).

The varying gender gaps in mathematics scores across countries together with the fact that students with high mathematics achievement do not necessarily contemplate a STEM career (Charles et al., 2014; OECD, 2012) suggest that the STEM gender gap might be more closely related to differences in attitudes towards STEM, the second explanation, including attitudes such as self-concept (Goldman & Penner, 2016). Although gender differences in mathematics achievement have proven to be small or even non-significant in many countries, there is still a significant gender gap favouring boys in terms of mathematics self-concept (Meelissen & Luyten 2008; Fan & Williams, 2010; Herbert & Stipek, 2005; OECD, 2013; Skaalvik & Skaalvik, 2004; Vandecandelaere, Speybroeck, Vanlaar, De Fraine & Van Damme, 2012; Wilkins, 2004).

Self-concept has been a popular topic of research in recent decades, with most of the research focused on the relationship between self-concept and achievement. This research consistently shows a positive correlation (e.g. Meelissen & Luyten 2008; OECD, 2016b; Wilkins, 2004). However, there is no clear consensus about the type of relationship between these variables. Calsyn and Kenny (1977) described two models for the relationship between self-concept and achievement: the self-enhancement model and the skills development model. In the self-enhancement model, perceptions of evaluations from others cause self-evaluation of ability and this self-evaluation has an impact on achievement. The skills development model posits that achievement has an influence on self-concept. A third model, known as the reciprocal effects model, assumes a reciprocal relationship between self-concept and achievement (Marsh, Trautwein, Ldtke, Kller & Baumert, 2005).

As previously mentioned, the theoretical notions regarding gender differences in self-concept originate mainly from research conducted in Western countries. Moreover, they sometimes rely on within-country analyses and use different instruments to measure the key variables studied. It is important to study whether the findings hold across a wide set of countries and using reliable and comparable measures. e24fc04721

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