This article highlights the role and importance of mathematics in preparing academic lyceum students for higher education. It also analyzes the pedagogical potential of mathematics in developing students’ logical thinking, analytical reasoning, problem-solving abilities, and professional competencies. The article discusses the effectiveness of teaching mathematics through modern pedagogical technologies, organizing independent learning, and applying innovative methods during the preparation process for higher education. Furthermore, scientific and methodological recommendations are provided to enhance the theoretical and practical significance of mathematics education in academic lyceums.

Ushbu maqolada yangi Konstitutsiyaning Ikkinchi bo'limi (V–XI boblar, 19–64-moddalar)da mustahkamlangan inson huquqlari kafolatlarining mazmuni, tarkibiy tuzilishi va huquqiy tabiati kompleks tarzda tahlil etiladi. Tadqiqot qiyosiy-huquqiy va matn tahlili metodlaridan foydalanib, inson huquqlarning bevosita amal qilishi tamoyili, aybsizlik prezumpsiyasi va ekologik huquq singari konstitutsiyaviy yangiliklardagi kontseptual siljishlarni aniqlaydi. Natijalar shuni ko'rsatadiki, 2023 yilgi yangi Konstitutsiya inson huquqlari himoyasida davlatning ijobiy majburiyatlarini sezilarli darajada kengaytirdi va "insonning qadr-qimmati oliy qadriyat" paradigmasini butun huquqiy tizim uchun markaziy asos sifatida belgiladi. Shu bilan birga, bir qator huquqlarning amaliy tatbiqini ta'minlash uchun qo'shimcha tarmoq qonunchiligi zarurligining qolib turishi muammo sifatida aniqlanadi.

Mazkur maqolada o‘smirlarda kasb tanlash jarayoniga ta’sir etuvchi psixologik omillar tahlil qilinadi. Jumladan, qiziqish, qobiliyat, motivatsiya, oilaviy muhit, tengdoshlar ta’siri hamda shaxsning o‘zini anglash darajasi kasbiy yo‘nalishni belgilashdagi muhim omillar sifatida yoritilgan. Shuningdek, o‘smirlik davrining psixologik xususiyatlari va ularning kasb tanlashdagi ahamiyati ilmiy manbalar asosida bayon etilgan. Maqolada o‘quvchilarning ongli ravishda kasb tanlashiga yordam beruvchi tavsiyalar ham keltiriladi.

This article highlights the issues of forming and developing students' creative abilities, which are among the most critical tasks of the modern education system. The study analyzes the psychological and pedagogical foundations of organizing interactive collective work during the lesson process and highlights the differences between traditional teaching methods. The role of the synergy effect, the exchange of ideas, and methods such as "Brainstorming," "Case Study," and "Project" in developing divergent thinking in a collaborative learning environment is revealed.

Maqalada joqarı oqıw orınlarında «Qaraqalpaq teatr óneriniń payda bolıwı hám rawajlanıwı» temasın oqıtıwda zamanagóy interaktiv usıllardan paydalanıw máseleleri sóz etiledi. Teatr tariyxın tek málimleme retinde emes, al studentlerdiń dıqqatın tartatuǵın hám olardıń kórkem-estetikalıq pikirlew qábiletin rawajlandıratuǵın innovaciyalıq pedagogikalıq texnologiyalar (keys-stadi, klaster, bleynd-test h.t.b.) arqalı ótiw jolları talqılanǵan. Sonday-aq, interaktiv metodlardıń studentlerdiń milliy mádeniyat hám kórkem ónerge bolǵan qızıǵıwshılıǵın arttırıwdaǵı áhmiyeti tiykarlanǵan.